Application of genetic algorithm in integrated setup planning and operation sequencing Sajad Kafashi a and Mohsen Shakeri b a
Department of Mechanical Engineering Babol University of Technology Babol, Mazandaran, Iran
[email protected]. b Department of Mechanical Engineering Babol University of Technology Babol, Mazandaran, Iran Abstract. Process planning is an essential component for linking design and manufacturing process. Setup planning and operation sequencing is two main tasks in process planning. Many researches solved these two problems separately. Considering the fact that the two functions are complementary, it is necessary to integrate them more tightly so that performance of a manufacturing system can be improved economically and competitively. This paper present a generative system and genetic algorithm (GA) approach to process plan the given part. The proposed approach and optimization methodology analyses the TAD (tool approach direction), tolerance relation between features and feature precedence relations to generate all possible setups and operations using workshop resource database. Based on these technological constraints the GA algorithm approach, which adopts the feature-based representation, optimizes the setup plan and sequence of operations using cost indices. Case study show that the developed system can generate satisfactory results in optimizing the setup planning and operation sequencing simultaneously in feasible condition. Keywords: process planning, setup planning, operation sequencing, integerated setup planning and operation sequencing (ISOS), genetic algorithm. PACS: 81.20.Wk
INTRODUCTION It is well known that there is a functional gap between CAD and CAM, which is expected to be bridged by computer-aided process planning (CAPP). Setup planning and operation sequencing are the most important activity in CAPP. While there have been great successes in automating setup planning and operation sequencing separately, the integeration between them still remain elusive. The most recent works related to setup planning and operation sequencing and optimization can be listed as follows: Huang et al. apply graphs to represent the tolerance and datum relationship among features in setup planning; the problem of identifying the optimal setup plan is transformed into a graph search problem [1]. Liu and Huang further proposed a concept of normalized tolerance to measure the tightness of tolerance, which is an angle representing the maximum permissible rotation error when locating a component, and therefore, the smaller the normalized tolerance, the tighter the underlying tolerance [2]. Ong applied a fuzzy-set based methodology to handle some CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER imprecise and qualitative information [3].Ong and Nee applied a hybrid GA and SA CP1315, International Conference on Advances in Materials and Processing Technologies (AMPT2010) Edited by F. Chinesta, Y. Chastel, and M. El Mansori © 2010 American Institute of Physics 978-0-7354-0871-5/10/$30.00
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approach for dynamic setup planning optimization. They used concurrent constraint planning methodology, a hybrid genetic algorithm (GA) and simulated annealing (SA) approach for set approach setup up planning and rere-set-up planning in a dynamic workshop environment [4]. Guo et al modeled operation sequencing as a combinatorial optimization problem, and a modern evolutionary algorithm, i.e. the particle swarm optimization (PSO) algorithm, has been employed and m modified odified to solve it effectively [5]. This research presents a GA-based optimization algorithm in integerated setup planning and operation sequencing (ISOS).
REPRESENTATION OF TH THE E ISOS PROBLEM Setup planning and operation sequencing are the basic issues in CAPP. These two problems have a strong impact on manufacturabilit manufacturability, y, total time and production cost. Setup planning is an intermediate phase of process planning, and automating setup planning constitutes the core of a CAPP system. Operation sequencing used to determine the sequence of machining operations required to produce a part. Fig. 1 shows a part composed of features. Each feature can be manufactured by one or more machining operations ( operations in total for the part). Each operation can be executed by several several alternative plans if different machines, cutting tools, or TADs are chosen for this operation. For machining a given prismatic part on 3-axis machine, there are six case of TAD ( ). Some features may have more than one TAD according according to the accessibility of tool into the feature. For example in Fig. 2, and 2, F1 (through hole) has two possible TADs, i.e. and F2 (corner slot) , and . has four possible TADs, i.e. ,
FIGURE 1. Representation Representation ao ISOS problem (a chromosome).
The constraints of ISOS ISOS is a sequence optimization problem subject to various geometrical and technological constraints. In order to reach optimum ISOS with high product quality and minimal cost and time in feasi feasible ble condition, these constraints should be considered in problem. The first and basic task in setup planning is to group features of the part. Based on TADs of features, the features which have same TADs can be classified in same group. Except TAD that men mentioned tioned, feature precedence relationship and tolerance tolerance relationship are main factors that constraint the ISOS problem and optimization. For example when two features have a geometrical tolerance relation, the datum feature (DF) should be machined before machining feature (MF (MF). ). Moreover the DF and MF should be allocated in same setup as much as it possible.
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FIGURE. 2. Tool approach directions (TAD).
In this research, all this constraints on setup planning are analyzed and converted to precedence relationships between operations by a precedence relation matrix ( ). For a part with features and operations, the feature precedence relations obtained will be stored in the PRM, which is a matrix:
If operation
must be executed before operation ,
, otherwise
!.
GENETIC ALGORITHM The GA mimics the process of natural evolution by combining the survival of the fittest among solution structures with a structured, yet randomized, information exchange and creates child. In GA, a candidate solution is represented by a sequence of numbers known as chromosome or string. In the present work, each element (gene) in a string (chromosome) represents an operation. The order of the elements in the string represents the sequence to be followed. The proposed operators of GA inculde crossover and mutation in this section are similar to the GA presented in Salehi and Tavakkoli- Moghaddam [6]. The probability of applying the mutation and crossover operators is defined as , " respectively. Fitness function: Machining cost can be used to measure the quality of a process plan quantitively. The cost factor is a composite of: (1) machine tool utilization (depreciation of machine tools), (2) tool utilization cost (due to wear and tear), (3) machine tool change cost (there are often waiting times for the needed machine tool to be available) (4) tool change cost, (5) setup change costs, (6) additional penalty costs ( a penalty cost for violated constraints). Using these cost factors to form a cost function as the optimization objective function for the algorithm, feasible setup plan and operation sequence with the minimum cost can be found. Thus the total cost (TC) of a particle defines as: #$ $ #$ # $$ #%$ ##$$ & $ (6) Where MC is the total costs of the machine tools used in a setup plan, TC is the total costs of the cutters, TMCC is the total machine change cost, TSC is the total setup change cost, TTCC is the total cutter change cost and APC total addentional penalty
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cost. The term of APC added to ensure that each particle matches with the constraints represented as PRM
CASE STUDY A prismatic part with 10 manufacturing features is used to demonstrate the capability of the proposed algorithm for a CAPP system (Fig. 2). These features can be machined with 12 operations ( ). Fig. 3 shows the RPM for given part. As an example, the PRM shows that Op5 should be operated before Op2 and Op4 (tolerance relation). Also, inorder to produce the part with considered tolerance specifications, fearture F3 must be machined through drilling, boring and reaming operations (the value of tolerance 0.01 on feature F3 is tight). The available workshop resource is assumed to consist of four machine tools and ten cutters. The information about the machines and tools and their cost and operation methods are listed in Table 1 and 2.
FIGURE 3. A sample of prismatic part.
FIGURE 4. PRM for case study part.
After many trials, Swarm Size has been set as 100 and Iteration Number as 60, which are large enough to obtain favorable results for the part. The values !' and " !'() have been shown to yield good performance of the PSO algorithm.
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TABLE 1. Available machine and tool resource and cost. Machine_id M1 M2 M3 M4 Tool_id C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 MCC=160
Type Drill press 3-axis vertical milling machine CNC 3-axis vertical milling machine Boring machine Type Drill 1 Drill 2 Drill 3 Drill 4 Mill cutter 1 Mill cutter 2 Mill cutter 3 Boring tool Reamer Slot cutter TCC=20 SCC=120
MCI 10 40 100 60 TCI 7 5 3 8 7 10 15 30 20 15 PC=650
TABLE 2. Operation method information. Feature
Feature type
Operation(Op_id)
Machine candidate
Tool candidate
F1 F2 F3
Pocket Blind hole Through hole
F4 F5 F6 F7 F8 F9 F10
Four Through hole Slot Slot Two Blind hole Two Slot Pocket Pocket
Milling(Op1) Drilling (Op2) Drilling (Op3) Reaming (Op4) Boring (Op5) Drilling (Op6) Milling (Op7) Milling (Op8) Drilling (Op9) Milling (Op10) Milling (Op11) Milling (Op12)
M2, M3 M1, M2, M3 M1, M2, M3 M1, M2, M3 M3, M4 M1, M2, M3 M2, M3 M2, M3 M1, M2, M3 M2, M3 M2, M3 M2, M3
T5, T6, T7 T2, T3, T4 T2, T3, T4 T9 T8 T2 T5, T6 T5, T6 T1 T6, T7, T10 T5, T6, T7 T5, T6, T7
TAD candidate
Results Table 3 shows an optimum setup plan and operation sequence for case study part. The sequence of operations is determined by the order of operations; the total cost of the chromosome is 1978. The setup planning strategy is shown in Table 4. The whole part can be machined in six setups with two machine tools. TABLE 3. Optimum result (total cost = 1978). Operation Machine Tool
Op11 M2 T6
Op12 M2 T6
Op1 M2 T7
Op6 M2 T2
Op10 M2 T10
Op3 M2 T4
Op8 M3 T6
Op9 M3 T1
Op5 M3 T8
Op7 M3 T6
Op4 M3 T9
Op2 M3 T3
TAD
Fig. 5 shows a typical evolutionary process for the example, which is plotted according to the average results of 5 trials. The optimal solution can be obtained on average at the 17th generation for the above parameter set.
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TABLE 4. Setup plan strategy. Setup Number 1 2 3 4 5 6
TAD -x +x -z +z +y -z
Machine M2 M2 M2 M2 M3 M3
Executing Operations Op11 Op12 Op1, Op6 Op10, Op3 Op9, Op8 Op4, Op2, Op5, Op7
FIGURE 5. Evolutionary process for the study case.
CONCLUSION This research aims to integrate the setup planning and operation sequencing problems for FMS (flexsible manufacturing system) environment. The developed optimization model can find the best setup plan and sequence of operations via minimum cost simultaneously. Precedence relationship and tolerance violation are two major problems that must be avoided in ISOS problem which is attached to the overall cost as penalty functions. To solve the problem, a GA approach is developed. For an industrial case study, we obtained an optimal solution. Various examples show that the proposed GA approach is efficient to the ISOS problems and can obtain a satisfactory result for the setup planning and sequencing problem in process planning.
REFERENCES 1. Huang, S.H., Zhang, H.-C. and Oldham, W.J.B. (1997) ‘Tolerance analysis for setup planning: a graph theoretical approach’, International Journal of Production Research, Vol. 35, No. 4, pp.1107– 1124. 2. Liu, Q. and Huang, S.H. (2000) ‘Geometric tolerance normalization and its application', Transactions of the North American Manufacturing Research Institution/SME, Vol. 28, pp.305–310. 3. ONG, S. K., 1995, an intelligent fuzzy set-up planner for the machining environment. PhD thesis, National University of Singapore. 4. Li, W. D., Ong, S. K., and Nee, A. Y. C. Hybrid genetic algorithm and simulated annealing approach for the optimization of process plans for prismatic parts. Int. J. Prod. Res., 2002, 40(8), 1899–1922. 5. Guo, Y. W., Mileham, A. R., Owen, G. W., and Li, W. D. Operation sequencing optimization using a particle swarm optimization approach. Proc. IMechE, Part B: J. Engineering Manufacture, 2006, 220(B12), 1945–1958. 6. Salehi,M.,&Tavakkoli-Moghaddam, R. (2009).Application of genetic algorithm to computer-aided process planning in preliminary and detailed planning. Engineering Applications of Artificial Intelligence, 22, 1179–1187.
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