Research ArticleMultiobjective Simulation-Based Optimization Based onArtificial Immune Systems for a Distribution Center

Chris S K Leung and Henry Y K Lau

Department of Industrial amp Manufacturing Systems Engineering The University of Hong Kong Pokfulam Hong Kong

Correspondence should be addressed to Chris S K Leung lskchrisyahoocom

Received 10 October 2017 Revised 27 March 2018 Accepted 19 April 2018 Published 21 May 2018

Academic Editor Efren Mezura-Montes

Copyright copy 2018 Chris S K Leung and Henry Y K Lau This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Competitive market factors such as more stringent government regulations larger number of competitors and shorter productlife cycle in recent years have created more significant pressure on the management in all supply chain parties To this end theability of analyzing and evaluating systems and related operations involving the deployment of complex multiobjective materialhandling systems is vital for distribution practitioners In this respect simulation modeling techniques together with optimizationhave emerged as a very useful tool to facilitate the effective analysis of these complex operations and systems In this paper we applyamultiobjective simulation-based optimization framework consisting of a hybrid immune-inspired algorithm named Suppression-controlled Multiobjective Immune Algorithm (SCMIA) and a simulation model for solving a real-life multiobjective optimizationproblem The results show that the framework is able to solve large scale problems with a large number of parameters operatorsand equipment involved

1 Introduction

Simulation modeling is indeed a powerful industrial engi-neering technique for studying the functioning performanceand operation of complex systems As such it becomes anextremely useful tool for stakeholders and decision-makersin various industries and domains including multiobjectiveoptimization By changing input data and operating param-eters of a system being studied with simulation predic-tions about the systemrsquos behaviors can be obtained throughcomputer-aided simulation for helping management makethe right decisions Unlike a mathematical model simulationcan handle a variety of complex factors that are commonlyfound in real world In addition simulation is a cost-effectivemeans for existing process redesign and new system designbecause alternative solutions can be studied and evaluatedfor correctness and feasibility before actual implementationMore importantly the accuracy of the performancemeasuresof the complex systems obtained from simulation modelsis normally higher than that of analytical methods becauseanalytical methods in general involve making unrealistic

assumptions for the systems or problems under investigation[1]

In real world many problems no matter whether theyare in the domain of engineering finance business orscience can be formulated into different forms of opti-mization problems These problems are characterized bythe requirement of finding the best possible solution thatfulfills certain criteria under certain constraints Most of thereal-world optimization problems normally involve multipleobjectives rather than one single objective in which someobjectives conflict with others Solving this kind of problemsis never an easy task because objectives of such problems areoften found to be noncommensurable and conflicting Veryoften there is no single best solution to the multiobjectivesoptimization problems but rather a set of optimal solutionsthat exists among the objectives However using simulationmodeling alone cannot provide us with optimal solutionsto these optimization problems Therefore an optimizationalgorithm is needed to guide the search process to theoptimal solutions Over the past decades different algorithmshave been developed for solving multiobjective optimization

HindawiJournal of OptimizationVolume 2018 Article ID 5852469 15 pageshttpsdoiorg10115520185852469

2 Journal of Optimization

problems However some algorithms such as SimulatedAnnealing (SA) [2] and Tabu Search (TS) [3ndash5] do not easilysolve multiobjective optimization problems since they areinitially developed for solving single objective optimizationproblems without having the ability to generate a set ofoptimal trade-off solutions One of the possible approachesfor them to solve the multiobjective optimization problems isto transform the multiple-objective problems into the singleobjective problems by emphasizing one particular optimalsolution at each run [6] Some other algorithms such asGenetic Algorithm (GA) [7] Evolutionary Strategy (ES) [8]and Artificial Immune Systems (AIS) [9] which are inspiredby natural processes have been proved to be the effectivealgorithms in both single objective and multiobjective opti-mization contexts Among these algorithms AIS based on theconcepts of biological immune system have received specialattention among the research community because the biolog-ical immune system provides a rich source of stimulation andinspiration to the research community with their interestingcharacteristics distributed nature self-organization mem-ory and learning capabilities Motivated by its great potentialfor solving multiple-objective optimization problems thestudy reported in this paper is to demonstrate how a real-life multiobjective simulation-based optimization problem inlogistics industry where material handling system (MHS) isinvolved can be solved by a simulation-based optimizationframework comprising a simulation tool together with anAIS-based algorithm

This paper proceeds as follows Section 2 starts by giving abrief overview of material handling and multiobjective opti-mization Section 3 introduces the multiobjective optimiza-tion framework for simulation-based optimization Section 4evaluates the performance of the framework through a real-life case study on a MHS by benchmarking with some well-known optimization algorithms Finally concluding remarksare presented in Section 5

2 Background

21 Importance of Material Handling in Distribution Indus-try Material handling which is the total management ofmaterial concerns in an operation is a vital element ofindustrial processes Material handling involves a variety ofoperations including the movement storage protection andcontrol of materials products and wastes throughout theprocesses of manufacturing distribution and disposal Hav-ing efficient MHS is of great importance to various industriesto maintain and facilitate a continuous flow of materialthrough theworkplace and guarantees that requiredmaterialsare available when needed It is especially important tologistics and manufacturing industries as it accounts for alarge percentage of the operation in these industries In themanufacturing sector the time spent on different kinds ofproduct handling and transportation can be as much as thetime used on the value-added processes Banks et al [10]claimed that the time of material handling accounts for about85 of the total manufacturing time In addition to time themoney used on material handling activities is equally highbecause thematerial handling equipment and systems require

large capital investment in terms of system design instal-lation operations maintenance and so forth A numberof studies conducted in different industries show that thecost of material handling alone is about 20ndash25 of the totalmanufacturing cost [11]

There are different kinds of material handling equipmentand systems available that range from simple hand truckand pallet rack to complex conveyor system and AutomatedStorage and Retrieval System (ASRS) A typical MHS iscomposed of different smaller components closely workingtogether thus making business activities more efficient andcost-effective Over the past decade MHS and its functionhave undergone a big change because of new advances intechnologies such as the development and applications ofautomation techniques and robotics bywhich a large numberof manual handling jobs are replaced by machines Since theentire production or distribution process is automated MHShas to respond just-in-time to the requirements of differentprocessing activities These new technologies today increas-ingly become prevalent in different industries as they helpease drudgery formanual labors and some of themechanizedor automated handling jobs are physically impossible to bedone by workers

Norman [12] claimed that equipment capacity speedand arrangement are the most critical considerations whenmodeling and optimizing MHS Capacity under this contextis the maximum quantity of products handled by the equip-ment Speed is the average operating speed of the equipmentwhich may include acceleration deceleration and speeds ofvarious equipment components Configuration is the layoutand structure of the MHS or its moving paths

22 Optimization of MHS via Simulation In the literaturethere are a number of studies that dedicatedly contribute tothe optimization of MHS via simulation For exampleEbbesen et al [13] studied the baggage handling system atairports They developed an approach to optimize the designof conveyor systems that is the design of tracks suitedfor baggage handling systems with the use of a time domainsimulation model of the entire system Sergueyevich etal [14] proposed a simulation model of the overhead mon-orail conveyor system coupled with statistical methods foranalyzing and solving the multiobjective optimization prob-lem regarding the manufacturing process The aim was todetermine the optimum speed of conveyor lengths of queuestime in system capacity of machines and so forth undercertain limitations Elahi et al [15] studied the GeneralMotors paint shop conveyor system by developing a sim-ulation model The model works firmly with a decisionoptimizer incorporating integer linear programming modeland dynamic programming model at critical points such asthe beginning and end of buffer conveyors in the system inorder to regroup batches of different color cars Leung andLau [16] proposed a simulation-based optimization frame-work that combines the processes of optimization andsimulation for solving typical linear optimization problemsrelated to logistics and production operationThe frameworkintegrates an AIS-based algorithm with a simulation tool

Journal of Optimization 3

for the evaluation of optimal system parameters and toreveal the performance of systems Subulan and Cakmakci[17] made use of ARENA simulation program and Taguchiexperimental design method to build a solution model foreffectively designing material handlingndashtransfer systems andoptimizing the performance of automation technologies inautomobile industry Chang et al [18] proposed a frameworkthat integrates simulation optimization and data envelop-ment analysis techniques to find out the optimal vehicle fleetsize for a multiobjective problem in automated materialshandling systems Lin and Huang [19] extended the optimalcomputing budget allocation by adding Genetic Algorithmtogether with the help of a simulation model for optimizingthe vehicle allocation for the automated material handlingsystem in semiconductor industry

23 Multiobjective Simulation-Based Optimization Approach-es In practice optimization problems involve several objec-tives that often conflict with each other and must be simul-taneously optimized so that a possibly uncountable set oftrade-off solutions rather than a single optimal point isfound with respect to the contradicting objectivesThereforethe aim of these problems is to find out the global trade-off solutions that effectively spread over the Pareto frontNo solution from the Pareto front is worse than any othersolution because it is better in at least one objective Theseproblems are normally termed as multiobjective problemswhich were first studied in an economic context and thenextended to the fields of science and engineering [20]Since multiobjective optimization problems involve severalobjectives the view towards optimum has changed hencechanging the aim fromfinding a single solution to obtaining aset of compromised solutions Today the notion of optimumfor amultiobjective optimization problem is frequently calledPareto optimum which was first proposed by Edgeworth [21]and then generalized by Pareto [22 23]

As is known the notion of optimality for multiobjectiveoptimization problems is different from that of single objec-tive optimization problems because the aim of multiobjectiveoptimization problems is to find a set of optimal trade-off solutions rather than a single optimal solution Thus inthe absence of preference information on the objectives theconcept of Pareto optimality is adopted in this study for solv-ing multiobjective optimization problems [24] and severaldefinitions about Pareto optimality [20 25 26] are consideredand stated below

Definition 1 (Pareto optimality) A point 119883lowast isin Ω in thesearch space is said to be Pareto optimalnondominated withrespect toΩ if and only if there are no other solutions119883 isin Ωfor which

997888rarr119891(119883) dominates997888rarr119891(119883lowast) In other words 119883lowast is

Pareto optimal with regard to the whole decision variablespace if it cannot be improved in any one objective withoutresulting in a simultaneous degradation in other objectives

Definition 2 (Pareto dominance) Consider without loss ofgenerality two decision vectors 119883119886 and 119883119887 isin X of aminimization problem Then a vector of decision variables119883119886 is said to dominate another vector 119883119887 which is denoted

by119883119886 ≺ 119883119887 if and only if119883119886 is partially less than119883119887 That isthe following two conditions must be satisfied

(1) 119883119886 is not worse than119883119887 in all objectives

119891119894 (119883119886) le 119891119894 (119883119887) forall119894 = 1 2 119903 (1)

(2) 119883119886 is better than119883119887 in at least one objective

119891119894 (119883119886) lt 119891119894 (119883119887) exist119894 = 1 2 119903 (2)

where 119894 is the number of objectives

However when any of these conditions are violated thetwo solutions 119883119886 and 119883119887 are said to be indifferent to eachother instead of dominating the other or being dominated bythe other Based on the above relations Pareto optimal setPareto front and nondominated set are defined below

Definition 3 (Pareto optimal set) Pareto optimal set ofsolutions is a collection of all Pareto optimal solutions whichis defined as

PS fl X isin Ω | not exist119883lowast isin Ω 119883lowast ≺ X (3)

Pareto optimal solutions are those solutions in the deci-sion variable space whose corresponding objective vectorelements cannot be all simultaneously improved [27] Thesolutions inside the Pareto optimal set may have no apparentrelationship except their membership in the set Paretooptimal solutions are classified as such based on their valuesbeing evaluated through whatever means

Definition 4 (Pareto front) A surface or line containingall nondominated solutions is called Pareto front which isrepresented by

PF fl 997888rarr119891 (X) | X isin PS (4)

According to the literature finding an analytical expres-sion of the Pareto front is a very difficult task Therefore acommon approach for Pareto front generation is to find outthe points withinΩ and their corresponding value119891(119883) 119883 isinΩ When this procedure is repeated a sufficient number oftimes the nondominated points and hence the Pareto frontare most likely to be found in the objective space [20]

Definition 5 (nondominated set) Of a solution set 119878 anondominated set of solutions 119878lowast comprises solutions that arenot dominated by other solutions in the set 119878 It is worthmen-tioning that while Pareto optimal solutions are always non-dominated solutions nondominated solutions may includeboth non-Pareto optimal solutions and Pareto optimal solu-tions thus revealing that the true Pareto optimal solutionscould hardly be represented by the nondominated solutionsobtained from running an optimizerThus the idea stated byvan Veldhuizen and Lamont [28] about the true Pareto frontPFtrue distinguishing it from the final set of nondominatedsolutions found by an algorithm is called known Pareto frontPFknown

4 Journal of Optimization

Feedback

Input parameters

Feedback

Output performance metrics

Initial inputs

Simulation model

Optimal Solutions

Multi-objective optimizer

Figure 1 The framework for multiobjective simulation-based optimization (source modified from Leung and Laursquos work [16])

Modern optimization approaches are very oftenpopulation-based and evolutionary in nature In suchmethods the search for the global optima essentiallycomprises an iterative process that replaces the candidatesolutions in the population by newly generated ones withan aim of achieving continuous improvement in theperformance of the best candidate solutions through thehelp of mechanisms that guide the search to find a set ofnondominated solutionsTheuse of themodern optimizationapproaches especially population-based evolutionary algo-rithms to solving the complex multiobjective optimizationproblems has beenmotivatedmainly because of the followingcritical reasons First population-based evolutionary algo-rithms can recognize the specificity of multiobjectiveoptimization problems by working simultaneously on allobjectives and finally generating a group of optimal trade-offsolutions thus forming a uniformly distributed Pareto frontSecond as the name implies the population-based ap-proaches can deal with a population of candidate solutionssimultaneously allowing the generation of several elements ofthe Pareto optimal set in a single run of an optimizer insteadof performing many separate runs when using classicalmathematical programming methods [29] This allows thedecision-makers to simply pick the one that best fits theproblem at hand thus preventing the need to reconfigure andto rerun the optimization tool for finding other alternativePareto optimal solutions Third their capability of main-taining diversity among the candidate solutions in thepopulation is important to prevent the search fromprematureconvergence to a specific region of the solution space thusallowing a better exploration of the solution space andminimizing the susceptibility of the search to the presenceof poor local optima in the optimization problems [30] Thefinal reason is that the population-based approaches are lesssusceptible to the continuity or shape of the Pareto front as

they can deal with concave and discontinuous Pareto frontswithout difficulty [27 31] Nevertheless on the other handthe weaknesses of these population-based methods are thatthey do not guarantee the identification of optimal trade-offsolutions and the solutions obtained are likely to be stuck atsome ldquogoodrdquo approximations [32]

During the past few decades a large number of pub-lications have been done in population-based evolutionaryalgorithms and proved to be effective for solving multiob-jective optimization problems since the first multiobjectiveevolutionary algorithm has been developed by Schaffer [33]These algorithms include PAES [34] NSGA-II [35] PESA[36] SPEA2 [37] PESA-II [38] micro-GA [39] micro-GA2[40] omni-aiNet [41] NNIA [42] omni-AIOS [43] MTLBO[44] and SCMIA [45]

3 A Multiobjective Simulation-BasedOptimization Framework

31 Mechanisms of the Multiobjective Simulation-Based Opti-mization Framework The optimization framework adoptedin this study is developed by taking advantage of the idea ofseparation between the optimizationmethod and the simula-tion model For this reason the optimization framework canremain the same or require only minor modifications such aschanging range of parameters data type of decision vari-ables and number of decision variables to optimize thesimulation model that incorporates new requirements Thisframework in fact is a modified version of Leung and Laursquoswork [16] which incorporates a multiobjective optimizationalgorithm instead of a single objective algorithm (Figure 1)The multiobjective algorithm adopted in the framework isSuppression-controlled Multiobjective Immune Algorithm(SCMIA) proposed by Leung and Lau [45] Concepts of thealgorithm are briefly discussed in the next section

Journal of Optimization 5

Table 1 Mapping between the biological immune system and SCMIA

Biological ImmuneSystem SCMIA

Antigen (Ag) Objective function (simulation model in simulation study) to be optimizedAntibody (Ab) Candidate solution (a set of decision variables) to be optimizedAg-Ab affinity Fitness value of each candidate solution evaluated based on Pareto dominanceAb-Ab affinity Crowding-distance proposed by Deb et al [6] working as a measure of population diversity

Immune suppression Mechanism to control the number of nearby candidate solutions based on similarity among candidate solutionsin both the objective space and decision variable space

Memory cell Current best nondominated solution

The framework consists of two critical componentsnamely (1) the simulation model and (2) the immunity-inspired multiobjective optimization algorithm A problemor a system to be optimized is represented by a discrete-eventsimulation model which is developed separately from theoptimization algorithm The simulation model under studytakes inputs (solutions) produced from the optimizationalgorithm (except the initial inputs which are entered byuser) Based on these inputs the simulation is executed auto-matically with various parameter settings In other wordsthe simulation of the system with the parameters underconsideration is iteratively conducted in an automatic man-ner And then the simulation model generates several outputperformance metrics as feedback on the quality of solutionsobtained from the optimization algorithm During the pro-cess of simulation-based optimization it is worth emphasiz-ing that the general guidelines of discrete-event simulationshould be followed such as performing multiple replicationsof the simulationwith the same input parameters but differentrandom number streams to minimize the variability of thesimulation outputs

In essence the AIS-based multiobjective optimizationalgorithm is a search algorithm The simulation results (out-put performance metrics) direct the algorithm to search fora new set of input parameters that takes the system towardsits optimal setting with respect to certain criteria Hence afeedback mechanism is incorporated to direct the search foroptimal solution in a controlled manner In other words thegeneration of a new set of input parameters for the simulationmodel is based on the simulation results of past evaluationsAs such the input parameters and the output performancemetrics shown in the figure in fact serve as the feedbackto the simulation model and the optimization algorithmrespectively This iterative process repeats until prespecifiedtermination criteria are met The criteria could include thefollowing for example no improving solutions can be foundor the predefined number of iterations is reached

In this framework the optimization algorithmwas imple-mented with Excel VBA whereas the simulation model wasdeveloped by using the FlexSim simulation tool [46]

32 Multiobjective Simulation-Based Optimization AlgorithmThe fundamental of the hybrid AIS-based optimizationalgorithm [45] adopted in the framework was inspired from

mechanisms of biological immune system and biological evo-lution It was developed by hybridizing the clonal selectionprinciple and immune network theory with the idea fromGenetic Algorithm (GA) The algorithm makes use of thePareto dominance for fitness assignment and some commonAIS-based algorithmrsquos features for guiding the search processsuch as clonal selection and expansion affinity matura-tion antibody concentration metadynamics and immunememory The interesting feature of this algorithm is theintroduction of an innovative suppression operator which isused to help eliminate similar antibodies hence significantlyminimizing the number of unnecessary searches and increas-ing the population diversityThe similarity among antibodiesis determined in terms of both the objective space and thedecision variable space to ensure that only similar antibodiesare eliminated in the suppression operation Moreover amodified crossover operator originated from the biologicalevolution was also developed to help further enhance thediversity of the clone population and the convergence of thealgorithmbecause some good genes from the elite parents canbe passed to the offspring for facilitating the search of optimalsolutions otherwise it may take a longer time to convergetowards the Pareto front [27] especially in simulation-basedoptimization context The mapping between the biologicalimmune system and the proposed artificial one is given inTable 1

The algorithm comprises five immune operators cloningoperator hypermutation operator suppression operatorselection and receptor editing operator and memory updat-ing operator and one genetic operator crossover operatorEach of them takes responsibility for different tasks for thepurpose of finding uniformly distributed Pareto front Theblock diagram showing the computational steps for SCMIAis presented in Figure 2 and the details of these operators areprovided as below

Nondominated Neighbor-Based Selection Based on the ideaproposed by Gong et al [42] only nondominated antibodiesare selected to form an active parent population A(119905) (where119905 is the iteration counter) with the size of119873119860 for undergoingcloning crossover and hypermutation This process mimicsthe biological immune system in which only those B-cells(antibodies) that are capable of binding with foreign antigenswill undergo clonal expansion and then hypermutation

6 Journal of Optimization

Yes

No

ClonePopulation

Mutation

Cloning

Initial Population

Initialization

Fitness Assignment

Non-dominated Neighbor-based Selection

ActivePopulation

Mutated Population

Suppression

Fitness Assignment

Crossover

Mature Population

New Population

Selection amp Receptor Editing Memory Updating

New Memory Set

Termination Condition Met

End

Figure 2 Computational steps for SCMIA

However if the number of nondominated antibodies is largerthan 119873119860 an antibody density measure called crowding-distance [6] analogous with Ab-Ab affinity in biologicalimmune system is employed for selecting the nondominatedantibodies The crowding-distance or Ab-Ab affinity for anondominated antibody is computed as follows

119889 (119886119887lowast119894 ) = 119903sum119895=1

10038161003816100381610038161003816119886119887lowast119894+1 (119891119895) minus 119886119887lowast119894minus1 (119891119895)10038161003816100381610038161003816119886119887 (119891max119895 ) minus 119886119887 (119891min

119895 ) (5)

where 119889(119886119887lowast119894 ) is the crowding-distance of the 119894th nondomi-nated antibody 119886119887lowast 119903 is the number of objectives 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119886119887lowast119894+1(119891119895) and 119886119887lowast119894minus1(119891119895) are the fitnessvalues of the nearest neighboring antibodies from both sides

Cloning Operator It enlarges the population by generating anumber of copies of each antibody in the active parent popu-lation A(t) and the number of copies is directly proportionalto its Ab-Ab affinity thus forming a clone population whichis denoted as C(119905) Hence the size of the population now is119873119860 + 119873119888 and119873119888 is obtained by

119888119894 = round (119888max times 119889 (119886119887lowast119894 )) 119873119888 = sum119888119894 (6)

where 119873119888 is the total number of copies produced 119888119894 is theclone size for the antibody 119886119887lowast119894 isin A(119905) 119888max is the predefinedmaximum clone size of each antibody and round() is anoperator for rounding its argument to the closest integerThus the higher the Ab-Ab affinity an antibody has the morethe number of copies it generates

Journal of Optimization 7

Hypermutation Operator It brings multipoint mutations tothe pool of clones hoping for producing better offspringThe mutations are dependent on the Ab-Ab affinity oftheir parents for the purpose of preventing the crowdingof antibodies and maintaining the population diversity Themechanism is that if the Ab-Ab affinity of an active parent islower themutation rate for the clones of the parent should behigher to obtain mutated children in sparse locations inorder to diversify the population The clones are mutatedproportionally as follows

120572 = 119890minus119901times119889(119886119887lowast)C119898 (119905) = C (119905) + 120572 times 119877 (7)

where 120572 represents the mutation rate inversely proportionalto the Ab-Ab affinity 119889(119886119887lowast) 119901 is an exponential coefficientcontrolling the decay of 120572 119877 isin [minus1 1] is a 119898-dimensionalrandom vector obtained with uniform distribution andC119898(119905) is the mutated clone population

Crossover Operator It works on the mutated clone popu-lation to generate a mature clone population denoted asC119888(119905) with the size of 119873119888 It is a modified single pointcrossover operator through which offspring is generated byrandomly selecting a single crossover point on a clone andthen swapping its content beyond that point with that of aparent antibody randomly selected from A(119905) This operatoris introduced to control the diversity of the clone populationand the convergence of the algorithm That being said thediversity can be enhanced while the quick convergence canbe ensured because some good genes from the active parentcan be passed to the offspring

Suppression Operator It works on the whole populationincluding the parent cells and mutated clones A(119905) cup C119888(119905) toeliminate similar individuals so as to avoid a particularsearch space being over exploited and acquire the uniformlydistributed Pareto front based on the idea of immunenetworktheory [47] such that B-cells are stimulated and suppressedby not only non-self-antigens but the interacted B-cellsDifferent from other AIS-based multiobjective optimizationalgorithms the similarity among antibodies in this algorithmis determined in terms of both the objective space and thedecision variable space so as to determinewhether to retain ordiscard individual antibodies Therefore the suppressionoperation in this algorithm has two phases in first phase thesuppressionwill be applied to all antibodies and the similaritybetween two antibodies is defined as follows

dO (119886119887119886 119886119887119887)119895 = 10038161003816100381610038161003816119886119887119886 (119891119895) minus 119886119887119887 (119891119895)10038161003816100381610038161003816 le 120575119895 (8)

where dO(119886119887119886 119886119887119887)119895 is the distance between antibodies 119886119887119886and 119886119887119887 in terms of 119895th objective and 120575119895 refers to the thresholdvalue for 119895th objective

In this phase if the distances for all objectives betweentwo antibodies are smaller than the thresholds the twoantibodies are said to be similar and hence the cell withpoorer Pareto fitness pf will be suppressed and eliminatedfrom the population

In second phase the suppression will only be applied tothe similarity between nondominated cells and dominatedcells and the similarity between two antibodies is defined asfollows

dV (119886119887119886 119886119887119887) = radic 119898sum119895=1

[119886119887119886 (119909119895) minus 119886119887119887 (119909119895)]2 le 120576 (9)

where dV(119886119887119886 119886119887119887) is the Euclidean distance in decisionvariable space between the two antibodies 119886119887119886 (dominatedcell) and 119886119887119887 (nondominated cell) isin A(119905) cup C119888(119905) 119898 is thelength of each antibody and 120576 refers to the threshold valuefor the decision variable space

In this phase if the distance between two cells is smallerthan the threshold in decision variable space the two cellsare said to be similar and hence the dominated cell will besuppressed and eliminated from the population Eventuallysurviving populations A119904(119905) cup C119904(119905) are obtained and thenenter into the selection and receptor editing process andmemory updating process simultaneously

To enhance the population diversity and facilitate thesearch of uniformly distributed nondominated solutions thethreshold values for the decision variable space and theobjective space are adaptive values that are dynamicallycalculated based on the maximum and minimum valuesfound at each iteration The adaptive threshold values arecomputed according to the following equations

120576 = 119886119887 (119909max) minus 119886119887 (119909min)119899 120575119895 = 119886119887 (119891max

119895 ) minus 119886119887 (119891min119895 )119899

(10)

where 119886119887(119909max) and 119886119887(119909min) are the maximum and mini-mum distance values in the decision variable space 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119899 is the number of antibodies in thepopulation under investigation

Selection and Receptor Editing Operator It works like adirector to guide the search towards the promising regionsby selecting all nondominated antibodies with respect tothe Pareto fitness pf from the populations A119904(119905) cup C119904(119905) toform a new population Ab(119905 + 1) with the size of 119873 forthe next generation 119905 + 1 If the new population Ab(119905 +1) is not full dominated antibodies with a better Paretofitness pf are selected and some genes of these antibodiesare then randomly selected to be replaced by randomlygenerated genes These restructured antibodies are finallyadded to the new population until the population is full inorder to further enhance the population diversity Thisprocess actually mimics the process of receptor editing in thebiological immune system However if the number ofnondominated antibodies found exceeds the limit of thepopulation size 119873 only 119873 nondominated antibodies withhigher Ab-Ab affinity 119889(119886119887) are selected

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

Journal of Optimization 3

for the evaluation of optimal system parameters and toreveal the performance of systems Subulan and Cakmakci[17] made use of ARENA simulation program and Taguchiexperimental design method to build a solution model foreffectively designing material handlingndashtransfer systems andoptimizing the performance of automation technologies inautomobile industry Chang et al [18] proposed a frameworkthat integrates simulation optimization and data envelop-ment analysis techniques to find out the optimal vehicle fleetsize for a multiobjective problem in automated materialshandling systems Lin and Huang [19] extended the optimalcomputing budget allocation by adding Genetic Algorithmtogether with the help of a simulation model for optimizingthe vehicle allocation for the automated material handlingsystem in semiconductor industry

23 Multiobjective Simulation-Based Optimization Approach-es In practice optimization problems involve several objec-tives that often conflict with each other and must be simul-taneously optimized so that a possibly uncountable set oftrade-off solutions rather than a single optimal point isfound with respect to the contradicting objectivesThereforethe aim of these problems is to find out the global trade-off solutions that effectively spread over the Pareto frontNo solution from the Pareto front is worse than any othersolution because it is better in at least one objective Theseproblems are normally termed as multiobjective problemswhich were first studied in an economic context and thenextended to the fields of science and engineering [20]Since multiobjective optimization problems involve severalobjectives the view towards optimum has changed hencechanging the aim fromfinding a single solution to obtaining aset of compromised solutions Today the notion of optimumfor amultiobjective optimization problem is frequently calledPareto optimum which was first proposed by Edgeworth [21]and then generalized by Pareto [22 23]

As is known the notion of optimality for multiobjectiveoptimization problems is different from that of single objec-tive optimization problems because the aim of multiobjectiveoptimization problems is to find a set of optimal trade-off solutions rather than a single optimal solution Thus inthe absence of preference information on the objectives theconcept of Pareto optimality is adopted in this study for solv-ing multiobjective optimization problems [24] and severaldefinitions about Pareto optimality [20 25 26] are consideredand stated below

Definition 1 (Pareto optimality) A point 119883lowast isin Ω in thesearch space is said to be Pareto optimalnondominated withrespect toΩ if and only if there are no other solutions119883 isin Ωfor which

997888rarr119891(119883) dominates997888rarr119891(119883lowast) In other words 119883lowast is

Pareto optimal with regard to the whole decision variablespace if it cannot be improved in any one objective withoutresulting in a simultaneous degradation in other objectives

Definition 2 (Pareto dominance) Consider without loss ofgenerality two decision vectors 119883119886 and 119883119887 isin X of aminimization problem Then a vector of decision variables119883119886 is said to dominate another vector 119883119887 which is denoted

by119883119886 ≺ 119883119887 if and only if119883119886 is partially less than119883119887 That isthe following two conditions must be satisfied

(1) 119883119886 is not worse than119883119887 in all objectives

119891119894 (119883119886) le 119891119894 (119883119887) forall119894 = 1 2 119903 (1)

(2) 119883119886 is better than119883119887 in at least one objective

119891119894 (119883119886) lt 119891119894 (119883119887) exist119894 = 1 2 119903 (2)

where 119894 is the number of objectives

However when any of these conditions are violated thetwo solutions 119883119886 and 119883119887 are said to be indifferent to eachother instead of dominating the other or being dominated bythe other Based on the above relations Pareto optimal setPareto front and nondominated set are defined below

Definition 3 (Pareto optimal set) Pareto optimal set ofsolutions is a collection of all Pareto optimal solutions whichis defined as

PS fl X isin Ω | not exist119883lowast isin Ω 119883lowast ≺ X (3)

Pareto optimal solutions are those solutions in the deci-sion variable space whose corresponding objective vectorelements cannot be all simultaneously improved [27] Thesolutions inside the Pareto optimal set may have no apparentrelationship except their membership in the set Paretooptimal solutions are classified as such based on their valuesbeing evaluated through whatever means

Definition 4 (Pareto front) A surface or line containingall nondominated solutions is called Pareto front which isrepresented by

PF fl 997888rarr119891 (X) | X isin PS (4)

According to the literature finding an analytical expres-sion of the Pareto front is a very difficult task Therefore acommon approach for Pareto front generation is to find outthe points withinΩ and their corresponding value119891(119883) 119883 isinΩ When this procedure is repeated a sufficient number oftimes the nondominated points and hence the Pareto frontare most likely to be found in the objective space [20]

Definition 5 (nondominated set) Of a solution set 119878 anondominated set of solutions 119878lowast comprises solutions that arenot dominated by other solutions in the set 119878 It is worthmen-tioning that while Pareto optimal solutions are always non-dominated solutions nondominated solutions may includeboth non-Pareto optimal solutions and Pareto optimal solu-tions thus revealing that the true Pareto optimal solutionscould hardly be represented by the nondominated solutionsobtained from running an optimizerThus the idea stated byvan Veldhuizen and Lamont [28] about the true Pareto frontPFtrue distinguishing it from the final set of nondominatedsolutions found by an algorithm is called known Pareto frontPFknown

4 Journal of Optimization

Feedback

Input parameters

Feedback

Output performance metrics

Initial inputs

Simulation model

Optimal Solutions

Multi-objective optimizer

Figure 1 The framework for multiobjective simulation-based optimization (source modified from Leung and Laursquos work [16])

Modern optimization approaches are very oftenpopulation-based and evolutionary in nature In suchmethods the search for the global optima essentiallycomprises an iterative process that replaces the candidatesolutions in the population by newly generated ones withan aim of achieving continuous improvement in theperformance of the best candidate solutions through thehelp of mechanisms that guide the search to find a set ofnondominated solutionsTheuse of themodern optimizationapproaches especially population-based evolutionary algo-rithms to solving the complex multiobjective optimizationproblems has beenmotivatedmainly because of the followingcritical reasons First population-based evolutionary algo-rithms can recognize the specificity of multiobjectiveoptimization problems by working simultaneously on allobjectives and finally generating a group of optimal trade-offsolutions thus forming a uniformly distributed Pareto frontSecond as the name implies the population-based ap-proaches can deal with a population of candidate solutionssimultaneously allowing the generation of several elements ofthe Pareto optimal set in a single run of an optimizer insteadof performing many separate runs when using classicalmathematical programming methods [29] This allows thedecision-makers to simply pick the one that best fits theproblem at hand thus preventing the need to reconfigure andto rerun the optimization tool for finding other alternativePareto optimal solutions Third their capability of main-taining diversity among the candidate solutions in thepopulation is important to prevent the search fromprematureconvergence to a specific region of the solution space thusallowing a better exploration of the solution space andminimizing the susceptibility of the search to the presenceof poor local optima in the optimization problems [30] Thefinal reason is that the population-based approaches are lesssusceptible to the continuity or shape of the Pareto front as

they can deal with concave and discontinuous Pareto frontswithout difficulty [27 31] Nevertheless on the other handthe weaknesses of these population-based methods are thatthey do not guarantee the identification of optimal trade-offsolutions and the solutions obtained are likely to be stuck atsome ldquogoodrdquo approximations [32]

During the past few decades a large number of pub-lications have been done in population-based evolutionaryalgorithms and proved to be effective for solving multiob-jective optimization problems since the first multiobjectiveevolutionary algorithm has been developed by Schaffer [33]These algorithms include PAES [34] NSGA-II [35] PESA[36] SPEA2 [37] PESA-II [38] micro-GA [39] micro-GA2[40] omni-aiNet [41] NNIA [42] omni-AIOS [43] MTLBO[44] and SCMIA [45]

3 A Multiobjective Simulation-BasedOptimization Framework

31 Mechanisms of the Multiobjective Simulation-Based Opti-mization Framework The optimization framework adoptedin this study is developed by taking advantage of the idea ofseparation between the optimizationmethod and the simula-tion model For this reason the optimization framework canremain the same or require only minor modifications such aschanging range of parameters data type of decision vari-ables and number of decision variables to optimize thesimulation model that incorporates new requirements Thisframework in fact is a modified version of Leung and Laursquoswork [16] which incorporates a multiobjective optimizationalgorithm instead of a single objective algorithm (Figure 1)The multiobjective algorithm adopted in the framework isSuppression-controlled Multiobjective Immune Algorithm(SCMIA) proposed by Leung and Lau [45] Concepts of thealgorithm are briefly discussed in the next section

Journal of Optimization 5

Table 1 Mapping between the biological immune system and SCMIA

Biological ImmuneSystem SCMIA

Antigen (Ag) Objective function (simulation model in simulation study) to be optimizedAntibody (Ab) Candidate solution (a set of decision variables) to be optimizedAg-Ab affinity Fitness value of each candidate solution evaluated based on Pareto dominanceAb-Ab affinity Crowding-distance proposed by Deb et al [6] working as a measure of population diversity

Immune suppression Mechanism to control the number of nearby candidate solutions based on similarity among candidate solutionsin both the objective space and decision variable space

Memory cell Current best nondominated solution

The framework consists of two critical componentsnamely (1) the simulation model and (2) the immunity-inspired multiobjective optimization algorithm A problemor a system to be optimized is represented by a discrete-eventsimulation model which is developed separately from theoptimization algorithm The simulation model under studytakes inputs (solutions) produced from the optimizationalgorithm (except the initial inputs which are entered byuser) Based on these inputs the simulation is executed auto-matically with various parameter settings In other wordsthe simulation of the system with the parameters underconsideration is iteratively conducted in an automatic man-ner And then the simulation model generates several outputperformance metrics as feedback on the quality of solutionsobtained from the optimization algorithm During the pro-cess of simulation-based optimization it is worth emphasiz-ing that the general guidelines of discrete-event simulationshould be followed such as performing multiple replicationsof the simulationwith the same input parameters but differentrandom number streams to minimize the variability of thesimulation outputs

In essence the AIS-based multiobjective optimizationalgorithm is a search algorithm The simulation results (out-put performance metrics) direct the algorithm to search fora new set of input parameters that takes the system towardsits optimal setting with respect to certain criteria Hence afeedback mechanism is incorporated to direct the search foroptimal solution in a controlled manner In other words thegeneration of a new set of input parameters for the simulationmodel is based on the simulation results of past evaluationsAs such the input parameters and the output performancemetrics shown in the figure in fact serve as the feedbackto the simulation model and the optimization algorithmrespectively This iterative process repeats until prespecifiedtermination criteria are met The criteria could include thefollowing for example no improving solutions can be foundor the predefined number of iterations is reached

In this framework the optimization algorithmwas imple-mented with Excel VBA whereas the simulation model wasdeveloped by using the FlexSim simulation tool [46]

32 Multiobjective Simulation-Based Optimization AlgorithmThe fundamental of the hybrid AIS-based optimizationalgorithm [45] adopted in the framework was inspired from

mechanisms of biological immune system and biological evo-lution It was developed by hybridizing the clonal selectionprinciple and immune network theory with the idea fromGenetic Algorithm (GA) The algorithm makes use of thePareto dominance for fitness assignment and some commonAIS-based algorithmrsquos features for guiding the search processsuch as clonal selection and expansion affinity matura-tion antibody concentration metadynamics and immunememory The interesting feature of this algorithm is theintroduction of an innovative suppression operator which isused to help eliminate similar antibodies hence significantlyminimizing the number of unnecessary searches and increas-ing the population diversityThe similarity among antibodiesis determined in terms of both the objective space and thedecision variable space to ensure that only similar antibodiesare eliminated in the suppression operation Moreover amodified crossover operator originated from the biologicalevolution was also developed to help further enhance thediversity of the clone population and the convergence of thealgorithmbecause some good genes from the elite parents canbe passed to the offspring for facilitating the search of optimalsolutions otherwise it may take a longer time to convergetowards the Pareto front [27] especially in simulation-basedoptimization context The mapping between the biologicalimmune system and the proposed artificial one is given inTable 1

The algorithm comprises five immune operators cloningoperator hypermutation operator suppression operatorselection and receptor editing operator and memory updat-ing operator and one genetic operator crossover operatorEach of them takes responsibility for different tasks for thepurpose of finding uniformly distributed Pareto front Theblock diagram showing the computational steps for SCMIAis presented in Figure 2 and the details of these operators areprovided as below

Nondominated Neighbor-Based Selection Based on the ideaproposed by Gong et al [42] only nondominated antibodiesare selected to form an active parent population A(119905) (where119905 is the iteration counter) with the size of119873119860 for undergoingcloning crossover and hypermutation This process mimicsthe biological immune system in which only those B-cells(antibodies) that are capable of binding with foreign antigenswill undergo clonal expansion and then hypermutation

6 Journal of Optimization

Yes

No

ClonePopulation

Mutation

Cloning

Initial Population

Initialization

Fitness Assignment

Non-dominated Neighbor-based Selection

ActivePopulation

Mutated Population

Suppression

Fitness Assignment

Crossover

Mature Population

New Population

Selection amp Receptor Editing Memory Updating

New Memory Set

Termination Condition Met

End

Figure 2 Computational steps for SCMIA

However if the number of nondominated antibodies is largerthan 119873119860 an antibody density measure called crowding-distance [6] analogous with Ab-Ab affinity in biologicalimmune system is employed for selecting the nondominatedantibodies The crowding-distance or Ab-Ab affinity for anondominated antibody is computed as follows

119889 (119886119887lowast119894 ) = 119903sum119895=1

10038161003816100381610038161003816119886119887lowast119894+1 (119891119895) minus 119886119887lowast119894minus1 (119891119895)10038161003816100381610038161003816119886119887 (119891max119895 ) minus 119886119887 (119891min

119895 ) (5)

where 119889(119886119887lowast119894 ) is the crowding-distance of the 119894th nondomi-nated antibody 119886119887lowast 119903 is the number of objectives 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119886119887lowast119894+1(119891119895) and 119886119887lowast119894minus1(119891119895) are the fitnessvalues of the nearest neighboring antibodies from both sides

Cloning Operator It enlarges the population by generating anumber of copies of each antibody in the active parent popu-lation A(t) and the number of copies is directly proportionalto its Ab-Ab affinity thus forming a clone population whichis denoted as C(119905) Hence the size of the population now is119873119860 + 119873119888 and119873119888 is obtained by

119888119894 = round (119888max times 119889 (119886119887lowast119894 )) 119873119888 = sum119888119894 (6)

where 119873119888 is the total number of copies produced 119888119894 is theclone size for the antibody 119886119887lowast119894 isin A(119905) 119888max is the predefinedmaximum clone size of each antibody and round() is anoperator for rounding its argument to the closest integerThus the higher the Ab-Ab affinity an antibody has the morethe number of copies it generates

Journal of Optimization 7

Hypermutation Operator It brings multipoint mutations tothe pool of clones hoping for producing better offspringThe mutations are dependent on the Ab-Ab affinity oftheir parents for the purpose of preventing the crowdingof antibodies and maintaining the population diversity Themechanism is that if the Ab-Ab affinity of an active parent islower themutation rate for the clones of the parent should behigher to obtain mutated children in sparse locations inorder to diversify the population The clones are mutatedproportionally as follows

120572 = 119890minus119901times119889(119886119887lowast)C119898 (119905) = C (119905) + 120572 times 119877 (7)

where 120572 represents the mutation rate inversely proportionalto the Ab-Ab affinity 119889(119886119887lowast) 119901 is an exponential coefficientcontrolling the decay of 120572 119877 isin [minus1 1] is a 119898-dimensionalrandom vector obtained with uniform distribution andC119898(119905) is the mutated clone population

Crossover Operator It works on the mutated clone popu-lation to generate a mature clone population denoted asC119888(119905) with the size of 119873119888 It is a modified single pointcrossover operator through which offspring is generated byrandomly selecting a single crossover point on a clone andthen swapping its content beyond that point with that of aparent antibody randomly selected from A(119905) This operatoris introduced to control the diversity of the clone populationand the convergence of the algorithm That being said thediversity can be enhanced while the quick convergence canbe ensured because some good genes from the active parentcan be passed to the offspring

Suppression Operator It works on the whole populationincluding the parent cells and mutated clones A(119905) cup C119888(119905) toeliminate similar individuals so as to avoid a particularsearch space being over exploited and acquire the uniformlydistributed Pareto front based on the idea of immunenetworktheory [47] such that B-cells are stimulated and suppressedby not only non-self-antigens but the interacted B-cellsDifferent from other AIS-based multiobjective optimizationalgorithms the similarity among antibodies in this algorithmis determined in terms of both the objective space and thedecision variable space so as to determinewhether to retain ordiscard individual antibodies Therefore the suppressionoperation in this algorithm has two phases in first phase thesuppressionwill be applied to all antibodies and the similaritybetween two antibodies is defined as follows

dO (119886119887119886 119886119887119887)119895 = 10038161003816100381610038161003816119886119887119886 (119891119895) minus 119886119887119887 (119891119895)10038161003816100381610038161003816 le 120575119895 (8)

where dO(119886119887119886 119886119887119887)119895 is the distance between antibodies 119886119887119886and 119886119887119887 in terms of 119895th objective and 120575119895 refers to the thresholdvalue for 119895th objective

In this phase if the distances for all objectives betweentwo antibodies are smaller than the thresholds the twoantibodies are said to be similar and hence the cell withpoorer Pareto fitness pf will be suppressed and eliminatedfrom the population

In second phase the suppression will only be applied tothe similarity between nondominated cells and dominatedcells and the similarity between two antibodies is defined asfollows

dV (119886119887119886 119886119887119887) = radic 119898sum119895=1

[119886119887119886 (119909119895) minus 119886119887119887 (119909119895)]2 le 120576 (9)

where dV(119886119887119886 119886119887119887) is the Euclidean distance in decisionvariable space between the two antibodies 119886119887119886 (dominatedcell) and 119886119887119887 (nondominated cell) isin A(119905) cup C119888(119905) 119898 is thelength of each antibody and 120576 refers to the threshold valuefor the decision variable space

In this phase if the distance between two cells is smallerthan the threshold in decision variable space the two cellsare said to be similar and hence the dominated cell will besuppressed and eliminated from the population Eventuallysurviving populations A119904(119905) cup C119904(119905) are obtained and thenenter into the selection and receptor editing process andmemory updating process simultaneously

To enhance the population diversity and facilitate thesearch of uniformly distributed nondominated solutions thethreshold values for the decision variable space and theobjective space are adaptive values that are dynamicallycalculated based on the maximum and minimum valuesfound at each iteration The adaptive threshold values arecomputed according to the following equations

120576 = 119886119887 (119909max) minus 119886119887 (119909min)119899 120575119895 = 119886119887 (119891max

119895 ) minus 119886119887 (119891min119895 )119899

(10)

where 119886119887(119909max) and 119886119887(119909min) are the maximum and mini-mum distance values in the decision variable space 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119899 is the number of antibodies in thepopulation under investigation

Selection and Receptor Editing Operator It works like adirector to guide the search towards the promising regionsby selecting all nondominated antibodies with respect tothe Pareto fitness pf from the populations A119904(119905) cup C119904(119905) toform a new population Ab(119905 + 1) with the size of 119873 forthe next generation 119905 + 1 If the new population Ab(119905 +1) is not full dominated antibodies with a better Paretofitness pf are selected and some genes of these antibodiesare then randomly selected to be replaced by randomlygenerated genes These restructured antibodies are finallyadded to the new population until the population is full inorder to further enhance the population diversity Thisprocess actually mimics the process of receptor editing in thebiological immune system However if the number ofnondominated antibodies found exceeds the limit of thepopulation size 119873 only 119873 nondominated antibodies withhigher Ab-Ab affinity 119889(119886119887) are selected

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

4 Journal of Optimization

Feedback

Input parameters

Feedback

Output performance metrics

Initial inputs

Simulation model

Optimal Solutions

Multi-objective optimizer

Figure 1 The framework for multiobjective simulation-based optimization (source modified from Leung and Laursquos work [16])

Modern optimization approaches are very oftenpopulation-based and evolutionary in nature In suchmethods the search for the global optima essentiallycomprises an iterative process that replaces the candidatesolutions in the population by newly generated ones withan aim of achieving continuous improvement in theperformance of the best candidate solutions through thehelp of mechanisms that guide the search to find a set ofnondominated solutionsTheuse of themodern optimizationapproaches especially population-based evolutionary algo-rithms to solving the complex multiobjective optimizationproblems has beenmotivatedmainly because of the followingcritical reasons First population-based evolutionary algo-rithms can recognize the specificity of multiobjectiveoptimization problems by working simultaneously on allobjectives and finally generating a group of optimal trade-offsolutions thus forming a uniformly distributed Pareto frontSecond as the name implies the population-based ap-proaches can deal with a population of candidate solutionssimultaneously allowing the generation of several elements ofthe Pareto optimal set in a single run of an optimizer insteadof performing many separate runs when using classicalmathematical programming methods [29] This allows thedecision-makers to simply pick the one that best fits theproblem at hand thus preventing the need to reconfigure andto rerun the optimization tool for finding other alternativePareto optimal solutions Third their capability of main-taining diversity among the candidate solutions in thepopulation is important to prevent the search fromprematureconvergence to a specific region of the solution space thusallowing a better exploration of the solution space andminimizing the susceptibility of the search to the presenceof poor local optima in the optimization problems [30] Thefinal reason is that the population-based approaches are lesssusceptible to the continuity or shape of the Pareto front as

they can deal with concave and discontinuous Pareto frontswithout difficulty [27 31] Nevertheless on the other handthe weaknesses of these population-based methods are thatthey do not guarantee the identification of optimal trade-offsolutions and the solutions obtained are likely to be stuck atsome ldquogoodrdquo approximations [32]

During the past few decades a large number of pub-lications have been done in population-based evolutionaryalgorithms and proved to be effective for solving multiob-jective optimization problems since the first multiobjectiveevolutionary algorithm has been developed by Schaffer [33]These algorithms include PAES [34] NSGA-II [35] PESA[36] SPEA2 [37] PESA-II [38] micro-GA [39] micro-GA2[40] omni-aiNet [41] NNIA [42] omni-AIOS [43] MTLBO[44] and SCMIA [45]

3 A Multiobjective Simulation-BasedOptimization Framework

31 Mechanisms of the Multiobjective Simulation-Based Opti-mization Framework The optimization framework adoptedin this study is developed by taking advantage of the idea ofseparation between the optimizationmethod and the simula-tion model For this reason the optimization framework canremain the same or require only minor modifications such aschanging range of parameters data type of decision vari-ables and number of decision variables to optimize thesimulation model that incorporates new requirements Thisframework in fact is a modified version of Leung and Laursquoswork [16] which incorporates a multiobjective optimizationalgorithm instead of a single objective algorithm (Figure 1)The multiobjective algorithm adopted in the framework isSuppression-controlled Multiobjective Immune Algorithm(SCMIA) proposed by Leung and Lau [45] Concepts of thealgorithm are briefly discussed in the next section

Journal of Optimization 5

Table 1 Mapping between the biological immune system and SCMIA

Biological ImmuneSystem SCMIA

Antigen (Ag) Objective function (simulation model in simulation study) to be optimizedAntibody (Ab) Candidate solution (a set of decision variables) to be optimizedAg-Ab affinity Fitness value of each candidate solution evaluated based on Pareto dominanceAb-Ab affinity Crowding-distance proposed by Deb et al [6] working as a measure of population diversity

Immune suppression Mechanism to control the number of nearby candidate solutions based on similarity among candidate solutionsin both the objective space and decision variable space

Memory cell Current best nondominated solution

The framework consists of two critical componentsnamely (1) the simulation model and (2) the immunity-inspired multiobjective optimization algorithm A problemor a system to be optimized is represented by a discrete-eventsimulation model which is developed separately from theoptimization algorithm The simulation model under studytakes inputs (solutions) produced from the optimizationalgorithm (except the initial inputs which are entered byuser) Based on these inputs the simulation is executed auto-matically with various parameter settings In other wordsthe simulation of the system with the parameters underconsideration is iteratively conducted in an automatic man-ner And then the simulation model generates several outputperformance metrics as feedback on the quality of solutionsobtained from the optimization algorithm During the pro-cess of simulation-based optimization it is worth emphasiz-ing that the general guidelines of discrete-event simulationshould be followed such as performing multiple replicationsof the simulationwith the same input parameters but differentrandom number streams to minimize the variability of thesimulation outputs

In essence the AIS-based multiobjective optimizationalgorithm is a search algorithm The simulation results (out-put performance metrics) direct the algorithm to search fora new set of input parameters that takes the system towardsits optimal setting with respect to certain criteria Hence afeedback mechanism is incorporated to direct the search foroptimal solution in a controlled manner In other words thegeneration of a new set of input parameters for the simulationmodel is based on the simulation results of past evaluationsAs such the input parameters and the output performancemetrics shown in the figure in fact serve as the feedbackto the simulation model and the optimization algorithmrespectively This iterative process repeats until prespecifiedtermination criteria are met The criteria could include thefollowing for example no improving solutions can be foundor the predefined number of iterations is reached

In this framework the optimization algorithmwas imple-mented with Excel VBA whereas the simulation model wasdeveloped by using the FlexSim simulation tool [46]

32 Multiobjective Simulation-Based Optimization AlgorithmThe fundamental of the hybrid AIS-based optimizationalgorithm [45] adopted in the framework was inspired from

mechanisms of biological immune system and biological evo-lution It was developed by hybridizing the clonal selectionprinciple and immune network theory with the idea fromGenetic Algorithm (GA) The algorithm makes use of thePareto dominance for fitness assignment and some commonAIS-based algorithmrsquos features for guiding the search processsuch as clonal selection and expansion affinity matura-tion antibody concentration metadynamics and immunememory The interesting feature of this algorithm is theintroduction of an innovative suppression operator which isused to help eliminate similar antibodies hence significantlyminimizing the number of unnecessary searches and increas-ing the population diversityThe similarity among antibodiesis determined in terms of both the objective space and thedecision variable space to ensure that only similar antibodiesare eliminated in the suppression operation Moreover amodified crossover operator originated from the biologicalevolution was also developed to help further enhance thediversity of the clone population and the convergence of thealgorithmbecause some good genes from the elite parents canbe passed to the offspring for facilitating the search of optimalsolutions otherwise it may take a longer time to convergetowards the Pareto front [27] especially in simulation-basedoptimization context The mapping between the biologicalimmune system and the proposed artificial one is given inTable 1

The algorithm comprises five immune operators cloningoperator hypermutation operator suppression operatorselection and receptor editing operator and memory updat-ing operator and one genetic operator crossover operatorEach of them takes responsibility for different tasks for thepurpose of finding uniformly distributed Pareto front Theblock diagram showing the computational steps for SCMIAis presented in Figure 2 and the details of these operators areprovided as below

Nondominated Neighbor-Based Selection Based on the ideaproposed by Gong et al [42] only nondominated antibodiesare selected to form an active parent population A(119905) (where119905 is the iteration counter) with the size of119873119860 for undergoingcloning crossover and hypermutation This process mimicsthe biological immune system in which only those B-cells(antibodies) that are capable of binding with foreign antigenswill undergo clonal expansion and then hypermutation

6 Journal of Optimization

Yes

No

ClonePopulation

Mutation

Cloning

Initial Population

Initialization

Fitness Assignment

Non-dominated Neighbor-based Selection

ActivePopulation

Mutated Population

Suppression

Fitness Assignment

Crossover

Mature Population

New Population

Selection amp Receptor Editing Memory Updating

New Memory Set

Termination Condition Met

End

Figure 2 Computational steps for SCMIA

However if the number of nondominated antibodies is largerthan 119873119860 an antibody density measure called crowding-distance [6] analogous with Ab-Ab affinity in biologicalimmune system is employed for selecting the nondominatedantibodies The crowding-distance or Ab-Ab affinity for anondominated antibody is computed as follows

119889 (119886119887lowast119894 ) = 119903sum119895=1

10038161003816100381610038161003816119886119887lowast119894+1 (119891119895) minus 119886119887lowast119894minus1 (119891119895)10038161003816100381610038161003816119886119887 (119891max119895 ) minus 119886119887 (119891min

119895 ) (5)

where 119889(119886119887lowast119894 ) is the crowding-distance of the 119894th nondomi-nated antibody 119886119887lowast 119903 is the number of objectives 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119886119887lowast119894+1(119891119895) and 119886119887lowast119894minus1(119891119895) are the fitnessvalues of the nearest neighboring antibodies from both sides

Cloning Operator It enlarges the population by generating anumber of copies of each antibody in the active parent popu-lation A(t) and the number of copies is directly proportionalto its Ab-Ab affinity thus forming a clone population whichis denoted as C(119905) Hence the size of the population now is119873119860 + 119873119888 and119873119888 is obtained by

119888119894 = round (119888max times 119889 (119886119887lowast119894 )) 119873119888 = sum119888119894 (6)

where 119873119888 is the total number of copies produced 119888119894 is theclone size for the antibody 119886119887lowast119894 isin A(119905) 119888max is the predefinedmaximum clone size of each antibody and round() is anoperator for rounding its argument to the closest integerThus the higher the Ab-Ab affinity an antibody has the morethe number of copies it generates

Journal of Optimization 7

Hypermutation Operator It brings multipoint mutations tothe pool of clones hoping for producing better offspringThe mutations are dependent on the Ab-Ab affinity oftheir parents for the purpose of preventing the crowdingof antibodies and maintaining the population diversity Themechanism is that if the Ab-Ab affinity of an active parent islower themutation rate for the clones of the parent should behigher to obtain mutated children in sparse locations inorder to diversify the population The clones are mutatedproportionally as follows

120572 = 119890minus119901times119889(119886119887lowast)C119898 (119905) = C (119905) + 120572 times 119877 (7)

where 120572 represents the mutation rate inversely proportionalto the Ab-Ab affinity 119889(119886119887lowast) 119901 is an exponential coefficientcontrolling the decay of 120572 119877 isin [minus1 1] is a 119898-dimensionalrandom vector obtained with uniform distribution andC119898(119905) is the mutated clone population

Crossover Operator It works on the mutated clone popu-lation to generate a mature clone population denoted asC119888(119905) with the size of 119873119888 It is a modified single pointcrossover operator through which offspring is generated byrandomly selecting a single crossover point on a clone andthen swapping its content beyond that point with that of aparent antibody randomly selected from A(119905) This operatoris introduced to control the diversity of the clone populationand the convergence of the algorithm That being said thediversity can be enhanced while the quick convergence canbe ensured because some good genes from the active parentcan be passed to the offspring

Suppression Operator It works on the whole populationincluding the parent cells and mutated clones A(119905) cup C119888(119905) toeliminate similar individuals so as to avoid a particularsearch space being over exploited and acquire the uniformlydistributed Pareto front based on the idea of immunenetworktheory [47] such that B-cells are stimulated and suppressedby not only non-self-antigens but the interacted B-cellsDifferent from other AIS-based multiobjective optimizationalgorithms the similarity among antibodies in this algorithmis determined in terms of both the objective space and thedecision variable space so as to determinewhether to retain ordiscard individual antibodies Therefore the suppressionoperation in this algorithm has two phases in first phase thesuppressionwill be applied to all antibodies and the similaritybetween two antibodies is defined as follows

dO (119886119887119886 119886119887119887)119895 = 10038161003816100381610038161003816119886119887119886 (119891119895) minus 119886119887119887 (119891119895)10038161003816100381610038161003816 le 120575119895 (8)

where dO(119886119887119886 119886119887119887)119895 is the distance between antibodies 119886119887119886and 119886119887119887 in terms of 119895th objective and 120575119895 refers to the thresholdvalue for 119895th objective

In this phase if the distances for all objectives betweentwo antibodies are smaller than the thresholds the twoantibodies are said to be similar and hence the cell withpoorer Pareto fitness pf will be suppressed and eliminatedfrom the population

In second phase the suppression will only be applied tothe similarity between nondominated cells and dominatedcells and the similarity between two antibodies is defined asfollows

dV (119886119887119886 119886119887119887) = radic 119898sum119895=1

[119886119887119886 (119909119895) minus 119886119887119887 (119909119895)]2 le 120576 (9)

where dV(119886119887119886 119886119887119887) is the Euclidean distance in decisionvariable space between the two antibodies 119886119887119886 (dominatedcell) and 119886119887119887 (nondominated cell) isin A(119905) cup C119888(119905) 119898 is thelength of each antibody and 120576 refers to the threshold valuefor the decision variable space

In this phase if the distance between two cells is smallerthan the threshold in decision variable space the two cellsare said to be similar and hence the dominated cell will besuppressed and eliminated from the population Eventuallysurviving populations A119904(119905) cup C119904(119905) are obtained and thenenter into the selection and receptor editing process andmemory updating process simultaneously

To enhance the population diversity and facilitate thesearch of uniformly distributed nondominated solutions thethreshold values for the decision variable space and theobjective space are adaptive values that are dynamicallycalculated based on the maximum and minimum valuesfound at each iteration The adaptive threshold values arecomputed according to the following equations

120576 = 119886119887 (119909max) minus 119886119887 (119909min)119899 120575119895 = 119886119887 (119891max

119895 ) minus 119886119887 (119891min119895 )119899

(10)

where 119886119887(119909max) and 119886119887(119909min) are the maximum and mini-mum distance values in the decision variable space 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119899 is the number of antibodies in thepopulation under investigation

Selection and Receptor Editing Operator It works like adirector to guide the search towards the promising regionsby selecting all nondominated antibodies with respect tothe Pareto fitness pf from the populations A119904(119905) cup C119904(119905) toform a new population Ab(119905 + 1) with the size of 119873 forthe next generation 119905 + 1 If the new population Ab(119905 +1) is not full dominated antibodies with a better Paretofitness pf are selected and some genes of these antibodiesare then randomly selected to be replaced by randomlygenerated genes These restructured antibodies are finallyadded to the new population until the population is full inorder to further enhance the population diversity Thisprocess actually mimics the process of receptor editing in thebiological immune system However if the number ofnondominated antibodies found exceeds the limit of thepopulation size 119873 only 119873 nondominated antibodies withhigher Ab-Ab affinity 119889(119886119887) are selected

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

Journal of Optimization 5

Table 1 Mapping between the biological immune system and SCMIA

Biological ImmuneSystem SCMIA

Antigen (Ag) Objective function (simulation model in simulation study) to be optimizedAntibody (Ab) Candidate solution (a set of decision variables) to be optimizedAg-Ab affinity Fitness value of each candidate solution evaluated based on Pareto dominanceAb-Ab affinity Crowding-distance proposed by Deb et al [6] working as a measure of population diversity

Immune suppression Mechanism to control the number of nearby candidate solutions based on similarity among candidate solutionsin both the objective space and decision variable space

Memory cell Current best nondominated solution

The framework consists of two critical componentsnamely (1) the simulation model and (2) the immunity-inspired multiobjective optimization algorithm A problemor a system to be optimized is represented by a discrete-eventsimulation model which is developed separately from theoptimization algorithm The simulation model under studytakes inputs (solutions) produced from the optimizationalgorithm (except the initial inputs which are entered byuser) Based on these inputs the simulation is executed auto-matically with various parameter settings In other wordsthe simulation of the system with the parameters underconsideration is iteratively conducted in an automatic man-ner And then the simulation model generates several outputperformance metrics as feedback on the quality of solutionsobtained from the optimization algorithm During the pro-cess of simulation-based optimization it is worth emphasiz-ing that the general guidelines of discrete-event simulationshould be followed such as performing multiple replicationsof the simulationwith the same input parameters but differentrandom number streams to minimize the variability of thesimulation outputs

In essence the AIS-based multiobjective optimizationalgorithm is a search algorithm The simulation results (out-put performance metrics) direct the algorithm to search fora new set of input parameters that takes the system towardsits optimal setting with respect to certain criteria Hence afeedback mechanism is incorporated to direct the search foroptimal solution in a controlled manner In other words thegeneration of a new set of input parameters for the simulationmodel is based on the simulation results of past evaluationsAs such the input parameters and the output performancemetrics shown in the figure in fact serve as the feedbackto the simulation model and the optimization algorithmrespectively This iterative process repeats until prespecifiedtermination criteria are met The criteria could include thefollowing for example no improving solutions can be foundor the predefined number of iterations is reached

In this framework the optimization algorithmwas imple-mented with Excel VBA whereas the simulation model wasdeveloped by using the FlexSim simulation tool [46]

32 Multiobjective Simulation-Based Optimization AlgorithmThe fundamental of the hybrid AIS-based optimizationalgorithm [45] adopted in the framework was inspired from

mechanisms of biological immune system and biological evo-lution It was developed by hybridizing the clonal selectionprinciple and immune network theory with the idea fromGenetic Algorithm (GA) The algorithm makes use of thePareto dominance for fitness assignment and some commonAIS-based algorithmrsquos features for guiding the search processsuch as clonal selection and expansion affinity matura-tion antibody concentration metadynamics and immunememory The interesting feature of this algorithm is theintroduction of an innovative suppression operator which isused to help eliminate similar antibodies hence significantlyminimizing the number of unnecessary searches and increas-ing the population diversityThe similarity among antibodiesis determined in terms of both the objective space and thedecision variable space to ensure that only similar antibodiesare eliminated in the suppression operation Moreover amodified crossover operator originated from the biologicalevolution was also developed to help further enhance thediversity of the clone population and the convergence of thealgorithmbecause some good genes from the elite parents canbe passed to the offspring for facilitating the search of optimalsolutions otherwise it may take a longer time to convergetowards the Pareto front [27] especially in simulation-basedoptimization context The mapping between the biologicalimmune system and the proposed artificial one is given inTable 1

The algorithm comprises five immune operators cloningoperator hypermutation operator suppression operatorselection and receptor editing operator and memory updat-ing operator and one genetic operator crossover operatorEach of them takes responsibility for different tasks for thepurpose of finding uniformly distributed Pareto front Theblock diagram showing the computational steps for SCMIAis presented in Figure 2 and the details of these operators areprovided as below

Nondominated Neighbor-Based Selection Based on the ideaproposed by Gong et al [42] only nondominated antibodiesare selected to form an active parent population A(119905) (where119905 is the iteration counter) with the size of119873119860 for undergoingcloning crossover and hypermutation This process mimicsthe biological immune system in which only those B-cells(antibodies) that are capable of binding with foreign antigenswill undergo clonal expansion and then hypermutation

6 Journal of Optimization

Yes

No

ClonePopulation

Mutation

Cloning

Initial Population

Initialization

Fitness Assignment

Non-dominated Neighbor-based Selection

ActivePopulation

Mutated Population

Suppression

Fitness Assignment

Crossover

Mature Population

New Population

Selection amp Receptor Editing Memory Updating

New Memory Set

Termination Condition Met

End

Figure 2 Computational steps for SCMIA

However if the number of nondominated antibodies is largerthan 119873119860 an antibody density measure called crowding-distance [6] analogous with Ab-Ab affinity in biologicalimmune system is employed for selecting the nondominatedantibodies The crowding-distance or Ab-Ab affinity for anondominated antibody is computed as follows

119889 (119886119887lowast119894 ) = 119903sum119895=1

10038161003816100381610038161003816119886119887lowast119894+1 (119891119895) minus 119886119887lowast119894minus1 (119891119895)10038161003816100381610038161003816119886119887 (119891max119895 ) minus 119886119887 (119891min

119895 ) (5)

where 119889(119886119887lowast119894 ) is the crowding-distance of the 119894th nondomi-nated antibody 119886119887lowast 119903 is the number of objectives 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119886119887lowast119894+1(119891119895) and 119886119887lowast119894minus1(119891119895) are the fitnessvalues of the nearest neighboring antibodies from both sides

Cloning Operator It enlarges the population by generating anumber of copies of each antibody in the active parent popu-lation A(t) and the number of copies is directly proportionalto its Ab-Ab affinity thus forming a clone population whichis denoted as C(119905) Hence the size of the population now is119873119860 + 119873119888 and119873119888 is obtained by

119888119894 = round (119888max times 119889 (119886119887lowast119894 )) 119873119888 = sum119888119894 (6)

where 119873119888 is the total number of copies produced 119888119894 is theclone size for the antibody 119886119887lowast119894 isin A(119905) 119888max is the predefinedmaximum clone size of each antibody and round() is anoperator for rounding its argument to the closest integerThus the higher the Ab-Ab affinity an antibody has the morethe number of copies it generates

Journal of Optimization 7

Hypermutation Operator It brings multipoint mutations tothe pool of clones hoping for producing better offspringThe mutations are dependent on the Ab-Ab affinity oftheir parents for the purpose of preventing the crowdingof antibodies and maintaining the population diversity Themechanism is that if the Ab-Ab affinity of an active parent islower themutation rate for the clones of the parent should behigher to obtain mutated children in sparse locations inorder to diversify the population The clones are mutatedproportionally as follows

120572 = 119890minus119901times119889(119886119887lowast)C119898 (119905) = C (119905) + 120572 times 119877 (7)

where 120572 represents the mutation rate inversely proportionalto the Ab-Ab affinity 119889(119886119887lowast) 119901 is an exponential coefficientcontrolling the decay of 120572 119877 isin [minus1 1] is a 119898-dimensionalrandom vector obtained with uniform distribution andC119898(119905) is the mutated clone population

Crossover Operator It works on the mutated clone popu-lation to generate a mature clone population denoted asC119888(119905) with the size of 119873119888 It is a modified single pointcrossover operator through which offspring is generated byrandomly selecting a single crossover point on a clone andthen swapping its content beyond that point with that of aparent antibody randomly selected from A(119905) This operatoris introduced to control the diversity of the clone populationand the convergence of the algorithm That being said thediversity can be enhanced while the quick convergence canbe ensured because some good genes from the active parentcan be passed to the offspring

Suppression Operator It works on the whole populationincluding the parent cells and mutated clones A(119905) cup C119888(119905) toeliminate similar individuals so as to avoid a particularsearch space being over exploited and acquire the uniformlydistributed Pareto front based on the idea of immunenetworktheory [47] such that B-cells are stimulated and suppressedby not only non-self-antigens but the interacted B-cellsDifferent from other AIS-based multiobjective optimizationalgorithms the similarity among antibodies in this algorithmis determined in terms of both the objective space and thedecision variable space so as to determinewhether to retain ordiscard individual antibodies Therefore the suppressionoperation in this algorithm has two phases in first phase thesuppressionwill be applied to all antibodies and the similaritybetween two antibodies is defined as follows

dO (119886119887119886 119886119887119887)119895 = 10038161003816100381610038161003816119886119887119886 (119891119895) minus 119886119887119887 (119891119895)10038161003816100381610038161003816 le 120575119895 (8)

where dO(119886119887119886 119886119887119887)119895 is the distance between antibodies 119886119887119886and 119886119887119887 in terms of 119895th objective and 120575119895 refers to the thresholdvalue for 119895th objective

In this phase if the distances for all objectives betweentwo antibodies are smaller than the thresholds the twoantibodies are said to be similar and hence the cell withpoorer Pareto fitness pf will be suppressed and eliminatedfrom the population

In second phase the suppression will only be applied tothe similarity between nondominated cells and dominatedcells and the similarity between two antibodies is defined asfollows

dV (119886119887119886 119886119887119887) = radic 119898sum119895=1

[119886119887119886 (119909119895) minus 119886119887119887 (119909119895)]2 le 120576 (9)

where dV(119886119887119886 119886119887119887) is the Euclidean distance in decisionvariable space between the two antibodies 119886119887119886 (dominatedcell) and 119886119887119887 (nondominated cell) isin A(119905) cup C119888(119905) 119898 is thelength of each antibody and 120576 refers to the threshold valuefor the decision variable space

In this phase if the distance between two cells is smallerthan the threshold in decision variable space the two cellsare said to be similar and hence the dominated cell will besuppressed and eliminated from the population Eventuallysurviving populations A119904(119905) cup C119904(119905) are obtained and thenenter into the selection and receptor editing process andmemory updating process simultaneously

To enhance the population diversity and facilitate thesearch of uniformly distributed nondominated solutions thethreshold values for the decision variable space and theobjective space are adaptive values that are dynamicallycalculated based on the maximum and minimum valuesfound at each iteration The adaptive threshold values arecomputed according to the following equations

120576 = 119886119887 (119909max) minus 119886119887 (119909min)119899 120575119895 = 119886119887 (119891max

119895 ) minus 119886119887 (119891min119895 )119899

(10)

where 119886119887(119909max) and 119886119887(119909min) are the maximum and mini-mum distance values in the decision variable space 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119899 is the number of antibodies in thepopulation under investigation

Selection and Receptor Editing Operator It works like adirector to guide the search towards the promising regionsby selecting all nondominated antibodies with respect tothe Pareto fitness pf from the populations A119904(119905) cup C119904(119905) toform a new population Ab(119905 + 1) with the size of 119873 forthe next generation 119905 + 1 If the new population Ab(119905 +1) is not full dominated antibodies with a better Paretofitness pf are selected and some genes of these antibodiesare then randomly selected to be replaced by randomlygenerated genes These restructured antibodies are finallyadded to the new population until the population is full inorder to further enhance the population diversity Thisprocess actually mimics the process of receptor editing in thebiological immune system However if the number ofnondominated antibodies found exceeds the limit of thepopulation size 119873 only 119873 nondominated antibodies withhigher Ab-Ab affinity 119889(119886119887) are selected

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

6 Journal of Optimization

Yes

No

ClonePopulation

Mutation

Cloning

Initial Population

Initialization

Fitness Assignment

Non-dominated Neighbor-based Selection

ActivePopulation

Mutated Population

Suppression

Fitness Assignment

Crossover

Mature Population

New Population

Selection amp Receptor Editing Memory Updating

New Memory Set

Termination Condition Met

End

Figure 2 Computational steps for SCMIA

However if the number of nondominated antibodies is largerthan 119873119860 an antibody density measure called crowding-distance [6] analogous with Ab-Ab affinity in biologicalimmune system is employed for selecting the nondominatedantibodies The crowding-distance or Ab-Ab affinity for anondominated antibody is computed as follows

119889 (119886119887lowast119894 ) = 119903sum119895=1

10038161003816100381610038161003816119886119887lowast119894+1 (119891119895) minus 119886119887lowast119894minus1 (119891119895)10038161003816100381610038161003816119886119887 (119891max119895 ) minus 119886119887 (119891min

119895 ) (5)

where 119889(119886119887lowast119894 ) is the crowding-distance of the 119894th nondomi-nated antibody 119886119887lowast 119903 is the number of objectives 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119886119887lowast119894+1(119891119895) and 119886119887lowast119894minus1(119891119895) are the fitnessvalues of the nearest neighboring antibodies from both sides

Cloning Operator It enlarges the population by generating anumber of copies of each antibody in the active parent popu-lation A(t) and the number of copies is directly proportionalto its Ab-Ab affinity thus forming a clone population whichis denoted as C(119905) Hence the size of the population now is119873119860 + 119873119888 and119873119888 is obtained by

119888119894 = round (119888max times 119889 (119886119887lowast119894 )) 119873119888 = sum119888119894 (6)

where 119873119888 is the total number of copies produced 119888119894 is theclone size for the antibody 119886119887lowast119894 isin A(119905) 119888max is the predefinedmaximum clone size of each antibody and round() is anoperator for rounding its argument to the closest integerThus the higher the Ab-Ab affinity an antibody has the morethe number of copies it generates

Journal of Optimization 7

Hypermutation Operator It brings multipoint mutations tothe pool of clones hoping for producing better offspringThe mutations are dependent on the Ab-Ab affinity oftheir parents for the purpose of preventing the crowdingof antibodies and maintaining the population diversity Themechanism is that if the Ab-Ab affinity of an active parent islower themutation rate for the clones of the parent should behigher to obtain mutated children in sparse locations inorder to diversify the population The clones are mutatedproportionally as follows

120572 = 119890minus119901times119889(119886119887lowast)C119898 (119905) = C (119905) + 120572 times 119877 (7)

where 120572 represents the mutation rate inversely proportionalto the Ab-Ab affinity 119889(119886119887lowast) 119901 is an exponential coefficientcontrolling the decay of 120572 119877 isin [minus1 1] is a 119898-dimensionalrandom vector obtained with uniform distribution andC119898(119905) is the mutated clone population

Crossover Operator It works on the mutated clone popu-lation to generate a mature clone population denoted asC119888(119905) with the size of 119873119888 It is a modified single pointcrossover operator through which offspring is generated byrandomly selecting a single crossover point on a clone andthen swapping its content beyond that point with that of aparent antibody randomly selected from A(119905) This operatoris introduced to control the diversity of the clone populationand the convergence of the algorithm That being said thediversity can be enhanced while the quick convergence canbe ensured because some good genes from the active parentcan be passed to the offspring

Suppression Operator It works on the whole populationincluding the parent cells and mutated clones A(119905) cup C119888(119905) toeliminate similar individuals so as to avoid a particularsearch space being over exploited and acquire the uniformlydistributed Pareto front based on the idea of immunenetworktheory [47] such that B-cells are stimulated and suppressedby not only non-self-antigens but the interacted B-cellsDifferent from other AIS-based multiobjective optimizationalgorithms the similarity among antibodies in this algorithmis determined in terms of both the objective space and thedecision variable space so as to determinewhether to retain ordiscard individual antibodies Therefore the suppressionoperation in this algorithm has two phases in first phase thesuppressionwill be applied to all antibodies and the similaritybetween two antibodies is defined as follows

dO (119886119887119886 119886119887119887)119895 = 10038161003816100381610038161003816119886119887119886 (119891119895) minus 119886119887119887 (119891119895)10038161003816100381610038161003816 le 120575119895 (8)

where dO(119886119887119886 119886119887119887)119895 is the distance between antibodies 119886119887119886and 119886119887119887 in terms of 119895th objective and 120575119895 refers to the thresholdvalue for 119895th objective

In this phase if the distances for all objectives betweentwo antibodies are smaller than the thresholds the twoantibodies are said to be similar and hence the cell withpoorer Pareto fitness pf will be suppressed and eliminatedfrom the population

In second phase the suppression will only be applied tothe similarity between nondominated cells and dominatedcells and the similarity between two antibodies is defined asfollows

dV (119886119887119886 119886119887119887) = radic 119898sum119895=1

[119886119887119886 (119909119895) minus 119886119887119887 (119909119895)]2 le 120576 (9)

where dV(119886119887119886 119886119887119887) is the Euclidean distance in decisionvariable space between the two antibodies 119886119887119886 (dominatedcell) and 119886119887119887 (nondominated cell) isin A(119905) cup C119888(119905) 119898 is thelength of each antibody and 120576 refers to the threshold valuefor the decision variable space

In this phase if the distance between two cells is smallerthan the threshold in decision variable space the two cellsare said to be similar and hence the dominated cell will besuppressed and eliminated from the population Eventuallysurviving populations A119904(119905) cup C119904(119905) are obtained and thenenter into the selection and receptor editing process andmemory updating process simultaneously

To enhance the population diversity and facilitate thesearch of uniformly distributed nondominated solutions thethreshold values for the decision variable space and theobjective space are adaptive values that are dynamicallycalculated based on the maximum and minimum valuesfound at each iteration The adaptive threshold values arecomputed according to the following equations

120576 = 119886119887 (119909max) minus 119886119887 (119909min)119899 120575119895 = 119886119887 (119891max

119895 ) minus 119886119887 (119891min119895 )119899

(10)

where 119886119887(119909max) and 119886119887(119909min) are the maximum and mini-mum distance values in the decision variable space 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119899 is the number of antibodies in thepopulation under investigation

Selection and Receptor Editing Operator It works like adirector to guide the search towards the promising regionsby selecting all nondominated antibodies with respect tothe Pareto fitness pf from the populations A119904(119905) cup C119904(119905) toform a new population Ab(119905 + 1) with the size of 119873 forthe next generation 119905 + 1 If the new population Ab(119905 +1) is not full dominated antibodies with a better Paretofitness pf are selected and some genes of these antibodiesare then randomly selected to be replaced by randomlygenerated genes These restructured antibodies are finallyadded to the new population until the population is full inorder to further enhance the population diversity Thisprocess actually mimics the process of receptor editing in thebiological immune system However if the number ofnondominated antibodies found exceeds the limit of thepopulation size 119873 only 119873 nondominated antibodies withhigher Ab-Ab affinity 119889(119886119887) are selected

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

Journal of Optimization 7

Hypermutation Operator It brings multipoint mutations tothe pool of clones hoping for producing better offspringThe mutations are dependent on the Ab-Ab affinity oftheir parents for the purpose of preventing the crowdingof antibodies and maintaining the population diversity Themechanism is that if the Ab-Ab affinity of an active parent islower themutation rate for the clones of the parent should behigher to obtain mutated children in sparse locations inorder to diversify the population The clones are mutatedproportionally as follows

120572 = 119890minus119901times119889(119886119887lowast)C119898 (119905) = C (119905) + 120572 times 119877 (7)

where 120572 represents the mutation rate inversely proportionalto the Ab-Ab affinity 119889(119886119887lowast) 119901 is an exponential coefficientcontrolling the decay of 120572 119877 isin [minus1 1] is a 119898-dimensionalrandom vector obtained with uniform distribution andC119898(119905) is the mutated clone population

Crossover Operator It works on the mutated clone popu-lation to generate a mature clone population denoted asC119888(119905) with the size of 119873119888 It is a modified single pointcrossover operator through which offspring is generated byrandomly selecting a single crossover point on a clone andthen swapping its content beyond that point with that of aparent antibody randomly selected from A(119905) This operatoris introduced to control the diversity of the clone populationand the convergence of the algorithm That being said thediversity can be enhanced while the quick convergence canbe ensured because some good genes from the active parentcan be passed to the offspring

Suppression Operator It works on the whole populationincluding the parent cells and mutated clones A(119905) cup C119888(119905) toeliminate similar individuals so as to avoid a particularsearch space being over exploited and acquire the uniformlydistributed Pareto front based on the idea of immunenetworktheory [47] such that B-cells are stimulated and suppressedby not only non-self-antigens but the interacted B-cellsDifferent from other AIS-based multiobjective optimizationalgorithms the similarity among antibodies in this algorithmis determined in terms of both the objective space and thedecision variable space so as to determinewhether to retain ordiscard individual antibodies Therefore the suppressionoperation in this algorithm has two phases in first phase thesuppressionwill be applied to all antibodies and the similaritybetween two antibodies is defined as follows

dO (119886119887119886 119886119887119887)119895 = 10038161003816100381610038161003816119886119887119886 (119891119895) minus 119886119887119887 (119891119895)10038161003816100381610038161003816 le 120575119895 (8)

where dO(119886119887119886 119886119887119887)119895 is the distance between antibodies 119886119887119886and 119886119887119887 in terms of 119895th objective and 120575119895 refers to the thresholdvalue for 119895th objective

In this phase if the distances for all objectives betweentwo antibodies are smaller than the thresholds the twoantibodies are said to be similar and hence the cell withpoorer Pareto fitness pf will be suppressed and eliminatedfrom the population

In second phase the suppression will only be applied tothe similarity between nondominated cells and dominatedcells and the similarity between two antibodies is defined asfollows

dV (119886119887119886 119886119887119887) = radic 119898sum119895=1

[119886119887119886 (119909119895) minus 119886119887119887 (119909119895)]2 le 120576 (9)

where dV(119886119887119886 119886119887119887) is the Euclidean distance in decisionvariable space between the two antibodies 119886119887119886 (dominatedcell) and 119886119887119887 (nondominated cell) isin A(119905) cup C119888(119905) 119898 is thelength of each antibody and 120576 refers to the threshold valuefor the decision variable space

In this phase if the distance between two cells is smallerthan the threshold in decision variable space the two cellsare said to be similar and hence the dominated cell will besuppressed and eliminated from the population Eventuallysurviving populations A119904(119905) cup C119904(119905) are obtained and thenenter into the selection and receptor editing process andmemory updating process simultaneously

To enhance the population diversity and facilitate thesearch of uniformly distributed nondominated solutions thethreshold values for the decision variable space and theobjective space are adaptive values that are dynamicallycalculated based on the maximum and minimum valuesfound at each iteration The adaptive threshold values arecomputed according to the following equations

120576 = 119886119887 (119909max) minus 119886119887 (119909min)119899 120575119895 = 119886119887 (119891max

119895 ) minus 119886119887 (119891min119895 )119899

(10)

where 119886119887(119909max) and 119886119887(119909min) are the maximum and mini-mum distance values in the decision variable space 119886119887(119891max

119895 )and 119886119887(119891min

119895 ) are the maximum and minimum fitness valuesof the 119895th objective and 119899 is the number of antibodies in thepopulation under investigation

Selection and Receptor Editing Operator It works like adirector to guide the search towards the promising regionsby selecting all nondominated antibodies with respect tothe Pareto fitness pf from the populations A119904(119905) cup C119904(119905) toform a new population Ab(119905 + 1) with the size of 119873 forthe next generation 119905 + 1 If the new population Ab(119905 +1) is not full dominated antibodies with a better Paretofitness pf are selected and some genes of these antibodiesare then randomly selected to be replaced by randomlygenerated genes These restructured antibodies are finallyadded to the new population until the population is full inorder to further enhance the population diversity Thisprocess actually mimics the process of receptor editing in thebiological immune system However if the number ofnondominated antibodies found exceeds the limit of thepopulation size 119873 only 119873 nondominated antibodies withhigher Ab-Ab affinity 119889(119886119887) are selected

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

8 Journal of Optimization

Memory Updating Operator It works as an elitist mechanismfor helping preserve the best solutions that represent thePareto front found over the search process The memory setis updated at each iteration through the following procedure

(1) If the size of P(119905) is equal to119873119898 there is no memoryarchiving procedure to proceed

(2) If the size of P(119905) is smaller than 119873119898 an archivingprocedure is triggered to copy some of the dominatedantibodies that have the best Pareto fitness pf and Ab-Ab affinity 119889(119886119887) toP(119905) for filling the vacant space up

(3) If the size of P(119905) is larger than 119873119898 an archivingprocedure is triggered to compress P(119905) based onthe antibody similarity (the measure used in thesuppression operator) until its size becomes119873119898

After performing the final memory updating procedureat the last iteration the memory set P(119905) obtained representsthe resulting solution set of the algorithm

The algorithm is conducted by applying these heuristicand stochastic operators on the antibody population forbalancing both the local and global search capabilities For thedetailed discussion of the hybrid multiobjective algorithmone can refer to [45]

4 Multiobjective Simulation-BasedOptimization Study

In this study a set of experiments based on a real-lifemultiob-jective optimization problem was performed to evaluate theperformance and capability of the optimization frameworkand algorithm In order to provide a better view on theperformance of each method both the graphical presenta-tions of the simulation results and the statistical results ofperformance metrics on the problem under investigationwere analyzed All these experiments were conducted usinga computer with Xeon E5-2620 2GHz CPU with 2GB RAM

41 Performance Metrics In this simulation-based optimiza-tion study two performancemetrics namely error ratio (ER)[48] and spacing (119878) [49] are adopted to examine the qualityof solution set in terms of the optimality and diversity

Error Ratio (ER) The PFtrue was originally used to computethis metric However since the PFtrue can hardly be foundfor the real-life problem under investigation in this paperwe use the reference Pareto front ldquoPFrefrdquo that is the bestapproximation of the true Pareto front for measuring theoptimality of each solution set The PFref is found by usingall of the algorithms used in this study To achieve this a setof nondominated solutions that is a Pareto front for eachalgorithm is firstly generated by running a very large numberof iterations eg 100 over 20 trials and then all the frontsobtained by all the trials of all the compared algorithms were

Figure 3 The distribution flow of SF Expressrsquos imported goods inHong Kong

merged together to form a reference Pareto front Hence thismetric is mathematically defined as

ER flsum119899119894=1 119890119894119899 119890119894 =

0 119909119894 isin PFref 1 119909119894 notin PFref (11)

where 119899 is the number of solutions in the PFknown found bythe algorithm being evaluated 119890119894 = 0 if solution 119894 belongs tothe PFref and 119890119894 = 1 otherwise ER = 0 indicates that all thegenerated solutions belong to the PFref

Spacing (119878) Thismetric is used for determining the diversityof the generated solutions That being said it shows how wellthe solutions are distributed in the PFknown This metric ismathematically defined as

119878 fl radicsum119899119894=1 (119889 minus 119889119894)2119899 minus 1 119889119894 = min

119895( 119898sum119896=1

100381610038161003816100381610038161198911198941 (119909) minus 1198911198951 (119909)10038161003816100381610038161003816) 119894 119895 = 1 119899(12)

where 119889 is the mean of all 119889119894 119896 is the number of objectivefunctions and 119899 is the number of solutions in the PFknown119878 = 0 indicates that all the nondominated solutions found areequally spaced and uniformly distributed in objective space

42 Experimental Setup In this section a real-life mul-tiobjective optimization problem that is the distributionoperation of the material handling system (MHS) imple-mented at the distribution center (DC) of SF Express (HongKong) Limited was studied through the simulation-basedoptimization approach SF Express launched its service inHongKong in 1993 At present its service network is coveringalmost all areas of Hong Kong which is mainly served bythe DC located in Tin Shui Wai (TSW) in northern NewTerritories (Figure 3) Its service stores are located in 30 areasof Hong Kong [50]

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

Journal of Optimization 9

Figure 4 Inbound docks connecting to the conveyor system

The DC has two major conveyor systems one for han-dling the exported goods and another for imported goodsIn this study we focus on the physical goods flow at theDC where the items are imported from China and thendistributed to all parts of Hong Kong At the DC most ofthe items received at inbound docks (Figure 4) are directlytransferred to outbound docks (Figure 5) and then shippedto the final destinations with little material handling inbetween such as deconsolidation and sortation As suchthe expensive physical distribution functions of putawayinventory holding and order picking from the DC are elim-inated This approach is called cross-docking To implementcross-docking effectively and efficiently timely distributionof freight and better synchronization of all inbound andoutbound shipments are required by making use of theinformation system infrastructure and advanced automatedMHS in the supply chain such as automated conveyor sys-tem Warehouse Management System (WMS) and real-timematerial identification and tracking system (eg barcode)

421 Current Physical Layout and Labor Deployment of theMHS The MHS is a circular shaped automated conveyorsystem which comprises a number of interconnected 5- 10- and 20-meter long straight modular conveyor unitsand 25-meter radius curved conveyor units The layout ofthe MHS is depicted in Figure 7 Each conveyor unit hasa programmable logic controller to control the movement(speed direction acceleration etc) of the items being put onit and to communicate with the central computer Theconveyor system has 4 entrances connecting to 4 inbounddocks and 16 exits connecting 30 outbound docks (eachoutbound dock serves trucks distributing parcels to onedestination) (Figure 6)

At each conveyor entrance 7 workers are deployedto deconsolidate the incoming bulky consolidated parcelsuploaded from the big inbound truck (16 tonnes) for facili-tating the subsequent sortation process To enable the distri-bution process to go well and items to be accurately sortedaccording to customer requirements 4 workers are assignedto each conveyor exit serving 2 destinations (except the 2 exitsclose to the entrances serving 1 destination that requires 2workers) and equipped a barcode reader for confirming thedestination of each small parcel and helping to load the parcelto the small outbound truck (55 tonnes)

422 Operation of the MHS Each step of the operation isperformed sequentially in the simulation process and theoperation is given as follows

(1) When the operation starts each of the incomingbulky consolidated parcels is unloaded by the workersfrom the 4 inbound trucks to the staging area of the 4inbound docks

(2) And then each bulky consolidated parcel is deconsol-idated into multiple small parcels and transported tothe conveyor entrances by the workers

(3) After the parcels arrive at the conveyor they aretransported to the different exits of the conveyorsystem according to their destinations

(4) When the parcels reach the corresponding exits theyare moved to the outbound docks by the workers andready for delivery

423 Assumptions To focus our study on the behavior of theMHS certain real-world factors were simplified Thus thefollowing assumptions were made

(1) Every day the DC handles around 3 to 4 batches ofparcels Since the operation is similar in each batchonly one batch in the simulation model is simulatedand studiedThere are 400 bulky consolidated parcelsin each batch coming from 4 supply sources (eachcontributes 100 bulky parcels) inwhich the processingtime (cycle time) in one batch and the workersrsquoutilization are studied

(2) The time for unloading bulky parcels follows a uni-form distribution

(3) The time for deconsolidation of the bulky parcelsfollows a normal distribution in which each bulkyparcel is separated into 10 small parcels Thereforethere are 4000 small parcels in total being handled bythe MHS

(4) The system only processes two types of parcels(namely bulky consolidated parcels and smallparcels) because they are packed similarly in terms ofvolume and weight

(5) The demand for each destination is similar whichfollows a uniform distribution that is the parcels areuniformly distributed among the 30 destinations

424 Simulation Model The simulation model with specificsystem configuration and behavior is implemented withFlexSim (Figure 7) Details of model components and initialmodel settings (Table 2) are as follows

(i) Entities are the 400 bulky consolidated parcels andthe 4000 small parcels deconsolidated from the bulkyparcels which are processed through the systemcausing changes in the system state over time

(ii) Activities are the deconsolidation of bulky consol-idated parcels unloaded from each incoming truck(represented by a source in the simulationmodel) the

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

10 Journal of Optimization

Figure 5 Outbound docks connecting to the conveyor system

Figure 6 The docks and trucks at the DC

Figure 7 The simulation model of the MHS implemented withFlexSim

picking of small parcels from the circular conveyorto each outgoing truck (represented by a sink in thesimulation model) according to their destinations

(iii) Item attribute is the product type associated with itsdestination (one product type corresponds to onespecific destination)

425 Parameter Setting Several parameters including num-ber of generations initial population size active populationsize maximum clone size and mutation factor are studiedthrough sensitivity analysis so as to examine the individualparametersrsquo impact on the overall performance of the systemand to determine the value for each parameter Givenwith theresults of the sensitivity analysis the parameters of SCMIAwere set as follows

Table 2 Initial model settings

Item ValueConveyor speed 25msec (limit 1ndash25msec)Conveyor spacing 1 parcelNumber of workers deployed foreach conveyor entrance 7 workers (limit 1ndash9 workers)

Number of workers deployed foreach conveyor exit (serving 1destination)

2 workers (limit 1ndash4 workers)

Number of workers deployed foreach conveyor exit (serving 2destinations)

4 workers (limit 1ndash6 workers)

Handling Capacity of Worker 1 parcel

Arrival pattern for each source Uniform distribution with a minof 5 sec and a max of 10 sec

Processing time ofdeconsolidation process

Normal distribution with a meanof 30 sec and a standard

deviation of 2 sec

Demand for each destinationUniform distribution with a minof 220 units and a max of 280

unitsThe above model parameters are set based on the real system settings andobservation

SCMIA Initial population size is 119873 = 30 size of activepopulation 119873119860 = 12 size of the memory population 119873119898 =30 maximum number of clones for each cell max clone =6 exponential distribution coefficient 120588 = 005 number ofsimulation replications per fitness evaluation replication =10

To allow a fair comparison among the algorithms com-pared the parameters of the benchmarking algorithms wereset with similar values and the values suggested by theauthors

MISA Initial population size is 119873 = 30 size of clonepopulation 119873119888 = 180 size of the memory population 119873119898= 30 number of grid subdivisions subd size = 25 initialmutation rate 120596 = 06 (it decreases linearly over time untilreaching the rate of 1m where 119898 is the number of decision

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

Journal of Optimization 11

variables) number of simulation replications per fitnessevaluation replication = 10

NNIA Size of dominant population is119873119901 = 30 size of activepopulation is 119873119860 = 8 size of clone population is 119873119888 = 30crossover probability is 119901119888 = 09 mutation probability is119901119898 = 1m distribution indexes for crossover and mutationoperators are 119899119888 and 119899119898 = 20 (crossover probability 119901119888 =1 mutation probability 119901119898 = 1m) number of simulationreplications per fitness evaluation is replication = 10

NSGA-II Initial population size is 119873 = 30 crossoverprobability is 119901119888 = 09 mutation probability is 119901119898 = 1mdistribution indexes for crossover andmutation operators are119899119888 and 119899119898 = 20 number of simulation replications per fitnessevaluation is replication = 10

SPEA2 Initial population size is 119873 = 30 archive size119873119898 = 30 crossover probability 119901119888 = 1 mutation probability119901119898 = 0006 number of simulation replications per fitnessevaluation replication = 10

Antibody Definition An antibody 119886119887 (a set of decision vari-ables) that has the direct impact on the systemrsquos performancein terms of cycle time (CT) and workersrsquo utilization (WU) isdefined as follows 1199091 is taken to be the conveyor speed 1199092 isthe number of workers deployed for each conveyor entrance1199093 is the number of workers deployed for each conveyor exit(serving 2 destinations) and 1199094 is the number of workersdeployed for each conveyor exit (serving 1 destination) Sincethe objective of the study is to optimize the performance ofthe MHS by minimizing the system cycle time and maximiz-ing the workersrsquo utilization the optimization problem can begiven by

Optimize

119886119887isinΩ

997888rarr119891 (119886119887) = 119864 [CTWU 120596] (13)

subject to

1 le 1199091 le 251 le 1199092 le 91 le 1199093 le 61 le 1199094 le 4

(14)

where a set of objective functions997888rarr119891(119886119887) to be optimized in

objective space are the expected values of the random outputvariables [CTWU 120596] that are obtained from running thesimulation model 120596 is a sample path (ie the sequence ofrandom numbers used in a simulation run) and (14) define aset of physical constraints

426 Experimental Results and Analysis We conducted twoexperiments to evaluate the performance of the SCMIAand the simulation-based optimization framework that is(1) to compare the results of integrating simulation and

Simulation Study

PFrefSCMIAMISA

NNIANSGA-IISPEA2

5500 6000 6500 7000 75005000Cycle Time (Second)

20

30

40

50

60

70

80

Util

izat

ion

()

Figure 8 Graphical comparisons of the known Pareto frontsgenerated by the five algorithms

optimization with the results without using any optimiza-tion algorithm and (2) to benchmark SCMIA against twoimmune-inspired algorithms MISA [20] and NNIA [42]and two other evolutionary algorithms NSGA-II [35] andSPEA2 [37] under the framework The first experimentwas conducted to evaluate the effectiveness of optimizationalgorithms when being employed in the simulation studywhile the second one was used to emphasize the comparisonamong the algorithms under investigation with respect to theoptimality and the diversity using the same simulation-basedoptimization framework All algorithms were run for 30generations over 30 trials to obtain the average performanceof each algorithm on the same condition

(1) Simulation without Optimization versus Simulation withOptimization The results shown in Table 3 are the optimizedresults obtained bymaking use of all optimization algorithmsstudied in this research

The table shows that the cycle time of the whole distri-bution system at the DC is reduced by about 12ndash16 and theworkersrsquo utilization is increased by 38ndash49 when optimiza-tion algorithms are deployed in the simulation process Thisproves that the use of the optimizers can enhance theperformance in the systemrsquos cycle time and the workersrsquoutilization However the higher the utilization achieved thelonger the cycle time spent and vice versa When comparingSCMIA with other benchmark algorithms SCMIA is able toproduce comparable results in both the cycle time andworkersrsquo utilization

(2) Performance Comparison between SCMIA and OtherBenchmark Algorithms The performance of the algorithmsstudied in this study was compared by using the graphicalrepresentation together with the application of the metricsmentioned in Section 41 The comparison between theknown Pareto fronts shown in Figure 8 suggests that theoverall Pareto front patterns generated by the five algorithmsare largely similar inwhich the cycle time ranges from around

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

12 Journal of Optimization

Table 3 Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimizationapproach by using different optimization algorithms (the best results are bolded)

Cycle Time (the improvement in compared with the one without

optimization)

Workersrsquo Utilization (the improvementin compared with the one without

optimization)Simulation without optimization 678864 sec 4504Simulation-based optimization with SCMIA 576386 sec (1510) 6546 (4534)Simulation-based optimization with MISA 575488 sec (1523) 6345 (4087)Simulation-based optimization with NNIA 567287 sec (1644) 6200 (3766)Simulation-based optimization with NSGA-II 568023 sec (1633) 6290 (3965)Simulation-based optimization with SPEA2 594853 sec (1238) 6710 (4876)

Table 4 Spacing and error ratio values generated by the five algorithms (the best results are bolded)

SCMIA MISA NNIA NSGA-II SPEA2Mean

(Standard Deviation)Error Ratio (ER) 071 (010) 085 (016) 078 (018) 076 (014) 074 (006)Spacing (119878) 3874 (1097) 5802 (5582) 4923 (2610) 5185 (1758) 3932 (3716)

Table 5 Computational times of the five algorithms

SCMIA MISA NNIA NSGA-II SPEA2Time (hours) 3375 10419 2446 2454 2375

5300 sec to 7000 sec and the workersrsquo utilization ranges fromaround 50 to 75 FromFigure 8 it is shown that the higherthe utilization achieved the longer the cycle time spent andvice versa This implies that increasing the utilization doesnot mean that the efficiency of the system can be increasedTherefore according to the figure although the optimalsolution with 75 utilization while spending almost 7000 secand another case achieving less than 50 utilization whilespending only around 5300 sec both fall within the referencePareto front PFref the latter case is preferred in practicebecause the cycle time is much shorter and hence theefficiency and productivity of the system are much higherThe utilization becoming lower in the latter case ismainly dueto the increased values in the decision variables namely con-veyor speed andnumber ofworkersThis implies that in orderto further enhance both objectives at the same time for theDC the company may need to do something other thanjust changing the system parameters such as redesigningthe layout of the material handling systems particularly theconveyor system

The performance regarding the optimality and diversityof SCMIA in this multiobjective optimization problem wasthen examined by applying the metrics namely spacing anderror ratio as shown in Table 4

In this experiment we compared the results of themean and standard deviation of the two metrics over 30trials obtained by SCMIA with that of the other benchmark

algorithms From the results shown in Table 4 we found thatSCMIA generally is able to provide the best results in termsof the diversity and optimality because it generates the lowestvalues in the metrics of ER (071) and 119878 (3874) and the lattermetric is significantly lower than most of the other algo-rithms This implies that the generated front is very close tothe PFref In terms of the stability SCMIA is also the bestone among these five algorithms in error ratio and spacingbecause it has much lower standard deviations (010) and(1097) respectively than other algorithms except SPEA2implying that SCMIA is able to provide a relatively consistentresult for each trial

(3) Comparison of Computational Time The computationaltimes of the investigated algorithms are provided in Table 5which are the mean times of 30 trials of each algorithmrunning for 30 generations It can be observed that the com-putational time of MISA is the longest (10419 hours) becauseMISA spends very much time in solution evaluation throughrunning the complex simulation model due to the largestnumber of candidate solutions being generated and evaluatedat each iterationThis is very time-consuming SCMIA comessecond (3375 hours) although the performance in terms ofcomputational time is much better than MISA The reasonis that SCMIA also generates a large number of solutions ateach iteration but the suppression operator adopted in thealgorithm helps reduce the number of similar solutions and

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] S L RosenAutomated Simulation Optimization of Systems withMultiple Performance Measures Through Preference ModelingPennsylvania State University State College Pa USA 2003

[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

Journal of Optimization 13

hence reduce the number of solution evaluations On thecontrary NNIA NSGA-II and SPEA2 consume less andsimilar computational resources largely due to the muchsmaller number of solution evaluations being conducted ateach iteration

5 Conclusion

This study applies a multiobjective simulation-based opti-mization framework incorporating a hybrid immune opti-mization algorithm SCMIA for the evaluation of the opti-mality of the distribution system with respect to two criteriasystem cycle time andworkersrsquo utilization through simulationmodeling Based on the results of the simulation-based opti-mization study the following conclusions and implicationscan be drawn regarding the performance of the frameworkand algorithm

SCMIA generally performs better than other benchmarkalgorithms especially in the diversity aspect This is largelyattributed to the operators employed in the algorithm Forexample the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies forundergoing the subsequent evolutionary processes so that theantibodies in less crowded regions will have a higher priorityto be selected The cloning operator and hypermutationoperator are based on the samemeasure to generate a numberof copies for exploring the solution space and bringingvariation to the clone population respectively where lesscrowded individuals are given more chances for cloning andhypermutation in order to hopefully produce better offspringand increase population diversity The crossover operatorhelps further enhance the diversity of the clone populationand the convergence of the algorithm because some goodgenes from the active parent can be passed to the offspringThe suppression operator helps reduce antibody redundancyby eliminating similar individuals hence significantly mini-mizing the number of unnecessary searches and increasingthe population diversity The memory updating operatortakes account of the antibody similarity in terms of both theobjective space and the decision variable space to formulatethe memory population As a result SCMIA is able togenerate a well-distributed set of solutions while it is a goodapproximation to the reference Pareto front Other than theoptimality and diversity the stability of each algorithm canalso be observed based on the standard deviations of themetrics shown in Table 4 It can be seen that the standarddeviation of spacing obtained by SCMIA is much smallerthan the other four algorithms In a word SCMIA is the moststable one among the five algorithms in terms of populationdiversity in simulation-based optimization

The results overall demonstrate the ability of themultiob-jective simulation-based optimization framework to serve asa decision support tool for helpingmanagement to effectivelyand efficiently find near optimal system operating parameterssuch as the speed of machines the number of workers or anyother decision variables of interest in order to fulfill differentobjectives including systemrsquos cycle time and workersrsquo uni-tization As a result significant savings in money energy

and so forth are achieved through the effective and effi-cient deployment of material handling systems and well-coordinated activities based on the optimized results Theresearch also sheds light into important issues of logisticssystem operation and management based on the case studysuch as manpower allocation and design capacity of facilities

Based on the findings of the current undertaking itis worthwhile to extend the framework to tackle othercomplex problems involving many objectives to be solvedin an efficient and effective manner in the future Futureresearch could also extend this approach to solve other real-world complex business problems other than the problemsassociated with material handling systems so as to establishthe practical value of the framework in the simulation-basedoptimization context

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

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[2] S Kirkpatrick J Gelatt andM P Vecchi ldquoOptimization by sim-ulated annealingrdquo American Association for the Advancement ofScience Science vol 220 no 4598 pp 671ndash680 1983

[3] F Glover ldquoHeuristics for integer programming using surrogateconstraintsrdquo Decision Sciences vol 8 no 1 pp 156ndash166 1977

[4] F Glover ldquoTabu searchmdashpart Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[5] F Glover ldquoTabu searchmdashpart IIrdquo ORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[6] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[7] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[8] J D Knowles and D W Corne ldquoApproximating the non-dominated front using the pareto archived evolution strategyrdquoEvolutionary Computation vol 8 no 2 pp 149ndash172 2000

[9] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[10] J Banks I John S Carson B L Nelson and D M NicolDiscrete-Event System Simulation Prentice Hall 4th edition2010

[11] Operations Management ldquoImportance and scope of materialhandlingrdquo March 2007 httpswwwcitemancom1413-impor-tance-and-scope-of-material-handlinghtml

[12] V B Norman Simulation of Automated Material Handling AndStorage Systems Auerbach Princeton NJ USA 1984

[13] M K Ebbesen M R Hansen and N L Pedersen ldquoDesignoptimization of conveyor systemsrdquo in III European ConferenceonComputationalMechanics C AMotasoares J A CMartinsH C Rodrigues J A C Ambrosio C A B Pina and C MMotasoares Eds pp 721-721 Springer Netherlands 2006

14 Journal of Optimization

[14] S V Sergueyevich M G O Rosales J M Garcıa L A ZQuintana and G R P Lopez ldquoChain conveyor system sim-ulation and optimizationrdquo in Proceedings of the 17th IASTEDInternational Conference on Modelling and Simulation pp 172ndash177 Canada May 2006

[15] M M L Elahi G V Zaruba J Rosenberger and K RajpurohitModeling and Simulation of a General Motors Conveyor SystemUsing a CustomDecision Optimizer University of Texas Arling-ton Va USA 2009

[16] C S K Leung and H Lau ldquoAn optimization framework formodeling and simulation of dynamic systems based on AISrdquo inProceedings of the International Federation of Automatic ControlWorld Congress Italy

[17] K Subulan and M Cakmakci ldquoA feasibility study usingsimulation-based optimization and Taguchi experimentaldesign method for material handling-transfer system in theautomobile industryrdquo The International Journal of AdvancedManufacturing Technology vol 59 no 5-8 pp 433ndash443 2012

[18] K-H Chang A-L Chang and C-Y Kuo ldquoA simulation-basedframework for multi-objective vehicle fleet sizing of automatedmaterial handling systems An empirical studyrdquo Journal ofSimulation vol 8 no 4 pp 271ndash280 2014

[19] J T Lin and C-J Huang ldquoSimulation-based evolution algo-rithm for automated material handling system in a semicon-ductor fabrication plantrdquo in Proceedings of the 4th InternationalAsia Conference on Industrial Engineering and ManagementInnovation IEMI 2013 pp 1035ndash1046 twn July 2013

[20] C A C Coello and N C Cortes ldquoSolving multiobjectiveoptimization problems using an artificial immune systemrdquoGenetic Programming and Evolvable Machines vol 6 no 2 pp163ndash190 2005

[21] F Y Edgeworth ldquoMathematical psychicsrdquoMind vol 6 pp 581ndash583 1881

[22] V ParetoCours drsquoEconomie Politique vol 1 F Rouge LausanneSwitzerland 1896

[23] V ParetoCours drsquoEconomie Politique vol 2 F Rouge LausanneSwitzerland 1897

[24] C M Fonseca and Fleming P J ldquoGenetic algorithms formultiobjective optimization formulation discussion and gen-eralizationrdquo in Proceedings of the 5th International Conferenceon Genetic Algorithms (ICGA rsquo93) pp 416ndash423 1993

[25] Y Hu and T Chen ldquoMulti-objective optimization algorithmbased on clonal selectionrdquo in Proceedings of the Second Interna-tional Conference on Genetic and Evolutionary Computing pp265ndash268 2008

[26] J Gao and JWang ldquoWBMOAIS A novel artificial immune sys-tem for multiobjective optimizationrdquo Computers amp OperationsResearch vol 37 no 1 pp 50ndash61 2010

[27] C A C Coello G B Lamont and D A van VeldhuizenEvolutionary Algorithms for Solving Multi-Objective Problemsvol 5 Springer New York NY USA 2nd edition 2007

[28] D A van Veldhuizen and G B Lamont ldquoOn measuring multi-objective evolutionary algorithm performancerdquo in Proceedingsof the 2000 Congress on Evolutionary Computation pp 204ndash211La Jolla Calif USA July 2000

[29] K Miettinen Nonlinear Multiobjective Optimization KluwerAcademic Publishers Norwell Mass USA 1999

[30] G P Coelho F O De Franca and F J V Zuben ldquoA con-centration-based artificial immune network for combinatorialoptimizationrdquo in Proceedings of the IEEE Congress of Evolution-ary Computation (CEC rsquo11) pp 1242ndash1249 New Orleans LaUSA June 2011

[31] K Deb Multiobjective Optimization Using Evolutionary Algo-rithms John Wiley amp Sons Inc Chichester UK 2001

[32] E Y C Wong H S C Yeung and H Y K Lau ldquoImmunity-based hybrid evolutionary algorithm for multi-objective opti-mization in global container repositioningrdquo Engineering Appli-cations of Artificial Intelligence vol 22 no 6 pp 842ndash854 2009

[33] J D Schaffer ldquoMultiple Objective Optimization with VectorEvaluated Genetic Algorithmsrdquo in Proceedings of the in 1stInternational Conference on Genetic Algorithms pp 93ndash1001985

[34] J Knowles and D Corne ldquoThe pareto archived evolutionstrategy a new baseline algorithm for Pareto multiobjectiveoptimisationrdquo in Proceedings of the Congress on EvolutionaryComputation (CEC rsquo99) vol 1 pp 98ndash105 July 1999

[35] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimization NSGA-IIrdquo in Proceedings of the 6th InternationalConference on Parallel Problem Solving from Nature pp 849ndash858 2000

[36] D W Corne J D Knowles and M J Oates ldquoThe Pareto-envelope based selection algorithm formultiobjective optimiza-tionrdquo in Parallel Problem Solving fromNature PPSN VI vol 1917of Lecture Notes in Computer Science pp 869ndash878 SpringerNew York NY USA 2000

[37] E Zitzler M Laumanns and L Thiele ldquoSPEA2 Improvingthe Strength Pareto Evolutionary Algorithmrdquo in ComputerEngineering and Communication Networks Lab (TIK) SwissFederal Institute of Technology (ETH) Zurich Switzerland2001

[38] D W Corne N R Jerram J Knowles and M J OatesldquoPESA-II Regionbased selection in evolutionarymultiobjectiveoptimizationrdquo in Proceeding of the Genetic and EvolutionaryComputation Conference pp 283ndash290 San Francisco CalifUSA 2001

[39] C A Coello Coello and G T Pulido ldquoA micro-genetic algo-rithm for multiobjective optimizationrdquo in Evolutionary multi-criterion optimization (Zurich 2001) vol 1993 of Lecture Notesin Comput Sci pp 126ndash140 Springer Berlin 2001

[40] G Toscano Pulido and A Coello Coello ldquoThe micro geneticalgorithm 2 towards online adaptation in evolutionary multi-objective optimizationrdquo in Proceedings of Evolutionary Multi-Criterion Optimization Second International Conference EMO2003 Faro Portugal April 8ndash11 2003 C Fonseca P FlemingE Zitzler L Thiele and K Deb Eds vol 2632 pp 252ndash266Springer Berlin Germany 2003

[41] G P Coelho and F J Von Zuben omni-aiNet An Immune-Inspired Approach for Omni Optimization 2006

[42] M Gong L Jiao H Du and L Bo ldquoMultiobjective immunealgorithm with nondominated neighbor-based selectionrdquo Evo-lutionary Computation vol 16 no 2 pp 225ndash255 2008

[43] Z Zhang ldquoArtificial immune optimization system solvingconstrained omni-optimizationrdquo Evolutionary Intelligence vol4 no 4 pp 203ndash218 2011

[44] T Niknam R Azizipanah-Abarghooee and M Rasoul Nari-mani ldquoA new multi objective optimization approach based onTLBO for location of automatic voltage regulators in distribu-tion systemsrdquo Engineering Applications of Artificial Intelligencevol 25 no 8 pp 1577ndash1588 2012

[45] C S Leung and H Y Lau ldquoA Hybrid Multi-objective ImmuneAlgorithm for Numerical Optimizationrdquo in Proceedings of the

Journal of Optimization 15

8th International Conference on Evolutionary ComputationThe-ory and Applications pp 105ndash114 Porto Portugal November2016

[46] Flexsim Software Products Inc httpswwwflexsimcom 2017[47] N K Jerne ldquoTowards a network theory of the immune systemrdquo

Annales DrsquoImmunologie vol 125 no C pp 373ndash389 1974[48] D A Van Veldhuizen Multiobjective Evolutionary Algorithms

Classifications Analyses And New Innovations Air Force Insti-tute of Technology Wright-Patterson Air Force Base OhioUSA 1999

[49] J Schott Fault Tolerant Design Using Single and MulticriteriaGenetic Algorithm Optimization Massachusetts Institute ofTechnology Cambridge Mass USA 1995

[50] SF Express (Hong Kong) Limited httpwwwsf-expresscomhktc 2018

Journal of Optimization 15

8th International Conference on Evolutionary ComputationThe-ory and Applications pp 105ndash114 Porto Portugal November2016

[46] Flexsim Software Products Inc httpswwwflexsimcom 2017[47] N K Jerne ldquoTowards a network theory of the immune systemrdquo

Annales DrsquoImmunologie vol 125 no C pp 373ndash389 1974[48] D A Van Veldhuizen Multiobjective Evolutionary Algorithms

Classifications Analyses And New Innovations Air Force Insti-tute of Technology Wright-Patterson Air Force Base OhioUSA 1999

[49] J Schott Fault Tolerant Design Using Single and MulticriteriaGenetic Algorithm Optimization Massachusetts Institute ofTechnology Cambridge Mass USA 1995

[50] SF Express (Hong Kong) Limited httpwwwsf-expresscomhktc 2018

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