Research Article Multiobjective Dynamic Vehicle...

Research ArticleMultiobjective Dynamic Vehicle Routing Problem and TimeSeed Based Solution Using Particle Swarm Optimization

Omprakash Kaiwartya1 Sushil Kumar1 D K Lobiyal1 Pawan Kumar Tiwari1

Abdul Hanan Abdullah2 and Ahmed Nazar Hassan2

1School of Computer and Systems Sciences Jawaharlal Nehru University New Delhi 110067 India2Faculty of Computing Universiti Teknologi Malaysia (UTM) 81310 Skudai Johor Malaysia

Correspondence should be addressed to Omprakash Kaiwartya omokopgmailcom

Received 22 August 2014 Accepted 15 December 2014

Academic Editor Tao Zhu

Copyright copy 2015 Omprakash Kaiwartya et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A multiobjective dynamic vehicle routing problem (M-DVRP) has been identified and a time seed based solution using particleswarm optimization (TS-PSO) for M-DVRP has been proposed M-DVRP considers five objectives namely geographical rankingof the request customer ranking service time expected reachability time and satisfaction level of the customersThemultiobjectivefunction ofM-DVRPhas four components namely number of vehicles expected reachability time and profit and satisfaction levelThree constraints of the objective function are vehicle capacity and reachability In TS-PSO first of all the problem is partitionedinto smaller size DVRPs Secondly the time horizon of each smaller size DVRP is divided into time seeds and the problem issolved in each time seed using particle swarm optimization The proposed solution has been simulated in ns-2 considering realroad network of New Delhi India and results are compared with those obtained from genetic algorithm (GA) simulations Thecomparison confirms that TS-PSO optimizes the multiobjective function of the identified problem better than what is offered byGA solution

1 Introduction

Recently intelligent transport system (ITS) has diversifiedthe application area of dynamic vehicle routing problem(DVRP) enormously E-commerce print media medicalpublic transportation andoil sector are only few examples [1]DVRP is an extension of traditional vehicle routing problem(VRP) in terms of complexity The traditional VRP can besymbolically stated on a connected network 119873

119888

(119873119904 119862119904 119862119898)

where 119873119904= 1198990 1198991 1198992 1198993 119899

119899 indicates the set of nodes

119862119904= (119899

119894 119899119895) 119899119894 119899119895

isin 119873119904and 119894 = 119895 represents the set of

connections and 119862119898

= 119862119898(119894 119895)(119899119894 119899119895)isin119862119904

denotes communi-cation cost matrix defined over 119862

119904 Traditionally the node

1198990is the central depot from where all the vehicles start

and end their services The remaining nodes of 119873119904denote

the customers spread over geographically distinct locationsThe VRP is nothing but finding a set of routes for a givenset of vehicles such that each vehicle visits the customersexactly once and overall travel cost of the vehicles should

be minimum [2] An example of traditional VRP has beenillustrated in Figure 1 The central depot has four deliveryvehicles to serve the demands of four customers According tothe availability of routes the journey for delivery vehicles hasbeen planned by the central depot Due to the rapid techno-logical advancements in real time wireless communicationthe shape of VRP has been transformed into DVRP (cfFigure 2) In the past a number of variants of traditional VRPas DVRP have been suggested by incorporating different setof constraints [3] Some variants of VRP have been illustratedin Table 1

An example of DVRP has been illustrated in Figure 2Due to real time communication among central depotnew customers and delivery vehicles the VRP depicted inFigure 1 has been transformed into DVRP shown in Figure 2The planned route of all the four delivery vehicles depictedin the VRP (cf Figure 1) has been changed dynamicallydue to real time communication of dynamic request Theoptimal solution of the above mentioned variants of VRP as

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 189832 14 pageshttpdxdoiorg1011552015189832

2 Journal of Sensors

Table 1 The most common variants of VRP

Serial number Problem Problem description Features Ref

1 VRP-PD VRP with pickup anddelivery

It is transportation problem for a given set of goods from some pickup locations tothe delivery locations No central depot for the delivery vehicles is required [37]

2 C-VRP Capacitated VRP It is a simple VRP with vehicles having prespecified and same goods carryingcapacity [38]

3 H-VRP Heterogeneous VRP It is slightly different from C-VRP Here the vehicles have prespecified but differentgoods carrying capacity [39]

4 VRP-LIFO VRP with last-in-firstout

In this VRP the items that have been picked up most recently must be the items thatneed to be delivered in the next locations [40]

5 VRP-TW VRP with timewindow

It is a VRP with delivery time interval for each customer The delivery vehicles canvisit the customers in the given time interval [41]

6 O-VRP Open VRP In this VRP the delivery vehicles are not required to report back to the centraldepot after visiting all the assigned customers [42]

7 DAF-VRP Dial-A-flight VRP It is a VRP in public transport through airline [43]8 DAR-VRP Dial-A-ride VRP It is an on-road general public transport problem [44]

9 VRP-MT VRP with multipletrips

In this VRP the delivery vehicles take more than one tour once it finishes theassigned tour [45]

DVRPs with large number of customers and their demandparameters could not be obtained within reasonable time dueto NP-hard nature of the problems [4] In the last ten yearsvarious nature inspired metaheuristic techniques have beenapplied to solve the customized instances of various DVRPsGenetic algorithm (GA) ant colony optimization (ACO) andparticle swarm optimization (PCO) have been commonlyused for solving the above listed DVRPs [5ndash7] Nowadaysthese techniques have also been gaining popularity in vehic-ular ad hoc networks (VANETs) [8] and high performancecomputing [9]

In this paper a multiobjective dynamic vehicle routingproblem (M-DVRP) has been identified A time seed basedsolution using particle swarm optimization (TS-PSO) for M-DVRP has been proposed The five objectives considered inthe proposed problem are geographical ranking of requestscustomer ranking service time expected reachability timeand satisfaction level of customers Each of these objectiveshas been materialized in terms of both conceptual andmathematical formulation A multiobjective function hasbeen generated having four components namely vehiclecountnumber of vehicles expected reachability time profitand satisfaction level The mathematical formulations havebeen derived for each of the component objectives using themetric of the problemThree constraints of themultiobjectivefunction namely vehicle capacity and reachability have beendefined The proposed solution TS-PSO broadly operatesinto two steps In the first step the identified problem ispartitioned into smaller size DVRPs In the second step timehorizon of each smaller sizeDVRPhas been divided into timeseeds and the problem has been solved in each time seedusing particle swarm optimization A complete algorithm hasalso been developed for the proposed solution techniqueThenetwork simulator ns-234 has been used for the simulationalong with two other supporting software programs MOVEand ArcGIS The fifteen data sets OPK-01 to OPK-15 used inthe simulation have been generated considering real vehicu-lar environment and highly dynamic customer requirements

The simulation results have been compared with the geneticalgorithm (GA) solution technique

The rest of the paper is organized as follows Section 2presents some early and recent developments in dynamicvehicle routing problem In Section 3 details of the identifiedproblemM-DVRP are described In Section 4 the TS-PSO isproposed anddescribedThe analytical and simulation resultsare presented in Section 5 Conclusion is derived in Section 6

2 Early and Recent Developmentsin VRP and DVRP

The VRP was first proposed by Dantzig and Ramser in1959 The authors optimized the routing of a fleet of gaso-line delivery trucks between a bulk terminal and a largenumber of service stations supplied by the terminal Theyhave used linear programing formulation for obtaining nearoptimal solution [10] After the induction VRP has beenone of the challenging areas of research that has witnessedconsistent attention of the researchers from both industriesand academia The research contribution can be categorizedinto two dimensions probabilistic optimization and staticoptimization In probabilistic optimization the componentsof the problem such as demand number of customers andservice time have been considered as future events andprobabilistic models have been used to predict the futurebehavior of these components [11 12] In static optimizationsavailable information about the components has been consid-ered without including future behavior of the componentsSome of the most recent works in DVRP have been describedbelow Multiobjective dynamic vehicle routing problem withfuzzy travel times and customersrsquo satisfaction in supply chainmanagement has been suggested in [13] The authors haveinvestigated fuzzy time window and fuzzy travel time indepth for the VRP The travel distance number of vehiclesand waiting time of vehicles have been minimized andthe satisfaction rate of customers has also been minimized

Journal of Sensors 3

Delivery vehicles

Customers

Central depot

Planned route

Figure 1 The traditional VRP

Real time communication betweencustomer and central depot

Real time communication betweencentral depot and delivery vehicles

Delivery vehicles

CustomersCentral depot

Change in planned route

Figure 2 Conversion of VRP into DVRP


A set based discrete particle swarm optimization approachfor optimizing vehicle routing problem (S-PSO-VRPTW)with time window has been suggested in [14] The solutionapproach selects an optimal subset from the universal setand subsequently solves the selected subset problem Theauthors have derived new mathematical formulations forvelocity and position update to realize discrete PSO A fitnessfunction for candidate solution evaluation has also beenformulated The line haul feeder vehicle routing problemwith virtual depots has been presented in [15] Feeder vehicleand virtual depot concepts have been introduced by theauthors Travel distance and waiting time for vehicles havebeen minimized using heuristic cost sharing methods Apatrol routing algorithm has been constructed in [16] forpolice ambulance and taxi services The algorithm has beenexplored in terms of expression execution evaluation andengagement A domain specific language (DSL) turn has beenused to express the algorithm PatrolSim a custom simulatorhas been used for the execution of the algorithm Responsetime network coverage and hotspot coverage metrics havebeen used for the evaluation of the algorithm For a webbased geographic information system (GIS) portal CAPSMap has been used for end user engagement of the algorithmMultidepot capacitated arc routing problem (MCARP) hasbeen introduced in [17] An evolutionary approach hasbeen constructed by integrating some classical heuristicsinto a canonical evolutionary framework The near optimumMCARP solution has been used to learn two distinct kindsof heuristic information The evolutionary process has beenguided by this heuristic information An arc guided evolu-tionary algorithm for solving vehicle routing problem withtime window has been developed in [18] In the populationindividuals have been represented using arcs so that evolutionstrategy can be adapted to the VRP-TW The ruin andrecreate principle have been used for mutation process Atrajectory local search algorithm has been developed tominimize distance A route elimination procedure has beenalso suggested Moreover VRP has always been in the fullattention of researchers

3 Multiple-Objective Dynamic VehicleRouting Problem (M-DVRP)

In this section a different aspect of DVRP is identified byincorporating five objectives namely geographical rankingof requests customer ranking service time expected reach-ability time and satisfaction level of customers The M-DVRP can be symbolically stated on a connected network119873119888

(119873119904 119862119904 119862119898 119862119898V) where 119873

119904= 1198990 1198991 1198992 1198993 119899

119899 indi-

cates the set of nodes 119862119904

= (119899119894 119899119895) 119899119894 119899119895

isin 119873119904and 119894 =

119895 represents the set of connections 119862119898

= 119862119898(119894 119895)(119899119894 119899119895)isin119862119904

denotes communication cost matrix defined over 119862119904and

matrix vector 119862119898V = (119862

1 1198622 1198623 1198624 1198625) is group of five

objectives attached with each requestThe DVRP in this con-sideration is nothing but finding a set of routes for a given setof vehicles such that it optimizes both119862

119898and119862

119898V In some ofthe earlier DVRP strict time window has been considered forservice time of the customers Consequently the customers

QI PLDT PUDT STIL STIU ECPUT

QI quantity of itemPLDT preferred lower limit for delivery timePUDT preferred upper limit for delivery timeSTIL satisfactory time interval for PLDTSTIU satisfactory time interval for PUDTECPUI extra cost on per unit item paid by the customer

Figure 3 Customer request vector

GR CR ST ERT SL PF

GR geographical ranking of the requestCR customer rankingST service time of the requestERT expected reachability time SL satisfaction level of the requestPF profit from the request

Figure 4 Order vector for each of the customer requests

provide their satisfaction values in binary digit that is 0 or1 for each request In other words the customer either isfully satisfied or rejects the requested order in its totality [19]But the binary digit satisfaction value consideration does notcomply with real scenario Inspired by the importance andcontinuous research in fuzzy set theory [20] the considera-tion of fuzzy time window is gaining momentum in VRP forcomplying with real customer scenario [21] For developinga mathematical model for M-DVRP a flexible time windowis considered in which customers are ready to accept thedelivery in relaxed time window The other two importantconsiderations of the problem are request vector and ordervector As soon as a customer enters in the system heshesends request information to the central depot via VANETscommunication [22ndash29] Each customer request is a vectorof length six as illustrated in Figure 3 Once a request vectorreaches the central depot system an order vector is generatedcorresponding to the request vector The order vector oflength six considered in the problem is shown in Figure 4The other considerations of M-DVRP are briefly described infollowing subsections

31 Geographical Ranking In M-DVRP the geographicalranking of a request not only is dependent on distance ofthe customer from the central depot but also is an implicitcomplex function of four variables namely average densityof request (ADR) distance (DIST) safety and reliability(SR) and road networks (RN) Thus a vector of length fouris associated with each request by central depot reflecting


ADR average density of requestDIST distance of the customer location

RN road network availabilitySR safety and reliability

Component weights

ADR

05

DIST

02

RN

01

SR

02

Figure 5 Geographical ranking of the request with weighingparameters

Customer

VIC

IC

RC

CC

1

0

075

05

GSL

VIC very important customerIC important customerRC regular customerCC casual customerGSL guaranteed satisfaction level

Rank =

4

Rank = 3

Rank = 2

Rank =1

Figure 6 Customer categorization ranking and guaranteed satis-faction level range

geographical ranking The components of the geographicalranking vector and corresponding weighting parametershave been shown in Figure 5 Considering 120572

119894as weighting

parameter and length of the vector |VGR| the constraintsum|VGR|119894=1

120572119894

= 1 always holds The geographical ranking of arequest can be calculated as

119866119903=

sum4

119894=1120572119894119903119894

1003816100381610038161003816VGR1003816100381610038161003816 minus 1

(1)

where 119903119894denotes the ranks and thus a request has been

geographically ranked between 0 and 1

32 Customer Ranking In M-DVRP the customers arecategorized into four categories namely very importantcustomer (VIC) important customer (IC) regular customer(RC) and casual customer (CC) A minimum guaranteedsatisfactory level in the range [0 1] is defined for each ofthese categories of customers (cf Figure 6) Based on theminimum guaranteed satisfaction level service time windowof the customers is also defined The VIC has strict servicetime window due to highest satisfactory level that is 1 Theminimum satisfactory level for IC is defined in the range[075 1) Although the IC also has smaller service timewindow but the system provides services in the maximum

possible relaxable timewindow Considering long run impor-tance of RC the minimum satisfactory level is defined in therange [05 075) for RCThe best possible service is providedin the flexible service time window The lowest satisfactorylevel range [0 05) is defined for the CC considering theirrandom entry and incredible request vector Based on theirdoubtable credibility the delivery of requests is processed onthe way during servicing the other category of customers

33 Service Time In M-DVRP once the order of itemsreaches customerrsquos place the time spent on delivering theitems to the customers is known as service time (ST) ofa request The service time is defined by considering thequantity and type of items of the request It is determined bythe central depot on receipt of a request from the customersin real time fashion The service time can be calculated as

ST =

119873item

sum

119894=1

119902119894119868119894

119878119903

119894

(2)

where119873item denotes number of items 119902119894is the quantity of 119894th

item 119868119894is the type of 119894th item and 119878

119903

119894is the service rate of 119894th

item

34 Expected Reachability Time In M-DVRP the averagetime required to reach a delivery vehicle from the centraldepot to the assigned customers is defined as expectedreachability time (ERT) It depends on current geographicalposition of vehicle GPVcurr the geographical position ofcustomer GP119888 average speed of vehicle 119904

Vavg and weightage

of geographical ranking GRwt It can be calculated as

ERT =

1003816100381610038161003816GPVcurr minus GP1198881003816100381610038161003816119904VavgGRwt

(3)

35 Satisfaction Level of Customers The delivery of serviceup to the customerrsquos expectation is the notion of satisfactionlevel (SL) for a particular request It is defined as a functionwith domain ERT and range [0 1] It is expressed as

SL (ERT)

=

0 (ERT lt PLDT minus STIL) or(ERT gt PUDT + STIU)

1 PLDT ≪ ERT ≪ PUDTERT minus (PLDT minus STIL)

STIL (PLDT minus STIL) lt ERT

lt PLDT(PUDT + STIU) minus ERT

STIL PUDT lt ERT

lt (PUDT + STIU)

(4)

After defining all the considered objective of the identifiedproblem the formulation of multiobjective function andcorresponding constraints is briefly described below Thereare four components in the multiobjective function namely


Rout of vehicle 1 Rout of vehicle 2 Rout of vehicle 3 Rout of vehicle 4 Open rout

minus1 minus1 minus1 minus1

Figure 7 Initial structure of a particle

number of vehicles or vehicle count119873V expected reachabilitytime profit PF and satisfaction level The three constraintsof the multiobjective function are vehicle capacity andreachabilityThe vehicle constraint states that only one vehiclecan be assigned to a customer for a request The capacityconstraint states that each vehicle has prespecified capacityand this capacity could not be exceeded to deliver therequest of customers The reachability constraint states thatthe difference of ERT between two successive customersmust be greater than or equal to the sum of service timeof the previous customer and the travel time between thecustomers For the multiobjective function its componentsand constraints are expressed below

Max (119891minus11

119891minus1

21198913 1198914) (5)

where

1198911= 119873V

1198912=

119873V

sum

119894=1

119873119888

sum

119895=1

119873119888

sum

119896=1

ERT119895119896120594119894

119895119896

1198913=

119873119888

sum

119895=1

PF119895

1198914=

119873119888

sum

119897=1

SL (ERT119897) sdot CPFwt

119897

120594119894

119895119896=

1 119894th vehicle goes from 119895thcustomer to 119896th customer

0 otherwise

CPFwt119897

=GR119897+ CR119897

Max GR119894119895+ CR119894119895 119894 = 1 2 3 119895 = 1 2 3 4

st119873V

sum

119894=1

119873119888

sum

119895

120594119894

119895119896= 1 119896 = 1 2 3 119873

119888

119873119888

sum

119895

119873119888

sum

119896

120594119894

119895119896sdot 119889119888

119896≪ 119888ℎ 119894 = 1 2 3 119873V

120594119894

119895119896(ERT119894119895+ 119905119895119896

+ ST119903) ≪ 120594

119894

119895119896sdot ERT119894119895

119903 = 1 2 3 119873119888 119894 = 1 2 3 119873V

(6)

where 119873V denotes the number of vehicles and 119873119888represents

the number of customers The 120594119894

119895119896is the characteristic

function and CPFwt119897

is the weight of preference of customer

For solving the above identified problem time seed basedsolution using particle swarm optimization has been pro-posed and described in the next section

4 TS-PSO for M-DVRP

The traditional particle swarm optimization (PSO) [30] hasbeen generally used in solving optimization problem incontinuous search space But a novel method set basedparticle swarm optimization (S-PSO) [31] has been suggestedfor solving combinatorial optimization problems in discretesearch space TS-PSO is inspired from the S-PSO In TS-PSOthe identified problem M-DVRP is partitioned into num-ber of smaller size DVRPs considering solution feasibilityThereafter the time horizon of each smaller size DVRP isdivided into a number of smaller time seeds The durationof time seeds in a particular DVRP depends on the degree ofdynamism Higher degree of dynamism in a DVRP requiressmaller time seeds as compared to a DVRP with lower degreeof dynamism A solution for a smaller size DVRP is generatedfor each of the time seeds The solutions of all the smallersize DVRPs are combined that represents the solution ofthe identified M-DVRP The partitioning of the problem anddivision of time seeds is more specifically presented below

119873119888

= Connectioned Component of

smaller DVRPs 119873119888

119896 119896 = 1 2 3 119899

and time horizon of 119896th smaller

size DVRP 119879119867

119896=

119873TS

sum

119894=1

119879119904

119894119896

(7)

In TS-PSO the search space is considered as set of allknown and dynamically appearing connections 119862

119904 in the

given time seed of a particular partition of the problemA particle in the search space also known as candidatesolution is an ordered vector of connected connections from119862119904with vehicle information Initially we generate particles

of some predefined length whose size can increasedecreasein successive time seeds to incorporate dynamic request ofcustomers in efficient manner The pictorial representationof initial structured of the vector which has been foundvery useful in the construction of particles is described inFigure 7 Initially the vector has been filled up with fixednumber of minus1rsquos randomly The vector has been kept opentowards the right-end to indicate that it can grow in sizein the successive time seeds The total number of minus1 inthe vector represents the number of vehicles used in thesolution The ordinal numbering of customers in a solutionvector or particle is based on initial order vectors calculated


3 14 6 4 8 9 2 5 11 13 10 7 1 12


minus1minus1minus1minus1

Figure 8 An instance of a particle in a time seed of a smaller size DVRP

by central depot for each customer request vector acceptedfor a particular times seed in a smaller size DVRP InFigure 8 a particle with 14 customers and 4 vehicles hasbeen depicted A vehicle is visiting the customers 3 14 and6 in order and returning to the depot represented by minus1Another vehicle is visiting 4 8 9 and 2 in order and returningto the depot Similarly the routes for other vehicle toursare shown In successive iterations particles are enhancedby incorporating new information from customers vehiclesand order vectors Due to these enhancements the ordinalnumbering of customers number of customers handled by aparticular vehicle and number of vehicles in a particle maychange

The mathematical formulation of the proposed solutionin terms of particle swarm optimization is given below Theformulas used for updating position and velocity of particlesin the traditional particle swarm optimization have beenexpressed as

1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)

where120596 denotes inertia weight 1205721and 1205722are the acceleration

coefficients that define the rate of impact of 119871best and 119866bestrespectively and 119903

119899

1and 119903

119899

2represent two random numbers

in the range [0 1] In TS-PSO the above two mathematicalformulations have been used for updating position andvelocity of the particles But each component operation of thetwo operations defined in (8) and (9) has been redefined inthe framework of TS-PSO in the next subsections

41 Position Representation of a Particle In TS-PSO positionof a particle is a vector of ordered connections along withvehicle information Actually an instance of a particle repre-sents the position of the particle (cf Figure 8) The positionvector of a particle is represented as

119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4

V2sdot sdot sdot V31198625049

1198991198625247

119899+1 ]

(10)

where 119862119897119898119894

is the 119894th connection between the customers 119897 and119898 and V

119895is the 119895th vehicle used by the group of following

customers

42 Velocity Representation of a Particle In TS-PSO thevelocity of a particle is a vector of connections associatedwith three inclusion probabilities Each connection of thevector is associated with three inclusion probabilities 119875ERT

119875PF and 119875SL 119875ERT isin [0 1] is the insertion probability of aconnection into solution giving importance to the expectedreachability time Similarly 119875PF isin [0 1] and 119875SL isin [0 1] areinsertion probability considering profit and satisfaction levelThe velocity vector of a particle is expressed as

119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)

43 Velocity Updating of a Particle As mentioned abovein TS-PSO the velocity of a particle is updated using thetraditional velocity updating equation (8) But the componentoperation is redefined in the framework of TS-PSO Thecomponent operation 120596 times 119881

119894changes the three probabilities

attached to the connections of 119881119894 The component operation

(119871bestminus119883119894) or (119866bestminus119883

119894) represents connection set reduction

operation and multiplication of coefficient into position thatis 1205721times119903119899

1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883

119894) associates the three

probabilities to each connection of the position Each of theseoperations has been more clearly defined below

120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840

ERT = 1 if (120596 times 119875ERT) gt 1

120596 times 119875ERT otherwise

1198751015840

PF = 1 if (120596 times 119875PF) gt 1

120596 times 119875PF otherwise

1198751015840

SL = 1 if (120596 times 119875SL) gt 1

120596 times 119875SL otherwise

119883119894minus 119883119895= [119862119897119898

119909V119905| forallV119905isin 119883119894 V119905isin 119883119895 119862119897119898

119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)


44 Position Updating of a Particle The position of a particleis updated using the traditional position updating equation(9) But the addition operation of the equation has been rede-fined in the framework of TS-PSO The addition operationreconfigures all connections of the position 119883

119894to generate

a new position 1198831015840

119894 The reconfigured connection of 119883

1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840

119894and satisfies 120588

119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)

where 120588119894denotes the constraint set and 119863

119888

119894is the dynamic

connection set for the 119894th time seed A complete algorithmfor the proposed solution approach TS-PSO is presented inAlgorithm 1

5 Simulation and Analysis of Results

In this section extensive simulations have been performed toanalyze the optimization accuracy of the proposed solutionTS-PSO in solving the identified problemM-DVRPThe fourobjectives considered for optimization accuracy assessmentare vehicle count expected reachability time profit andsatisfaction level The simulation results have been comparedwith that of genetic algorithm (GA) based solution

51 Simulation Environment andMethodology Network sim-ulator ns-234 has been used in the simulation of TS-PSOalgorithm The realistic mobility model and realistic urbantraffic environment have been generated using mobilitymodel generator for vehicular networks (MOVE) [32] Anopen-source micro-traffic simulator known as simulation ofurban mobility (SUMO) has been used to develop MOVE[33] Most of the necessary scenario of urban traffic envi-ronment such as roads lanes in each road number of flowsin each lane junctions traffic lights in a particular junctionvehicle speed left or right turning probability of a vehicle ata particular point and static nodes as customers has been setup through two main modules of MOVE namely road mapeditor and vehiclemovement editorThemobility trace gener-ated byMOVEwith the help of SUMOhas been directly usedin ns-2The performance of TS-PSOhas been tested using thefifteen data sets namely OPK-01OPK-02 OPK-15 gen-erated by considering realistic vehicular traffic environmentand highly dynamic customer requirements These datasetshave been generated using real traffic data of CaliforniaVehicle Activity Database (CalVAD) [34] and US Depart-ment of Transportation [35] which can be downloaded fromthe website ldquoWireless Communication Research Labrdquo [36]The reason behind generating the data sets is that a lot ofdynamic features such as geographical ranking customerranking expected reachability time satisfaction level anddynamic traffic hazards have been considered in the proposedsolution TS-PSO that could not be tested with the existing

Table 2 Simulation parameters

Parameters ValuesSimulation area 1500 times 1000m2

Simulation time 1380 sNumber of vehicles 28ndash115Vehicle speed 14ndash167msTransmission range 250mPacket senders 30

Traffic type CBRPacket size 512 bytesPacket type UDPIfqlen 50

CBR rate 6 packetssChannel type WirelessPropagation model ShadowingAntenna model OmnidirectionalMAC protocol IEEE 80211pMAC data rate 5MbpsQuery period 3 sHello time-out 1 sFrequency 59GHzRouting protocols P-GEDIR

VRP or modified-VRP data sets To realize the twenty-three hoursrsquo time horizon between 6 AM and 5 AM inthe next morning in the simulation twenty- three-minutetime horizon has been considered in the closed interval[0 1380] secondsThe other important simulation parameteris summarized in Table 2 After setting the network and trafficflow with the above discussed parameters the simulation hasbeen performed using the different data sets The completesimulation process has been summarized in Figure 9 Thesatellite image of New Delhi India (cf Figure 10) has beenobtained via Google Earth and it is imported in ArcGIS1022 for the coordinate assignmentsThe data set containingcustomer vehicle route and connection information hasbeen given input to MOVE that generates New Delhi Mapwith network information Thereafter configuration andtrace file have been generated and ultimately vehicular trafficflow in the New Delhi Map has been produced TS-PSOhas been implemented in ns-2 using the trace file generatedthrough MOVE

52 Result Analysis In this analysis we have consideredwhether the Pareto based solution generated by the proposedalgorithm TS-PSO covers the solution achieved by GAconsidering only one objective function while keeping othersas constantThe comparison results between TS-PSO andGAhave been depicted in Table 3

The results depicted in Table 2 show that the solution pro-vided by the proposed algorithm is found to be competitiveenough as compared to the solution provided by the geneticalgorithm It is also noteworthy that our algorithm considersall the objective functions of M-DVRP model concurrently


Table 3 Simulation results

Data set Functions TS-PSO Randomized solution119873

GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721

Data set1 Customer information via MOVE as nodxml2 Vehicle information via MOVE as nodxml3 Route information via MOVE as edgxml4 Connection information via Dreamweaver CS6 as conxml

Satellite image of New Delhi India viaGoogle Earth

2D coordinates of the satellite image viaArcGIS

New Delhi Map viaNETCONVERT as netxml

Configure via MOVEas cfgxml

Trace file via MOVEas sumotr

Vehicular traffic flow via traffic model generatorof MOVE as tcl

NS-2simulation

Figure 9 Work flow diagram of the simulation process

Figure 10The satellite image of NewDelhi India via Google Earth

whereas single objective has been considered in genetic algo-rithms Additionally in GA solution by increasing numberof vehicles two times 119873

GAV = lceil2119873

TS-PSOV rceil as compared to

TS-PSO the solutions provided by GA come close to theproposed solution in terms of SL but the profit earned bythe TS-PSO is far better than what is offered by GA solutionTo closely analyze the performance of TS-PSO in optimizingthe functions 119891minus1

2 1198913 and 119891

4 the following results have been

obtainedThe results in Figure 11(a) show the comparison of opti-

mization of function 119891minus1

2 that is ERT between TS-PSO and

GA solutions It can be clearly observed that the proposedsolution optimizes the function far better than that of thecomparedGA solutions considering equal vehicle countThiscan be attributed to the fact that the geographical rankingof requests in the proposed solution results in better ERTThe optimization accuracy of GA in terms of ERT improveswith increasing vehicle count in the solution as 119873119877V = 119873

SDPV

119873119877

V = lceil15119873SDPV rceil 119873119877V = lceil18119873

SDPV rceil and 119873

119877

V = lceil2119873SDPV rceil due

to easy availability of vehicles for individual customersThusTS-PSO uses lesser number of vehicles while reducing ERTas compared to GA solutions The results of comparison ofoptimization accuracy for function119891

3 that is PF betweenTS-

PSO and GA solutions have been depicted in Figure 11(b) Itclearly reveals that the TS-PSO more effectively maximizesthe PF as compared to GA solutions This is due to theeffective customer ranking in the proposed solution It isalso noteworthy that increasing the vehicle count beyond aparticular optimized point deteriorates the PF earned by thesolutionThe optimization accuracy of 119891

4 that is SL between

the proposed solution and GA has been compared in theresults shown in Figure 11(c) The results confirm that themaximization of SL by the proposed solution is significantlyhigher than the compared GA solutions This is due to theconsideration of CPFwt

119897in the proposed solution Moreover

the maximization of SL increases with increasing vehiclecount for both the solution approaches But the difference inmaximization of SL between the proposed solution and GAis clearly visible in the results


Notations119873119888 Connected network graph119873

119907 Number of vehicles119873sr Number of static request ST Service time

CRV Customer Request Vector OV Order vector GR Geographical Ranking CRK Customer ranking vector119873119888

119894 Number of customers in 119894th partition of network119873119894dr Number of dynamic request in 119894th partition of network

119883119892best

(119866) Global best position of 119866th generation119883119897best119894

(119866) Local best position of 119894th particle in 119866th generation119879119867

119896 Time horizon for 119896th sub-networks 119879119878

119894119896 119894th time seed of the 119896th sub-network ERT Expected reachability time

119883120572 Threshold solution used for stopping criteria Input- 119873

119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)

Process-(1) Initialize a connected network119873

119888

(119873119904 119862119904 119862119898 119862119907)

(2) for 119894 = 1 to119873sr Generating CRV(4) generate CRV (119876 PLDT PUDT STIL STIU ECPUT) randomly(5) endfor(6) for 119894 = 1 to119873sr Generating OV(7) generate GR vector (ADR Dist RN SR) randomly and calculate Gr using (1)(8) generate CRK vector (VIC IC RC CC) randomly and assign weight according to ranks(9) calculate ST using (2)(10) calculate ERT using (3)(11) endfor(12) Partition 119873

119888

(119873119904 119862119904 119862119898 119862V) into 119896 sub-networks as 119873

119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896

(14) Divide time horizon 119879119867

119896into 119905 time seeds as 119879119867

119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896

(15) for each time seed 119879119878

119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894

dr Generating Customer Request Vector for Dynamic Requests(18) generate CRV (119876 PLDT PUDT STIL STIU ECPUT) randomly(19) endfor(20) for 119894 = 1 to119873

119894

dr Generating Customer Order Vector for Dynamic Requests(21) generate GR vector (ADR Dist RN SR) randomly and calculate Gr using (1)(22) generate CRK vector (VIC IC RC CC) and assign weight according to ranks(23) calculate ST using (2)(24) calculate ERT using (3)(25) endfor(26) 119866 = 0

(27) Generate position119883119895(119866) and velocity 119881

119895(119866) for 119895th particle in 119866th generation from COV

(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1

(30) for each particle 119875119895(119883119895(119866) 119881

119895(119866)) of the search space

(31) evaluate fitness using objective function (5) as Fitt[119875119895(119883119895(119866) 119881

119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)

(36) for 119895 = 2 to number of particles in the swarm(37) if (Fitt[119875

119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)

(39) endfor(40) endwhile(41) store 119883

119892best(119866) for 119894th time seed

(42) endfor(43) store the set of 119883

119892best(119866) for 119896th partition

(44) endfor

Algorithm 1 TS-PSO

6 Conclusion

In this paper a novel variation of DVRP has been iden-tified by incorporating multiple objectives such as geo-graphical ranking customer ranking service time expected

reachability time and satisfaction level The identified DVRPis called multiobjective dynamic vehicle routing problem(M-DVRP) A time seed based solution using particleswarm optimization (TS-PSO) for the identified problemhas been proposed The proposed solution could be useful


60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2

Number of vehicles (N)

(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO

NGA = 15 lowast NTS-PSO



TS-PSO


(c)

Figure 11 The optimization performance of TS-PSO in optimizing (a) 119891minus12 (b) 119891

3 and (c) 119891

4

in the framework of various dynamic vehicle routing prob-lems of real environments such as logistics courier and E-commerce because the M-DVRP has more realistic assump-tions about the real environment It effectively optimizes theconsidered parameters of the problem for example vehiclecount expected reachability time profit and satisfactionlevel The optimization of expected reachability time by TS-PSO is far better than what is obtained from GA solutionIt should also be noted that TS-PSO uses less vehicles Theoptimization of profit by TS-PSO is almost three times better

thanwhat is obtained in case ofGAapproachThe satisfactionlevel has been effectively optimized by TS-PSO In futureresearch authors will explore evolutionary multiobjectiveoptimization (EMO) for solving M-DVRP

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Authorsrsquo Contribution

Omprakash Kaiwartya conceived designed and performedthe experiments Sushil Kumar D K Lobiyal Pawan KumarTiwari andAbdulHananAbdullah analyzed the data FinallyOmprakash Kaiwartya wrote the paper with the help ofAhmed Nazar Hassan

Acknowledgments

The research is supported by Ministry of Education Malaysia(MOE) and conducted in collaboration with Research Man-agement Center (RMC) at Universiti Teknologi Malaysia(UTM) under VOT no QJ130000252803H19 Dr VikashRai is thanked for helpful discussions

References

[1] B Golden S Raghavan and E WasilThe vehicle routing prob-lem latest advances and new challenges vol 43 of OperationsResearchComputer Science Interfaces Springer New York NYUSA 2008

[2] C Lin K L Choy G T S Ho S H Chung and H YLam ldquoSurvey of green vehicle routing problem past and futuretrendsrdquo Expert Systems with Applications vol 41 no 4 pp 1118ndash1138 2014

[3] V Pillac M Gendreau C Gueret and A L Medaglia ldquoAreview of dynamic vehicle routing problemsrdquo European Journalof Operational Research vol 225 no 1 pp 1ndash11 2013

[4] MW Savelsbergh ldquoLocal search in routing problems with timewindowsrdquo Annals of Operations Research vol 4 no 1 pp 285ndash305 1985

[5] H C W Lau T M Chan W T Tsui and W K PangldquoApplication of genetic algorithms to solve the multidepotvehicle routing problemrdquo IEEE Transactions on AutomationScience and Engineering vol 7 no 2 pp 383ndash392 2010

[6] L-N Xing P Rohlfshagen Y-W Chen and X Yao ldquoA hybridant colony optimization algorithm for the extended capacitatedarc routing problemrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 4 pp 1110ndash1123 2011

[7] F P Goksal I Karaoglan and F Altiparmak ldquoA hybrid discreteparticle swarm optimization for vehicle routing problem withsimultaneous pickup and deliveryrdquo Computers and IndustrialEngineering vol 65 no 1 pp 39ndash53 2013

[8] O Kaiwartya and S Kumar ldquoGeoPSO geocasting in vehicularadhoc networks using particle swarm optimizationrdquo in Pro-ceedings of the Conference on Information Systems and Designof Communication (ISDOC rsquo14) pp 62ndash66 ACM LisboanPortugal May 2014

[9] P K Tiwari and D P Vidyarthi ldquoObserving the effect ofinterprocess communication in auto controlled ant colonyoptimization-based scheduling on computational gridrdquo Con-currency Computation Practice and Experience vol 26 no 1pp 241ndash270 2014

[10] G B Dantzig and J H Ramser ldquoThe truck dispatchingproblemrdquoManagement Science Journal of the Institute of Man-agement Science Application andTheory Series vol 6 pp 80ndash911959

[11] H Lei G Laporte and B Guo ldquoThe capacitated vehiclerouting problem with stochastic demands and time windowsrdquo

Computers amp Operations Research vol 38 no 12 pp 1775ndash17832011

[12] X Li P Tian and S C H Leung ldquoVehicle routing problemswith time windows and stochastic travel and service timesmodels and algorithmrdquo International Journal of ProductionEconomics vol 125 no 1 pp 137ndash145 2010

[13] S F Ghannadpour S Noori and R Tavakkoli-MoghaddamldquoMultiobjective dynamic vehicle routing problem with fuzzytravel times and customersrsquo satisfaction in supply chain man-agementrdquo IEEE Transactions on Engineering Management vol60 no 4 pp 777ndash790 2013

[14] Y-J Gong J Zhang O Liu R-Z Huang H S-H Chung andY-H Shi ldquoOptimizing the vehicle routing problem with timewindows a discrete particle swarm optimization approachrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 42 no 2 pp 254ndash267 2012

[15] H-K Chen H-W Chou C-F Hsueh and T-Y Ho ldquoThelinehaul-feeder vehicle routing problem with virtual depotsrdquoIEEE Transactions on Automation Science and Engineering vol8 no 4 pp 694ndash704 2011

[16] D A Steil J R Pate N A Kraft et al ldquoPatrol routing expres-sion execution evaluation and engagementrdquo IEEE Transac-tions on Intelligent Transportation Systems vol 12 no 1 pp 58ndash72 2011

[17] L Xing P Rohlfshagen Y Chen and X Yao ldquoAn evolutionaryapproach to the multidepot capacitated Arc routing problemrdquoIEEE Transactions on Evolutionary Computation vol 14 no 3pp 356ndash374 2010

[18] P P Repoussis C D Tarantilis and G Ioannou ldquoArc-guidedevolutionary algorithm for the vehicle routing problem withtime windowsrdquo IEEE Transactions on Evolutionary Computa-tion vol 13 no 3 pp 624ndash647 2009

[19] J Zhang W Wang Y Zhao and C Cattani ldquoMultiobjec-tive quantum evolutionary algorithm for the vehicle routingproblem with customer satisfactionrdquoMathematical Problems inEngineering vol 2012 Article ID 879614 19 pages 2012

[20] P K Tiwari and A K Srivastava ldquoZadeh extension principle anoterdquo Annals of Fuzzy Mathematics and Informatics vol 9 no1 pp 37ndash41 2014

[21] S F Ghannadpour S Noori R Tavakkoli-Moghaddam and KGhoseiri ldquoA multi-objective dynamic vehicle routing problemwith fuzzy time windows model solution and applicationrdquoApplied Soft Computing Journal vol 14 no 1 pp 504ndash527 2014

[22] R S Rao S K Soni N Singh andOKaiwartya ldquoA probabilisticanalysis of path duration using routing protocol in VANETsrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 495036 10 pages 2014

[23] R Kumar S Kumar D Shukla R S Raw and O KaiwartyaldquoGeometrical localization algorithm for three dimensionalwireless sensor networksrdquo Wireless Personal Communicationsvol 79 no 1 pp 249ndash264 2014

[24] O Kaiwartya and S Kumar ldquoCache agent based geocasting(CAG) in VANETsrdquo International Journal of Information andCommunication Technology In press

[25] K Gupta K Gupta and O Kaiwartya ldquoDynamic ad hoctransport protocol (D-ATP) for mobile ad hoc networksrdquo inProceedings of the 5th International Conference- Confluence-TheNext Generation Information Technology Summit pp 411ndash415Noida India September 2014

[26] O Kaiwartya and S Kumar ldquoGeocast routing recent advancesand future challenges in vehicular adhoc networksrdquo in Proceed-ings of the International Conference on Signal Processing and


Integrated Networks (SPIN rsquo14) pp 291ndash296 IEEE Noida IndiaFeburary 2014

[27] O Kaiwartya S Kumar and R Kasana ldquoTraffic light basedtime stable geocast (T-TSG) routing for urban VANETsrdquo inProceedings of the 6th International Conference onContemporaryComputing (IC3 rsquo13) pp 113ndash117 Noida India August 2013

[28] O Kaiwartya and S Kumar ldquoEnhanced caching for geocastrouting in vehicular Ad-Hoc networks (ECGR)rdquo in Proceedingsof the International Conference on Advanced Computing Net-working and Informatics (ICACNI rsquo13) vol 243 pp 213ndash220Raipur India June 2013

[29] OKaiwartya S KumarDK Lobiyal AHAbdullah andANHassan ldquoPerformance improvement in geographic routing forvehicular ad hoc networksrdquo Sensors vol 14 no 12 pp 22342ndash22371 2014

[30] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

[31] W N Chen J Zhang H S H Chung W L Zhong W G Wuand Y H Shi ldquoA novel set-based particle swarm optimizationmethod for discrete optimization problemsrdquo IEEE Transactionson Evolutionary Computation vol 14 no 2 pp 278ndash300 2010

[32] F K Karnadi Z H Mo and K-C Lan ldquoRapid generationof realistic mobility models for VANETrdquo in Proceedings of theWireless Communications and Networking Conference (WCNCrsquo07) pp 2508ndash2513 IEEE Kowloon China March 2007

[33] D Krajzewicz J Erdmann M Behrisch and L Bieker ldquoRecentdevelopment and applications of sumomdashsimulation of urbanmobilityrdquo International Journal On Advances in Systems andMeasurement vol 5 no 3-4 pp 128ndash138 2012

[34] ldquoThe California Vehicle Activity Database (CalVAD)rdquohttpcalvadctmlabsnet

[35] The US Department of transportation httpswwwfhwadotgovpolicyinformationindexcfm

[36] httpwwwkaiwartyacompublications[37] M I Hosny and C L Mumford ldquoConstructing initial solutions

for the multiple vehicle pickup and delivery problem withtime windowsrdquo Journal of King Saud University Computer andInformation Sciences vol 24 no 1 pp 59ndash69 2012

[38] Y Zhou J Xie and H Zheng ldquoA hybrid bat algorithmwith path relinking for capacitated vehicle routing problemrdquoMathematical Problems in Engineering vol 2013 Article ID392789 10 pages 2013

[39] P H V Penna A Subramanian and L S Ochi ldquoAn iteratedlocal search heuristic for the heterogeneous fleet vehicle routingproblemrdquo Journal of Heuristics vol 19 no 2 pp 201ndash232 2013

[40] X Gao L Andrew Q Hu and Z Wenbin ldquoMultiple pickupand delivery TSP with LIFO and distance constraints a VNSapproachrdquo in Modern Approaches in Applied Intelligence vol6704 of Lecture Notes in Computer Science pp 193ndash202Springer 2011

[41] Y J Gong J Zhang O Liu R Z Huang H S H Chung andY-H Shi ldquoOptimizing the vehicle routing problem with timewindows a discrete particle swarm optimization approachrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 42 no 2 pp 254ndash267 2012

[42] E Cao M Lai and H Yang ldquoOpen vehicle routing problemwith demand uncertainty and its robust strategiesrdquo ExpertSystems with Applications vol 41 no 7 pp 3569ndash3575 2014

[43] M Romero S Leonid and S Angel ldquoA genetic algorithmfor the pickup and delivery problem an application to thehelicopter offshore transportationrdquo inTheoretical Advances andApplications of Fuzzy Logic and SoftComputing vol 42 pp 435ndash444 Springer Berlin Germany 2007

[44] E Melachrinoudis A B Ilhan and H Min ldquoA dial-a-rideproblem for client transportation in a health-care organizationrdquoComputers amp Operations Research vol 34 no 3 pp 742ndash7592007

[45] D Cattaruzza N Absi D Feillet and T Vidal ldquoA memeticalgorithm for the multi trip vehicle routing problemrdquo EuropeanJournal of Operational Research vol 236 no 3 pp 833ndash8482014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 The most common variants of VRP

Serial number Problem Problem description Features Ref

1 VRP-PD VRP with pickup anddelivery

It is transportation problem for a given set of goods from some pickup locations tothe delivery locations No central depot for the delivery vehicles is required [37]

2 C-VRP Capacitated VRP It is a simple VRP with vehicles having prespecified and same goods carryingcapacity [38]

3 H-VRP Heterogeneous VRP It is slightly different from C-VRP Here the vehicles have prespecified but differentgoods carrying capacity [39]

4 VRP-LIFO VRP with last-in-firstout

In this VRP the items that have been picked up most recently must be the items thatneed to be delivered in the next locations [40]

5 VRP-TW VRP with timewindow

It is a VRP with delivery time interval for each customer The delivery vehicles canvisit the customers in the given time interval [41]

6 O-VRP Open VRP In this VRP the delivery vehicles are not required to report back to the centraldepot after visiting all the assigned customers [42]

7 DAF-VRP Dial-A-flight VRP It is a VRP in public transport through airline [43]8 DAR-VRP Dial-A-ride VRP It is an on-road general public transport problem [44]

9 VRP-MT VRP with multipletrips

In this VRP the delivery vehicles take more than one tour once it finishes theassigned tour [45]

DVRPs with large number of customers and their demandparameters could not be obtained within reasonable time dueto NP-hard nature of the problems [4] In the last ten yearsvarious nature inspired metaheuristic techniques have beenapplied to solve the customized instances of various DVRPsGenetic algorithm (GA) ant colony optimization (ACO) andparticle swarm optimization (PCO) have been commonlyused for solving the above listed DVRPs [5ndash7] Nowadaysthese techniques have also been gaining popularity in vehic-ular ad hoc networks (VANETs) [8] and high performancecomputing [9]

In this paper a multiobjective dynamic vehicle routingproblem (M-DVRP) has been identified A time seed basedsolution using particle swarm optimization (TS-PSO) for M-DVRP has been proposed The five objectives considered inthe proposed problem are geographical ranking of requestscustomer ranking service time expected reachability timeand satisfaction level of customers Each of these objectiveshas been materialized in terms of both conceptual andmathematical formulation A multiobjective function hasbeen generated having four components namely vehiclecountnumber of vehicles expected reachability time profitand satisfaction level The mathematical formulations havebeen derived for each of the component objectives using themetric of the problemThree constraints of themultiobjectivefunction namely vehicle capacity and reachability have beendefined The proposed solution TS-PSO broadly operatesinto two steps In the first step the identified problem ispartitioned into smaller size DVRPs In the second step timehorizon of each smaller sizeDVRPhas been divided into timeseeds and the problem has been solved in each time seedusing particle swarm optimization A complete algorithm hasalso been developed for the proposed solution techniqueThenetwork simulator ns-234 has been used for the simulationalong with two other supporting software programs MOVEand ArcGIS The fifteen data sets OPK-01 to OPK-15 used inthe simulation have been generated considering real vehicu-lar environment and highly dynamic customer requirements

The simulation results have been compared with the geneticalgorithm (GA) solution technique

The rest of the paper is organized as follows Section 2presents some early and recent developments in dynamicvehicle routing problem In Section 3 details of the identifiedproblemM-DVRP are described In Section 4 the TS-PSO isproposed anddescribedThe analytical and simulation resultsare presented in Section 5 Conclusion is derived in Section 6

2 Early and Recent Developmentsin VRP and DVRP

The VRP was first proposed by Dantzig and Ramser in1959 The authors optimized the routing of a fleet of gaso-line delivery trucks between a bulk terminal and a largenumber of service stations supplied by the terminal Theyhave used linear programing formulation for obtaining nearoptimal solution [10] After the induction VRP has beenone of the challenging areas of research that has witnessedconsistent attention of the researchers from both industriesand academia The research contribution can be categorizedinto two dimensions probabilistic optimization and staticoptimization In probabilistic optimization the componentsof the problem such as demand number of customers andservice time have been considered as future events andprobabilistic models have been used to predict the futurebehavior of these components [11 12] In static optimizationsavailable information about the components has been consid-ered without including future behavior of the componentsSome of the most recent works in DVRP have been describedbelow Multiobjective dynamic vehicle routing problem withfuzzy travel times and customersrsquo satisfaction in supply chainmanagement has been suggested in [13] The authors haveinvestigated fuzzy time window and fuzzy travel time indepth for the VRP The travel distance number of vehiclesand waiting time of vehicles have been minimized andthe satisfaction rate of customers has also been minimized


Delivery vehicles

Customers

Central depot

Planned route




Delivery vehicles








(119873119904 119862119904 119862119898 119862119898V) where 119873

119904= 1198990 1198991 1198992 1198993 119899

119899 indi-


= (119899119894 119899119895) 119899119894 119899119895

isin 119873119904and 119894 =


= 119862119898(119894 119895)(119899119894 119899119895)isin119862119904


matrix vector 119862119898V = (119862

1 1198622 1198623 1198624 1198625) is group of five


119898and119862





GR CR ST ERT SL PF








Component weights

ADR

05

DIST

02

RN

01

SR

02


Customer

VIC

IC

RC

CC

1

0

075

05

GSL


Rank =

4

Rank = 3

Rank = 2

Rank =1



119894as weighting


120572119894


119866119903=

sum4

119894=1120572119894119903119894

1003816100381610038161003816VGR1003816100381610038161003816 minus 1

(1)






ST =

119873item

sum

119894=1

119902119894119868119894

119878119903

119894

(2)



119903


item


Vavg and weightage


ERT =


(3)


SL (ERT)

=





STIL PUDT lt ERT

lt (PUDT + STIU)

(4)







Max (119891minus11

119891minus1

21198913 1198914) (5)

where

1198911= 119873V

1198912=

119873V

sum

119894=1

119873119888

sum

119895=1

119873119888

sum

119896=1

ERT119895119896120594119894

119895119896

1198913=

119873119888

sum

119895=1

PF119895

1198914=

119873119888

sum

119897=1


119897

120594119894

119895119896=


0 otherwise

CPFwt119897

=GR119897+ CR119897

Max GR119894119895+ CR119894119895 119894 = 1 2 3 119895 = 1 2 3 4

st119873V

sum

119894=1

119873119888

sum

119895

120594119894

119895119896= 1 119896 = 1 2 3 119873

119888

119873119888

sum

119895

119873119888

sum

119896

120594119894

119895119896sdot 119889119888

119896≪ 119888ℎ 119894 = 1 2 3 119873V

120594119894

119895119896(ERT119894119895+ 119905119895119896

+ ST119903) ≪ 120594

119894

119895119896sdot ERT119894119895

119903 = 1 2 3 119873119888 119894 = 1 2 3 119873V

(6)







4 TS-PSO for M-DVRP


119873119888



119896 119896 = 1 2 3 119899


size DVRP 119879119867

119896=

119873TS

sum

119894=1

119879119904

119894119896

(7)


119904 in the




3 14 6 4 8 9 2 5 11 13 10 7 1 12






1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)



119899

1and 119903

119899




119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4


1198991198625247

119899+1 ]

(10)

where 119862119897119898119894



customers



119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)







1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883



120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840



1198751015840

PF = 1 if (120596 times 119875PF) gt 1


1198751015840

SL = 1 if (120596 times 119875SL) gt 1


119883119894minus 119883119895= [119862119897119898


119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)



119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Delivery vehicles

Customers

Central depot

Planned route




Delivery vehicles








(119873119904 119862119904 119862119898 119862119898V) where 119873

119904= 1198990 1198991 1198992 1198993 119899

119899 indi-


= (119899119894 119899119895) 119899119894 119899119895

isin 119873119904and 119894 =


= 119862119898(119894 119895)(119899119894 119899119895)isin119862119904


matrix vector 119862119898V = (119862

1 1198622 1198623 1198624 1198625) is group of five


119898and119862





GR CR ST ERT SL PF








Component weights

ADR

05

DIST

02

RN

01

SR

02


Customer

VIC

IC

RC

CC

1

0

075

05

GSL


Rank =

4

Rank = 3

Rank = 2

Rank =1



119894as weighting


120572119894


119866119903=

sum4

119894=1120572119894119903119894

1003816100381610038161003816VGR1003816100381610038161003816 minus 1

(1)






ST =

119873item

sum

119894=1

119902119894119868119894

119878119903

119894

(2)



119903


item


Vavg and weightage


ERT =


(3)


SL (ERT)

=





STIL PUDT lt ERT

lt (PUDT + STIU)

(4)







Max (119891minus11

119891minus1

21198913 1198914) (5)

where

1198911= 119873V

1198912=

119873V

sum

119894=1

119873119888

sum

119895=1

119873119888

sum

119896=1

ERT119895119896120594119894

119895119896

1198913=

119873119888

sum

119895=1

PF119895

1198914=

119873119888

sum

119897=1


119897

120594119894

119895119896=


0 otherwise

CPFwt119897

=GR119897+ CR119897

Max GR119894119895+ CR119894119895 119894 = 1 2 3 119895 = 1 2 3 4

st119873V

sum

119894=1

119873119888

sum

119895

120594119894

119895119896= 1 119896 = 1 2 3 119873

119888

119873119888

sum

119895

119873119888

sum

119896

120594119894

119895119896sdot 119889119888

119896≪ 119888ℎ 119894 = 1 2 3 119873V

120594119894

119895119896(ERT119894119895+ 119905119895119896

+ ST119903) ≪ 120594

119894

119895119896sdot ERT119894119895

119903 = 1 2 3 119873119888 119894 = 1 2 3 119873V

(6)







4 TS-PSO for M-DVRP


119873119888



119896 119896 = 1 2 3 119899


size DVRP 119879119867

119896=

119873TS

sum

119894=1

119879119904

119894119896

(7)


119904 in the




3 14 6 4 8 9 2 5 11 13 10 7 1 12






1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)



119899

1and 119903

119899




119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4


1198991198625247

119899+1 ]

(10)

where 119862119897119898119894



customers



119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)







1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883



120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840



1198751015840

PF = 1 if (120596 times 119875PF) gt 1


1198751015840

SL = 1 if (120596 times 119875SL) gt 1


119883119894minus 119883119895= [119862119897119898


119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)



119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(119873119904 119862119904 119862119898 119862119898V) where 119873

119904= 1198990 1198991 1198992 1198993 119899

119899 indi-


= (119899119894 119899119895) 119899119894 119899119895

isin 119873119904and 119894 =


= 119862119898(119894 119895)(119899119894 119899119895)isin119862119904


matrix vector 119862119898V = (119862

1 1198622 1198623 1198624 1198625) is group of five


119898and119862





GR CR ST ERT SL PF








Component weights

ADR

05

DIST

02

RN

01

SR

02


Customer

VIC

IC

RC

CC

1

0

075

05

GSL


Rank =

4

Rank = 3

Rank = 2

Rank =1



119894as weighting


120572119894


119866119903=

sum4

119894=1120572119894119903119894

1003816100381610038161003816VGR1003816100381610038161003816 minus 1

(1)






ST =

119873item

sum

119894=1

119902119894119868119894

119878119903

119894

(2)



119903


item


Vavg and weightage


ERT =


(3)


SL (ERT)

=





STIL PUDT lt ERT

lt (PUDT + STIU)

(4)







Max (119891minus11

119891minus1

21198913 1198914) (5)

where

1198911= 119873V

1198912=

119873V

sum

119894=1

119873119888

sum

119895=1

119873119888

sum

119896=1

ERT119895119896120594119894

119895119896

1198913=

119873119888

sum

119895=1

PF119895

1198914=

119873119888

sum

119897=1


119897

120594119894

119895119896=


0 otherwise

CPFwt119897

=GR119897+ CR119897

Max GR119894119895+ CR119894119895 119894 = 1 2 3 119895 = 1 2 3 4

st119873V

sum

119894=1

119873119888

sum

119895

120594119894

119895119896= 1 119896 = 1 2 3 119873

119888

119873119888

sum

119895

119873119888

sum

119896

120594119894

119895119896sdot 119889119888

119896≪ 119888ℎ 119894 = 1 2 3 119873V

120594119894

119895119896(ERT119894119895+ 119905119895119896

+ ST119903) ≪ 120594

119894

119895119896sdot ERT119894119895

119903 = 1 2 3 119873119888 119894 = 1 2 3 119873V

(6)







4 TS-PSO for M-DVRP


119873119888



119896 119896 = 1 2 3 119899


size DVRP 119879119867

119896=

119873TS

sum

119894=1

119879119904

119894119896

(7)


119904 in the




3 14 6 4 8 9 2 5 11 13 10 7 1 12






1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)



119899

1and 119903

119899




119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4


1198991198625247

119899+1 ]

(10)

where 119862119897119898119894



customers



119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)







1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883



120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840



1198751015840

PF = 1 if (120596 times 119875PF) gt 1


1198751015840

SL = 1 if (120596 times 119875SL) gt 1


119883119894minus 119883119895= [119862119897119898


119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)



119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Component weights

ADR

05

DIST

02

RN

01

SR

02


Customer

VIC

IC

RC

CC

1

0

075

05

GSL


Rank =

4

Rank = 3

Rank = 2

Rank =1



119894as weighting


120572119894


119866119903=

sum4

119894=1120572119894119903119894

1003816100381610038161003816VGR1003816100381610038161003816 minus 1

(1)






ST =

119873item

sum

119894=1

119902119894119868119894

119878119903

119894

(2)



119903


item


Vavg and weightage


ERT =


(3)


SL (ERT)

=





STIL PUDT lt ERT

lt (PUDT + STIU)

(4)







Max (119891minus11

119891minus1

21198913 1198914) (5)

where

1198911= 119873V

1198912=

119873V

sum

119894=1

119873119888

sum

119895=1

119873119888

sum

119896=1

ERT119895119896120594119894

119895119896

1198913=

119873119888

sum

119895=1

PF119895

1198914=

119873119888

sum

119897=1


119897

120594119894

119895119896=


0 otherwise

CPFwt119897

=GR119897+ CR119897

Max GR119894119895+ CR119894119895 119894 = 1 2 3 119895 = 1 2 3 4

st119873V

sum

119894=1

119873119888

sum

119895

120594119894

119895119896= 1 119896 = 1 2 3 119873

119888

119873119888

sum

119895

119873119888

sum

119896

120594119894

119895119896sdot 119889119888

119896≪ 119888ℎ 119894 = 1 2 3 119873V

120594119894

119895119896(ERT119894119895+ 119905119895119896

+ ST119903) ≪ 120594

119894

119895119896sdot ERT119894119895

119903 = 1 2 3 119873119888 119894 = 1 2 3 119873V

(6)







4 TS-PSO for M-DVRP


119873119888



119896 119896 = 1 2 3 119899


size DVRP 119879119867

119896=

119873TS

sum

119894=1

119879119904

119894119896

(7)


119904 in the




3 14 6 4 8 9 2 5 11 13 10 7 1 12






1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)



119899

1and 119903

119899




119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4


1198991198625247

119899+1 ]

(10)

where 119862119897119898119894



customers



119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)







1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883



120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840



1198751015840

PF = 1 if (120596 times 119875PF) gt 1


1198751015840

SL = 1 if (120596 times 119875SL) gt 1


119883119894minus 119883119895= [119862119897119898


119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)



119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Max (119891minus11

119891minus1

21198913 1198914) (5)

where

1198911= 119873V

1198912=

119873V

sum

119894=1

119873119888

sum

119895=1

119873119888

sum

119896=1

ERT119895119896120594119894

119895119896

1198913=

119873119888

sum

119895=1

PF119895

1198914=

119873119888

sum

119897=1


119897

120594119894

119895119896=


0 otherwise

CPFwt119897

=GR119897+ CR119897

Max GR119894119895+ CR119894119895 119894 = 1 2 3 119895 = 1 2 3 4

st119873V

sum

119894=1

119873119888

sum

119895

120594119894

119895119896= 1 119896 = 1 2 3 119873

119888

119873119888

sum

119895

119873119888

sum

119896

120594119894

119895119896sdot 119889119888

119896≪ 119888ℎ 119894 = 1 2 3 119873V

120594119894

119895119896(ERT119894119895+ 119905119895119896

+ ST119903) ≪ 120594

119894

119895119896sdot ERT119894119895

119903 = 1 2 3 119873119888 119894 = 1 2 3 119873V

(6)







4 TS-PSO for M-DVRP


119873119888



119896 119896 = 1 2 3 119899


size DVRP 119879119867

119896=

119873TS

sum

119894=1

119879119904

119894119896

(7)


119904 in the




3 14 6 4 8 9 2 5 11 13 10 7 1 12






1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)



119899

1and 119903

119899




119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4


1198991198625247

119899+1 ]

(10)

where 119862119897119898119894



customers



119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)







1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883



120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840



1198751015840

PF = 1 if (120596 times 119875PF) gt 1


1198751015840

SL = 1 if (120596 times 119875SL) gt 1


119883119894minus 119883119895= [119862119897119898


119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)



119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3 14 6 4 8 9 2 5 11 13 10 7 1 12






1198811015840

119894= 120596 times 119881

119894+ 1205721times 119903119899

1(119871best minus 119883

119894)

+ 1205722times 119903119899

2(119866best minus 119883

119894)

(8)

1198831015840

119894= 119883119894+ 1198811015840

119894 (9)



119899

1and 119903

119899




119883119894= [11986257

111986294

2 11986226

3 V111986231

3 119862128

4


1198991198625247

119899+1 ]

(10)

where 119862119897119898119894



customers



119881119894= [1198621517

1(02 04 05) 119862

1924

2(01 02 03)

V1 119862

5049

119898(06 09 08) V

119904]

(11)







1(119871best minus119883

119894) or 1205722times119903119899

2(119866best minus119883



120596 times 119881119894= [119862119897119898

119895(1198751015840

ERT 1198751015840

PF 1198751015840

SL) | 119895 isin 119862119904 119897 119898 isin 119873

119904]

1198751015840



1198751015840

PF = 1 if (120596 times 119875PF) gt 1


1198751015840

SL = 1 if (120596 times 119875SL) gt 1


119883119894minus 119883119895= [119862119897119898


119909isin 119883119894

119862119897119898

119909notin 119883119895]

1205721 or 2 times 119903

119899

1 or 2 (119883119894)

= [119862119897119898

119895(119875ERT 119875PF 119875SL) | 119895 isin 119883

119894 119897 119898 isin 119873

119904]

119875ERT = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875PF = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

119875SL = 1 if (120572

1 or 2 times 119903119899

1 or 2) gt 1

1205721 or 2 times 119903

119899

1 or 2 otherwise

(12)



119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119894to generate



1015840

119894is

defined as

1198831015840

119894= [1198621198971198981015840

119895V119905| forall119862119897119898

119895 V119905isin 119883119894]

1198981015840

=

119901 if 119862119897119901119895

isin 1198811015840


119894

119902 if 119862119897119902119895

isin 119863119888


119894

119898 otherwise

(13)


119888

















GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-01

1198911

minus1 00357 00357 00238 00198 001791198912

minus1 00008 00007 00007 00007 000081198913

86U 8U 13U 16U 21U1198914

0665 0195 0237 0264 0289

OPK-02

1198911

minus1 00244 00244 00163 00136 001221198912

minus1 00009 00007 00007 00007 000081198913

105U 19U 25U 30U 35U1198914

0713 0234 0284 0301 0325

OPK-03

1198911

minus1 00179 00179 00119 00099 000891198912

minus1 00012 00008 00009 00009 000111198913

137U 36U 44U 48U 52U1198914

0742 0306 0368 0397 0437

OPK-04

1198911

minus1 00167 00167 00111 00093 000831198912

minus1 00013 00008 00009 00010 000121198913

149U 41U 48U 53U 56U1198914

0752 0342 0395 0425 0456

OPK-05

1198911

minus1 00154 00154 00103 00085 000771198912

minus1 00014 00008 00010 00011 000131198913

162U 47U 55U 58U 62U1198914

0764 0368 0426 0453 0483

OPK-06

1198911

minus1 00143 00143 00095 00079 000711198912

minus1 00015 00008 00011 00012 000141198913

178U 53U 61U 64U 68U1198914

0773 0417 0443 0478 0501

OPK-07

1198911

minus1 00133 00133 00089 00074 000671198912

minus1 00016 00009 00012 00014 000161198913

196U 61U 66U 69U 72U1198914

0782 0436 0471 0492 0532

OPK-08

1198911

minus1 00125 00125 00083 00069 000631198912

minus1 00018 00009 00013 00015 000171198913

207U 68U 70U 73U 76U1198914

0795 0465 0490 0520 0554

OPK-09

1198911

minus1 00118 00118 00078 00065 000591198912

minus1 00020 00009 00015 00018 000201198913

219U 77U 76U 79U 83U1198914

0807 0483 0514 0542 0568

OPK-10

1198911

minus1 00111 00111 00074 00062 000561198912

minus1 00024 00009 00017 00021 000231198913

239U 83U 81U 84U 87U1198914

0812 0516 0532 0571 0595

OPK-11

1198911

minus1 00105 00105 00070 00058 000531198912

minus1 00027 00010 00019 00025 000261198913

253U 89U 87U 90U 92U1198914

0823 0542 0563 0594 0617

OPK-12

1198911

minus1 00100 00100 00067 00056 000501198912

minus1 00033 00010 00022 00030 000311198913

269U 96U 91U 95U 98U1198914

0831 0589 0601 0637 0650


Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 3 Continued


GA119907

= 119873TS-PSO119907

119873GA119907

= lceil15119873TS-PSO119907

rceil 119873GA119907

= lceil18119873TS-PSO119907

rceil 119873GA119907

= lceil2119873TS-PSO119907

rceil

OPK-13

1198911

minus1 00095 00095 00063 00053 000481198912

minus1 00041 00010 00026 00037 000391198913

204U 73U 69U 64U 56U1198914

0844 0593 0627 0650 0674

OPK-14

1198911

minus1 00091 00091 00060 00051 000451198912

minus1 00054 00011 00031 00050 000511198913

183U 69U 62U 53U 49U1198914

0856 0618 0649 0663 0685

OPK-15

1198911

minus1 00087 00087 00058 00048 000431198912

minus1 00076 00011 00039 00065 000711198913

172U 64U 57U 48U 41U1198914

0862 0631 0672 0691 0721








NS-2simulation




GAV = lceil2119873



2 1198913 and 119891






SDPV

119873119877



119877














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














119883119892best






119888

(119873119904 119862119904 119862119898 119862119907)119873119907119873sr119873

119894

drOutput-119883119892best(119866)


119888

(119873119904 119862119904 119862119898 119862119907)


119888


119888

= ⋃119896

119894=1119873119888

119894

(13) for 119894 = 1 to 119896



119896= 119879119878

1 119896+ 119879119878

2 119896+ 119879119878

3 119896sdot sdot sdot + 119879

119878

119905 119896


119894 119896

(16) 119873119894

dr = rand(0 minus 119873119894

119888)

(17) for 119894 = 1 to119873119894


119894




(28) while (|119883119892best

(119866) minus 119883119892best

(119866 minus 1) lt 119883120572

|) do(29) 119866 = 119866 + 1




119895(119866))]

(32) if (Fitt[119875119895(119883119895(119866) 119881

119895(119866))] == Fitt[119875

119895(119883119895(119866 minus 1) 119881

119895(119866 minus 1))])

(33) 119883119897best119895

(119866) = 119883119895(119866)

(34) endfor(35) 119883

119892best(119866) = 119883

119897best1

(119866)


119895(119883119897best119895

(119866) 119881119895(119866))] gt Fitt[119875

119898(119883119892best

(119866) 119881119898(119866))])

(38) 119883119892best

(119866) = 119883119897best119895

(119866)





(44) endfor

Algorithm 1 TS-PSO

6 Conclusion




60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










60 65 70 75 80 85 90 95 100 105 110 1150

0001

0002

0003

0004

0005

0006

0007

0008fminus1

2


(a)

60 65 70 75 80 85 90 95 100 105 110 1150

50

100

150

200

250

300

350

400

f3


(b)

60 65 70 75 80 85 90 95 100 105 110 1150

01

02

03

04

05

06

07

08

09

1

f4

NGA = NTS-PSO




TS-PSO


(c)


3 and (c) 119891

4








Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Acknowledgments


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Multiobjective Dynamic Vehicle...

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