V. Palade, R.J. Howlett, and L.C. Jain (Eds.): KES 2003, LNAI 2774, pp. 1000-1007, 2003. Springer-Verlag Berlin Heidelberg 2003

A Tabu Search-Based Optimization Approachfor Process Planning

WD Li1, SK Ong2, YQ Lu1, and AYC Nee2

1 Singapore Institute of Manufacturing Technology71 Nanyang Drive, Singapore 638075

wdli,yqlu@SIMTech.a-star.edu.sg2 Department of Mechanical Engineering, National University of Singapore

10 Kent Ridge Crescent, Singapore 119260mpeongsk, mpeneeyc@nus.edu.sg

Abstract. In this paper, crucial processes in a computer-aided processplanning system, such as selecting machining resources, determiningset-up plans and sequencing operations of a part, have been consideredsimultaneously and modelled as a constraint-based optimization prob-lem, and a Tabu search-based approach has been proposed to solve iteffectively. In the optimization model, costs of the utilized machinesand cutting tools, machine changes, tool changes, set-ups and departureof good manufacturing practices (penalty function) are integrated as anoptimization evaluation criterion. A case study, which is used to com-pare this approach with the genetic algorithm and simulated annealingapproaches, is discussed to highlight the advantages of this approach interms of solution quality, computation efficiency and the robustness ofthe algorithm.

1 Introduction

Computer-Aided Process Planning (CAPP) is an essential component for linking thevarious models and processes in a Computer-Integrated Manufacturing System(CIMS). Process plans generated by a CAPP system should ensure the consistency ofthe desired functional specifications of a part during its production processes and theobservation of good practices to manufacture the part economically and competi-tively. Conventionally, a generative CAPP system consists of three main consecutiveactivities: (1) recognizing manufacturing features from a designed part; (2) deter-mining machining operation types and enumerating alternative set-up plans as well asapplicable machining resources in a dynamic workshop environment; and (3) select-ing suitable set-up plans and machining resources, and sequencing machining opera-tions to seek the lowest machining cost of the part. A global optimum process plancan be achieved from an optimization of each individual activity. The above thirdactivity, which is the focus of this paper, can be modelled as an optimization problemand solved using some intelligent techniques. Recently, many approaches have been

A Tabu Search-Based Optimization Approach for Process Planning 1001

developed and the appeared work can be categorized as the knowledge-based rea-soning approach [1, 2], graph manipulation approach [3], Petri-nets-based approach[4], fuzzy logic reasoning approach [5], evolutional algorithm and heuristic reason-ing-based approach [6, 7], etc. However, such a problem is well known to be an in-tractable reasoning and decision-making process considering the inter-related geomet-ric relationships between features, the complex technological requirements and themultiple evaluation criteria. To address this problem effectively, effort should bemade to design a more apt optimization model and develop a more efficient optimi-zation method.

In this paper, selecting machining resources, determining set-up plans and se-quencing operations for the process planning of a prismatic part are incorporated asan optimization model. In this model, six criteria are evaluated: (1) cost of machinesutilization, (2) cost of cutting tools utilization, (3) number of machine changes, (4)number of tool changes, (5) number of set-ups, and (6) number of violated constraints(a penalty function). A Tabu Search (TS)-based approach has been developed toeffectively search for optimized process plans in a large-size multiple-dimensionalspace. Through comparisons of this approach with a Genetic Algorithm (GA) and aSimulated Annealing (SA) approach for a prismatic part under different workingconditions, the merits of the approach can be illustrated clearly.

2 Knowledge Representation of Process Planning

A process plan for a part consists of a set of machining operations. Each operation isrepresented as a bit and the set of the bits for a process plan is arranged as a sequence.In each operation, there is a set of alternative machines, cutting tools and set-ups(here simplified and represented as Tool Approach Directions (TADs)) under whichthe operations can be executed. The proposed TS approach is used to determine theoptimized sequence of the operations and the utilized machine, cutting tool and TADchosen from their corresponding candidates according to certain optimization criteria.In an object-oriented description, an operation (bit) and a process plan can be repre-sented as follows.

class operation // An operation // The id of the operation int Operation_id; // The id of a machine chosen to execute the operation int Machine_id; // The alternative machines for executing the operation int[] Mac_list = new int[20]; // The id of a cutting tool chosen to execute the operation int Tool_id; // The alternative cutting tools for executing the operation int[] Tool_list = new int[20]; // The id of a TAD to apply the operation int TAD_id; // The alternative TADs for applying the operation int[] TAD_list = new int[20]; // The machining parameters of the operation data_type Oper_para; // A process plan with n operations

operation[] Oper = new operation[ n ];

1002 WD Li et al.

The optimization criteria can be represented as follows.

(1) Total Machine Cost (TMC )

∑==

n

iidMachineiOperMCidMachineiOperTMC

1])_].[[*_].[( (1)

where MC is the Machine Cost of a machine.

(2) Total Tool Cost (TTC )

∑==

n

iidTooliOperTCidTooliOperTTC

1])_].[[*_].[( (2)

where TC is the Tool Cost of a tool.

(3) Number of Set-up Changes ( NSC ), Number of Set-up ( NS ), and Total Set-upCost (TSC )

))_].1[,_].[(),_].1[,_].[(( 111

12 idTADiOperidTADiOperidMachineiOperidMachineiOperNSC

n

i+Ω+Ω∑Ω=

−

=(3)

NSCNS +=1 (4)

∑==

NS

iSCTSC

1(5)

where YXYX

YX=≠

=Ω01

),(1 , otherwise

YXYX

010

),(2==

=Ω .

(4) Number of Machine Changes ( NMC ) and Total Machine Change Cost (TMCC )

∑ +Ω=−

=

1

11 )_].1[,_].[(

n

iidMachineiOperidMachineiOperNMC (6)

∑==

NMC

iMCCTMCC

1(7)

(5) Number of Tool Changes ( NTC ) and Total Tool Change Cost (TTCC )

∑ +Ω+ΩΩ=−

=

1

1112 ))_].1[,_].[(),_].1[,_].[((

n

iidTooliOperidTooliOperidMachineiOperidMachineiOperNTC (8)

∑==

NTC

iTCCTTCC

1(9)

(6) Number of Violating Constraints ( NVC ) and Additional Penalty Cost ( APC )

∑ Ω∑=−

= +=

1

13

1))_].[,_].[(

n

i

n

ijidOperationjOperidOperationiOperNVC (10)

A Tabu Search-Based Optimization Approach for Process Planning 1003

A fixed Penalty Cost ( PC ) is applied to each violated constraint. Thus

∑==

NVC

iPCAPC

2(11)

Where

sconstraint toaccordancein is operations and of sequence The sconstraint violatesoperations and of sequence The

01

),(3 YXYX

YX =Ω

.

(7) The Total Weighed Cost (TWC )

APCwTCCwMCCwSCwTCwMCwTWC ****** 654321 +++++= (12)

where 61 ww − are the weights.Based on these concepts, the process planning optimization model can be repre-

sented as follows:)( xTWCMin

x

0)( .. =xNVCts for all constraintsplans process Trial∈x

3 TS-Based Optimization Algorithm

A typical TS is used here and it consists of three main strategies, viz., the forbiddingstrategy, freeing strategy and aspiration strategy [8]. The forbidding strategy controlsthe solution that enters a Tabu list. The freeing strategy is used to manage the solutionthat exits the Tabu list and when. The aspiration strategy is the interplay between theforbidding and freeing strategies for selecting trial solutions. Some basic elements inthe algorithm are briefly stated as follows.

1. Initial plan, current plan and elite plan. An initial plan is generated with n op-erations. The sequence of the n operations is randomly arranged, and the ma-chine, tool and TAD for the execution of an operation in the plan are randomlydetermined from the corresponding candidate lists. The current plan is the opti-mized solution in each iteration and is used for generating the neighbourhoodtrial solutions. An elite plan records the best solution found so far.

2. Neighbourhood strategies. A set of variant plans can be generated from a currentplan for trials using neighbourhood strategies. The neighbourhood strategies in-clude two basic manipulations. The first mutation manipulation randomlychooses a set of machines, tools and TADs from the alternative lists to replacethe current ones in the operations of a plan. The second manipulation changes thesequence of two operations in a plan using shifting, swapping or adjacent swap-ping operations [7].

1004 WD Li et al.

3. Forbidding and freeing strategies. The forbidding strategy can avoid cycling andlocal minimums by forbidding certain moves during the most recent computa-tional iterations. The freeing strategy is used to delete the forbidding restrictionsof some solutions so that they can be reconsidered in the future search. A Tabulist, which is stored as a linked list and managed as a “first-in-first-out” (FIFO)queue, is employed to store recently visited current plans to realize the abovestrategies. Using a Hamming Distance ( HD ) defined in equation (13), a currentplan iOper can be compared with a plan jOper stored in the Tabu list to determinetheir similarity, and whether and when to apply the forbidding or freeing strate-gies.

different. be toconsidered are plans twoThe same. theconsidered are plans twoThe

0

])[],[(1

1∑ =Ω==

n

lji otherslOperlOperHD (13)

4. Aspiration strategy. When a plan is forbidden by Tabu restrictions, an aspirationstrategy can enable this plan to become acceptable as a current plan if it satisfiesa certain criterion. This strategy can provide some flexibility to the Tabu restric-tions by leading the move in a desirable direction. A common criterion is to over-ride a tabooed plan if its machining cost is lower than that of the elite plan.

5. Stopping criteria. Termination conditions for the searching algorithm can be setusing one of the following criteria: (a) the iterations reach a pre-defined number;and (b) the elite plan is kept unchanged for a pre-defined number of iterations.

4 A Case Study

A sample prismatic part illustrated in Figure 1 is used to demonstrate the perform-ances of TS, SA and GA on the same optimization model to highlight their charac-teristics. The part consists of 14 STEP-defined manufacturing features and machiningoperations ( 14=n ). The relevant information for machining resources, features andoperations of the part are given in Table 1.

Fig. 1. A sample part with 14 features

A Tabu Search-Based Optimization Approach for Process Planning 1005

Table 1. The operation and machining information

Features Operations TADs Machines ToolsF1 Drilling (Oper1) +z, -z M1, M2, M3 C1

F2 Milling (Oper2) -x, +y,-y, -z

M2, M3 C8

F3 Milling (Oper3) +y M2, M3 C5, C6

F4 Milling (Oper4) +y M2 C5, C6

F5 Milling (Oper5) +y, -z M2, M3 C5, C6

F6 Drilling (Oper6) +z, -z M1, M2, M3 C2

F7 Drilling (Oper7) +z, -z M1, M2, M3 C1

F8 Milling (Oper8) +x M2, M3 C5, C6

F9 Drilling (Oper9) -z M1, M2, M3 C1

F10 Milling (Oper10) -y M2, M3 C5, C6

F11 Milling (Oper11) -y M2, M3 C5, C7

F12 Drilling (Oper12) +z, -z M1, M2, M3 C1

F13 Milling (Oper13) -x, -y M2, M3 C5, C6

F14 Drilling (Oper14) -y M1, M2, M3 C1

The following two conditions are chosen for the studies.

(1) All machines and tools are available, and 51 ww − in equation (12) are set as 1; and

(2) All machines and tools are available, and 1,0 43152 ===== wwwww .

The computations illustrated in Figures 2 were made for the part under Condition(1). In Table 2, more thorough comparisons for the three algorithms under the twoconditions were made. It shows that the decreasing trends of the curves for TS andGA are smoother than that of SA. Generally, TS and SA can achieve better (lowermachining costs) solutions than GA, while TS can achieve more stable performancethan SA and GA in terms of lower mean, maximum and minimum machining costs ofthe obtained best process plans. These observations are in accordance with the maincharacteristics of GA, which is prone to “premature” (convergent too early and hardto find the optimal or near-optimal solutions), and SA, which is vigilant to parametersand problems.

(a) Optimized results for intermediate (b) Optimized results for intermediatecurrent plans elite plans

Fig. 2. Comparison studies of three algorithms under Condition (1)

1006 WD Li et al.

Table 2. Comparison studies of three algorithms under two conditions

Tabu SearchSimulatedAnnealing

GeneticAlgorithm

Mean 1342.0 1373.5 1611.0Maximum 1378.0 1518.0 1778.0Condition

(1) Minimum 1328.0 1328.0 1478.0Mean 1194.0 1217.0 1482.0

Maximum 1290.0 1345.0 1650.0Condition(2) Minimum 1170.0 1170.0 1410.0

5 Conclusions

In this paper, a TS-based approach has been developed to optimize the processes ofselecting machining resources, determining set-up plans and sequencing operationsfor process planning of a prismatic part. The proposed approach can generate optimalor near-optimal process plans for a prismatic part with good computation efficiencybased on a combined machining cost criterion with weights. The optimization modelcan conveniently simulate a practical dynamic workshop through changing the strat-egy of cost evaluation. Through comparison studies, the characteristics and advan-tages of the approach are highlighted.

References

[1] Chang, T.C., Expert Process Planning for Manufacturing. New York: Addison-Wesley, (1990).

[2] Tseng, Y.J., Liu, C.C., Concurrent analysis of machining sequences and fix-turing set-ups for minimizing set-up changes for machining mill-turn parts. In-ternational Journal of Production Research, (1998) 39, 4197-4214.

[3] Lin, A.C., Lin, S.Y., Diganta, D. and Lu, W.F., An integrated approach todetermining the sequence of machining operations for prismatic parts with in-teracting features. Journal of Materials Processing Technology, (1998) 73, 234-250.

[4] Kruth, J.R. and Detand, J., A CAPP system for nonlinear process plans. Annalsof the CIRP, (1992) 41, 489-492.

[5] Ong, S.K. and Nee, A.Y.C., Application of fuzzy set theory to set-up planning.Annals of the CIRP, (1994) 43, 137-144.

[6] Zhang, F., Zhang, Y.F. and Nee, A.Y.C., Using genetic algorithms in processplanning for job shop machining. IEEE Transactions on Evolutional Computa-tion, (1997) 1, 278-289.

A Tabu Search-Based Optimization Approach for Process Planning 1007

[7] Li, W.D., Ong, S.K. and Nee, A.Y.C., 2002, Hybrid genetic algorithm andsimulated annealing approach for the optimization of process plans for pris-matic parts. International Journal of Production Research, (2002) 40, 1899-1922.

[8] Glover, F. Tabu Search, Kluwer Academic Publishers, US. (1997).