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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

AN ANT COLONY OPTIMIZATION ALGORITHMFOR OPTIMIZATION OF PROCESS PLANS

P S Srinivas1*, V Ramachandra Raju2 and C S P Rao3

*Corresponding Author: P S Srinivas,vasupragada@yahoo.com

The decision of selecting a process plan in a manufacturing system is crucial. Any sequence ofmanufacturing operations that is generated in a process plan cannot be the best possiblesequence every time in a changing production environment. As the complexity of the productincreases, the number of feasible sequences increases exponentially and there is a need tochoose the best among them. In a dynamic workshop environment, the availability of alternatemachines, tools and fixtures must be considered to achieve the global lowest machining cost.In this paper process planning is modeled as a combinatorial optimization problem withconstraints, and an Ant Colony Optimization (ACO) approach has been used to solve it. AntColony Optimization (ACO) is a paradigm for designing metaheuristic algorithms for combinatorialoptimization problems. The natural metaphor on which ant algorithms are based is that of antcolonies. Fascinated by the ability of the almost blind ants to establish the shortest route fromtheir nests to the food source and back, researchers found out that these ants secrete a substancecalled ‘pheromone’ and use its trails as a medium for communicating information among eachother The ant algorithm is simple to implement and results of the case studies show its ability toprovide speedy and accurate solutions.

Keywords: Process planning, Ant colony optimization, Precedence relationship matrix

INTRODUCTIONOne of the most important steps in convertinga design concept into a manufactured productis process planning. Process planningactivities basically include the following:interpretation of product design data, selection

ISSN 2278 – 0149 www.ijmerr.comVol. 1, No. 3, October 2012

© 2012 IJMERR. All Rights Reserved

Int. J. Mech. Eng. & Rob. Res. 2012

1 V R Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India.2 JNTUCE, Vjayanagaram, Andhra Pradesh, India.3 Department of Mechanical Engineering, NIT, Warangal, Andhra Pradesh, India.

of machining processes, selection of cuttingtools, selection of machine tools,determination of setup requirements,sequencing of operations, determination of theproduction tolerances, determination of thecutting conditions, design of jigs and fixtures,

Research Paper

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

calculation of process times, tool path planningand NC program generation, generation ofprocess route sheets, etc.

In this paper, we propose an approximatemethod to resolve a multi product batch flowshop schedule. Our paper is based on theKoonce’s and Tsai (2000) work that uses datamining techniques to extract forms fromGenetic Algorithm solution, but we propose anant colony algorithm that is fast and easy toimplement for generating a learningpopulation. Further we propose anothermethod of knowledge extraction that willgenerate decision rules finding the affectionorder of operation on all machines. We studiedan 8 4 benchmark problem of Tailard (1993)to compare our results.

This paper is divided in to two sections. Thefirst section describes the ant colony algorithm(AC) and the method to generate a populationof the optimal sequences. The second sectiondeals with mining the solutions given by AC toextract from them the decision rules. Theserules are based on several attributes likeprocessing time, position in the job, remainingtime of the job, machine loading, etc. to findthe affection order of operation on everymachines.

Optimization of process planning is one ofthe foremost targets of manufacturing systems,since it is believed that only those industriescapable of making effective productions wouldwithstand international competition. Theoptimum process plan may be on the basis oftime or cost or on the basis of some weightedcombination of these two. Tool selection,machine selection, process selection and toolpath selection, process parameter selection

are the most important areas for optimizationin process planning.

RELEVANT LITERATUREAnts are social insects. They live in coloniesand all their actions are towards the survivalof the colony as a whole, rather than thebenefit of a single individual of the society.The individual ants have no special abilities.They communicate between each other usingchemical substances, the pheromones. Thisindirect communication allows the entirecolony to perform complex tasks, such asestablishing the shortest route paths fromtheir nests to feeding sources. In (Dorigoet al., 1996) an optimization algorithm wasproposed that tries to mimic the foragingbehavior of real ants, i.e., the behavior ofwandering in the search for food. Thisalgorithm has already been successfully usedto solve the TSP (Gambardella and Dorigo,1996), and other NP hard optimizationproblems (Silva et al., 2002).

Shen et al. (2006) describes the complexityof manufacturing process-planning andscheduling problems, and reviews theresearch literature in manufacturing processplanning, manufacturing scheduling, and theintegration of process planning andscheduling, particularly focusing on agent-based approaches in these areas.

Krishna and Mallikarjuna (2006) presentsan application of a newly developed meta-heuristic called the ant colony algorithm as aglobal search technique for the quickidentification of the optimal operationssequence by considering various feasibilityconstrains. A couple of case studies are taken

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

from the literature to comparing the resultsobtained by the proposed method.

Jain and Gupta (2005) uses ant colonyoptimization technique to solve the operationsequencing problem. Their approach analysesthe precedence relationships among featuresto generate a precedence relationship matrix(PRM). The operation-sequencing problem inprocess planning is considered to produce apart with the objective of minimizing the sumof machine, setup and tool change costs.

Li et al. (2002) proposed a hybrid GeneticAlgorithm (GA) and Simulated Annealing (SA)approach to consider concurrently theprocesses of selecting machining resources,determining set-up plans and sequencingoperations for a prismatic part in anoptimization procedure.

Ahmad et al. (2001) discussed acomprehensive overview of the current trendin research works on CAPP, classifying thoseworks into several categories according totheir focus.

Marri et al. (1998) has made an attempt intheir paper to review the existing literature withthe objective of gaining insights into the designand implementation of CAPP systems.

Tiwari et al. (2008) used GA to obtain a setof process plans for a given variety of partsand production volume with the objective ofminimizing the total processing time, setuptime and material handling time constrainedby not overloading the machines.

ACO IMPLEMENTATIONIn the Ant Colony Optimization (ACO)metaheuristic a colony of artificial ants,cooperates in finding good solutions to difficult

discrete optimization problems. Cooperationis a key design component of ACO algorithmsand good solutions are an emergent propertyof the ant’s cooperative interaction. Thetechnique involves observing the part featuredetails form available drawings, andoperations required for each feature, and alsoprecedence relations among operations.Generate ‘A’ number of artificial ants, where‘A’ is assumed to be equal to the number ofoperations ‘n’. Set initial value of pheromone(

ij) equal to a constant value (e = 0.1) for

every pair of operations (i.e., ij = e).

ij is the

pheromone present on the link joiningoperations i and j. Assign ‘n’ operations to‘A’ ants in sequence starting with firstoperation. Now move all ants to positions,which ant’s position didn’t follow precedencegive move probability ‘0’. By following this forall operations, few ants can only completetheir sequence. The objective function (FF

k)

for each completed sequence is calculated.Now update the pheromone differentially. Asshortest path is the emergent property of ACO,the completed sequences should bestrengthened and the incomplete sequencesshould be weakened. This step helps in theeliminating the incomplete sequences formthe future iterations. Separate the antscompleting operation sequences from theants unable to complete their operationsequences. For each of these completeoperation sequences add pheromone on theiredges, to improve their chances of selectionin next iteration also. The amount ofpheromone to be added on the edges of asequence completed by kth ant (say) is givenby the following expression.

k

kij FF

Q ...(1)

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

Where, Q is a pheromone depositionconstant. In the present study, a value of ‘10’was taken from literature. FF

k is the value of

the objective function for the sequence underconsideration (i.e., sequence generated bykth ant). Reduce pheromone on the edges ofincomplete sequences to weaken it chancesfor selection in the next iteration. Thefollowing expression is used to reduce thepheromone on the edges of an incompletesequence.

ijij 1 ...(2)

Where, [0, 1] is the persistence of thepheromone trail, and (1 – ) represents theevaporation of pheromone from edge (i, j).Moreover parameter also avoids unlimitedaccumulation of the pheromone trails on theedges and thus allows the algorithm to forgetpreviously done bad choices. Researches inthe past have used a range of values for varying from ‘0’ to ‘0.5’, but in our algorithm avalue of 0.1 for has taken. After each iterationthe pheromone updation and evaporationtakes place after certain number of iterationsor position values of each operations are notimproving then pick the highest pheromoneposition for each operation according toprecedence constraints, this is the bestsequence.

Precedence Relationship BetweenOperations

The Precedence Relationships (PRs)between operations come from geometricaland technological consideration to produceevery feature with the best possibleaccuracy. They must be satisfied by the finaloperations sequence. Some of the feasibilityconstraints are:

• Types of constraints, i.e., f ixturerequirement, datum requirement, goodmanufacturing practice, and geometrictolerance are considered to determine theprecedence relationships betweenfeatures.

– Fixture Requirement: Precedencerelationship between two features existswhen machining one feature first maycause another to be unfixturable. Anexample is given in Figure 1 where F1(through hole) must be drilled before F2(slot) is machined. Otherwise,deformation of the slot shoulder wouldoccur.

– Datum Requirement: When two featureshave a dimensional or geometricaltolerance relationship, the featurecontaining the datum should bemachined first. For example, F2 shouldbe machined before F4 (blind-hole)since the bottom face of F2 is the datumof F4.

– Good Manufacturing Practice: Goodmanufacturing practice or rules-of-thumbmay also result in precedencerelationships between features. In Figure1, F4 sits on F3 (slant face). F4 shouldbe drilled before F3 to avoid tooldamage.

– Geometric Tolerance: The last constraintpertains to the geometric tolerancesdefine for the part. The types oftolerances that affect sequencinginclude: profile of a line and surface,perpendicularity, angularity, parallelism,total and circular runout, position,symmetry, and concentricity. The result

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

of this analysis is the identification ofthose features which must be cut in thesame setup.

• PR’s among the set of OPT’s for a feature:for every set of OPT’s (An OPT refers to anoperation without any attachment ofmachine (M), tool (T), and tool approachdirection (TAD), e.g., drilling and milling)obtained through mapping from a feature,there exists a fixed precedence relationshipamong those OPT’s, i.e., roughingoperations come before finishingoperations. Some examples are drillingcomes before reaming, milling comesbefore grinding, etc.

Tool cost,

n

i

iTCITC1

...(4)

Where TCIi is the tool cost index for using

tool i.

Machine Change Cost (MCC): A machinechange is needed when two adjacentoperations are performed on differentmachines,

1

1

11n

i

ii MMMCCIMCC ...(5)

Where MCCI is the machine change costindex, and M

i is the machine ID used for

operation i.

,10

11

ii MM if Mi M

j

and 0, if Mi = M

j...(6)

Setup Change Cost (SCC): A setup changeis needed when two adjacent OpM’sperformed on the same machine havedifferent TADs.

1

1

11 *1n

i

iiii TADTADMMSCCISCC

...(7)

Where SCCI is the setup change cost index(Table 1).

Figure 1: An Example Part for theOperations Selection and Precedence

Relationships Identification

Criteria for Optimizing thePrecedence Sequence

The precedence sequence optimization isbased on the weighted cost, which consistsof,

Machine cost,

n

i

iMCIMC1

...(3)

Where n is the total number of OpM’s andMCI

i is the machine cost index for using

machine i.

Same TAD and same M/C No

Same TAD and different M/Cs Yes

Different TAD and same M/C Yes

Different TAD and different M/Cs Yes

Table 1: Setup Change Considerations

Conditions for Machining TwoConsequent Operations

SetupChange

Tool Change Cost (TCC): A tool change isneeded when two adjacent OpM’s performedon the same machine use different tools.

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

1

1

11 *1n

i

iiii TTMMTCCITCC ...(8)

Where TCCI is the tool change cost index(Table 2).

optimization of process plans (Figure 2) forprismatic parts” (Dorigo and Gambardella,1997). Here a job shop has been considered;the details are given in Tables 3 to 6.

M/C Change Cost Index (MCCI) = INR300.00

Tool Change Cost Index (TCCI) = INR 10.00

Setup Change Cost Index (SCCI) = INR90.00

The shop floor details with their cost andthe part details are given as input to thealgorithm. The output file contains finalpheromone matrix and optimal process plan.

Same Tool and same M/C No

Same Tool and different M/Cs No

Different Tools and same M/C Yes

Different Tools and different M/Cs No

Table 2: Tool Change Considerations

Conditions for Machining TwoConsequent Operations

ToolChange

Total Manufacturing Cost

MFGC = MC + TC + MCC + TCC + SCC...(9)

These cost factors can be used eitherindividually or collectively as a cost compoundbased on the requirement and the dataavailability of the job shop.

CASE STUDYThe efficacy of the developed program hasbeen tested for the following problemscollected from “Hybrid genetic algorithm andsimulated annealing approach for the

Figure 2: Part Considered for theGeneration Process Plan

Table 3: List of Machines

Machine Type M/C Cost (INR/min)

M1 T1(3): Drill 1 3

M2 T2(3): Drill 2 3

M3 T3(8): Reamer 8

M4 T4(15): Boring tool 15

T5(10): Milling cutter 1 10

T6(15): Milling cutter 2 15

T7(10): Chamfer tool 10

T8 (10): Slot cutter 10

Table 4: List of Tools

Tool Type Tool Cost (INR/min)

T1 Drill 1 0.7

T2 Drill 2 0.5

T3 Drill 3 0.3

T4 Drill 4 0.8

T5 Tapping tool 0.7

T6 Mill 1 1.0

T7 Mill 2 1.5

T8 Mill 3 3.0

T9 Ream 1.5

T10 Boring tool 2.0

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

Feature Op. No. Machining Time (min) M/C No. Tool No. TAD

F1 1 3 1 2 3 1 4

F2 2 3 1 2 3 1 6

F3 3 3 2 3 7 6

F4 4 3 2 3 5 6 7

F5 5 5 2 3 5 6 2

F6 6 3 2 3 5 6 6

F7 7 8 9 5 2 3 2 3 4 2

F8 10 1 2 3 4 1

F9 11 12 13 1 2 3 4 2 3 4

F10 14 2 3 5 6

F11 15 1 2 3 1

F12 16 1 2 3 1

F13 17 2 3 5 8

F14 18 2 3 5 6

F15 19 1 2 3 1

F16 20 1 2 3 1

F17 21 2 3 5 6

F18 22 1 2 3 1

F19 23 1 2 3 1

Table 5: Feature Details of the Part

Table 6: Precedence Constraints Between Features and Operations of the Part

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

Figure 3: Flow Chart for the Ant ColonyAlgorithm for Process Planning

Start

Generate Initial Random Sequences

Rearrange the Random Sequences Accordingto Precedence Constraints

Cost Calculation

Initialization of Pheromone

Send 90% of ‘G’ Global Ants for Crossover

Constraint Adjustment Algorithm

Cost Calculation

Update Pheromone Trail Values

Mutation

Send 10% of ‘G’ Global Antsfor Trail Diffusion

Evaporation of Pheromone Trail Value

No If Iteration =Given Iteration

Yes

Generate a Sequence Accordingto Highest Pheromone Value

Constraint Checking and Cost Calculation

Print the Operation Sequence Details with Cost

End

The pheromone matrix generated for the partunder consideration is shown in Table 7.

Two evaluating criteria were used to test theGA’s capability and flexibility of handlingprocess planning problems under differentrequirements. To evaluate the GA’sperformance, 60 trials were conducted(Figure 3). The results are:

Criterion 1: Minimizing total, i.e., CC = MC +TC + MCC + SCC + TCC. The averagemachining cost over 60 trials IS 1751. Theminimum machining cost among is 1739; themaximum machining cost is 1789. One of theprocess plans with a machining cost of 1739is shown in Table 4 together with its number ofmachine changes, setup changes, and toolchanges.

OP: 14 5 6 4 21 1817 22 23 15 1 162 19 20 7 8 39 11 12 13 10

M: 2 2 2 2 2 22 2 2 2 2 22 2 2 2 2 23 3 3 3 3

T: 5 5 5 5 5 55 1 1 1 1 11 1 1 2 3 74 2 3 4 1

TAD: +x +y +y +y –y –y–y –y –y –z –z –z–z –z –z –z –z –z–z –z –z –z –z

Op = Operation; M = Machine; T = Tool;TAD: Tool approach direction number ofmachine changes = 1 Number of setupchanges = 3 Number of tool changes = 8.

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

Total Machining Cost = 1925

CONCLUSIONThe generation of various feasible plans andto find the best among them constitutes anNP-complete combinatorial problem. Hencean efficient heuristic search is required tosolve such problem. We applied the ant colonyalgorithm to solve the problem of generatingoptimal process plan for a given part. Theapproach models process planningconsidering the machine, tool, and toolapproach directions for each operation.Precedence relationships among all theoperations required for a given part are usedas the constraints for the solution space. Thevarious costs considered for finding the optimalplan are machine change cost, tool changecost, setup change cost, machine usage costand tool usage cost. The optimal process planis found based on the minimum total costcriteria. The proposed ant colony algorithm iscoded in Micro Soft Visual C++ and executedon P3 personal computer with 1 GHzprocessor.

The system is developed based on acustomizable job shop environment so thatusers can modify the manufacturing database

Total Machining Cost = 1739

Criterion 2: Minimizing number of machinechanges only, i.e., CC= MCC. Each of the 60trials finds a process plan with zero machinechanges. One of the process plans is shownin Table 5. It can be seen that only onemachine is selected, i.e., the CNC millingmachine.

OP: 14 5 6 4 21 2223 20 1 2 15 1817 16 19 7 8 911 12 13 10 3

M: 3 3 3 3 3 33 3 3 3 3 33 3 3 3 3 33 3 3 3 3

T: 5 5 5 5 5 11 1 1 1 1 58 1 1 2 3 42 3 4 1 7

TAD: +x +y +y +y –y –y–y –y –y ­–z –z –z–z –z –z –z –z –z–z –z –z –z –z

Number of machine changes = 0 Number ofsetup changes = 11 number of tool changes =13.

1 2 3 4 5 6 7

1. 0.000572642 0.001006460 0.899999000 0.000572642 0.000572642 0.000572642 0.000572642

2. 0.000572642 0.000572642 0.000644945 0.899999000 0.000572642 0.000572642 0.000572642

3. 0.899999000 0.000572642 0.000572642 0.000572642 0.000572642 0.000572642 0.000572642

4. 0.000572642 0.000572642 0.000572642 0.000572642 0.000572642 0.000572642 0.899999000

5. 0.899999000 0.000572642 0.000934158 0.000644945 0.000572642 0.000572642 0.000572642

6. 0.000572642 0.000572642 0.000572642 0.000572642 0.899999000 0.000572642 0.000572642

7. 0.000572642 0.000572642 0.000572642 0.000572642 0.000572642 0.899999000 0.000572642

Table 7: Pheromone Matrix for the Part Shown in Figure 2

Note: X-axis = Position; and Y-axis = Operation.

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Int. J. Mech. Eng. & Rob. Res. 2012 P S Srinivas et al., 2012

to suit their needs. This makes the systemmore realistic compared to the approaches inwhich a fixed machining environment isassumed. This is found to be advantageousover the previous approaches. This work canbe further extended by integrating the processplanning with scheduling with an objective ofminimizing the makespan.

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