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1 An Adaptive GA for Multi Objective Flexible Manufacturing Systems A. Younes, H. Ghenniwa, S. Areibi uoguelph.ca July 2002 GECCO 2002, New York

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2 Outline Introduction Background (Flexible Manufacturing Systems) Motivation/Contributions Example Mathematical Formulation Genetic Algorithm Implementation Numerical Testing and Comparison. Conclusions & Future Work. GECCO 2002, New York

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3 Introduction Flexible Manufacturing Systems consist of multiple heterogenous machines (robots/computers). Ultimate goal: is to maximize the FMS throughput. Several problems such as part type partitioning, assignment and sequencing must be solved before this goal can be achieved. This work is an initial investigation for the suitability of Genetic Algorithms to solve Dynamic Optimization problems associated with scheduling/sequencing in FMS systems. GECCO 2002, New York

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4 Background The goodness of an assignment is measured in terms of minimizing part transfer (primary) and balancing the work-load of the machines (secondary). The aim is to facilitate the creation of machine cells with minimum part transfer while maximizing the utilization of machines. While minimizing part transfer tends to favor the assignment of the whole of a part to a single machine, balancing work-load tries to make the work-load distribution even among the machines. GECCO 2002, New York

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5 Motivation A large number of combinatorial problems are associated with Manufacturing Optimization. Many short comings from current techniques used for dynamic optimization problems. This work is used as foundation for future work in the area of dynamic scheduling/sequencing of Flexible Manufacturing Systems. Techniques developed for such problems can be easily adapted for other type of problems that are dynamic in nature. GECCO 2002, New York

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6 Contribution One of the main contribution of this work is developing an automated technique to generate benchmarks for Flexible Manufacturing Systems (both Static and Dynamic Benchmarks) Several crossover techniques have been developed and tested for Flexible Manufacturing Systems. Not too much work has been done in the literature on solving dynamic optimization problems for Flexible Manufacturing Systems. This work lays the foundation for Evolutionary dynamic optimization strategy for scheduling/sequencing of FMS. GECCO 2002, New York

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7 Mathematical Formulation F 1 : Minimization of part transfer (by minimizing the number of machines required to process the part) F 2 : Minimization of the number of necessary operations required from each machine over the possible processing choices. F 3 : Load balancing by minimizing the cardinality distance between the workload of any pair of machines. Over multi-objective mathematical model of FMS is to solve for F 1, F 2, F 3 Subject to a part being processed by a single machine. GECCO 2002, New York

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8 FMS Example M1 O1 O2 O3 O5 M2 O2 O3 O5 M3 O4 O5 P1 O1 O2O3 O5 P2 O2 O3O5 P1 P2 Four operations needed to process P1 Three operations needed to process P2 M1 can perform Four operations Two part types & Three Machines GECCO 2002, New York M2 can perform three operations M3 can perform two operations This choice tries to minimize part transfer between machines

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9 FMS Example M1 O1 O2 O3 O5 M2 O2 O3 O5 M3 O4 O5 P1 P2 Two part types & Three Machines GECCO 2002, New York This choice tries to distribute workload (operations) evenly between machines P1 O1 O2O3 O5 P2 O2 O3O5

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10 A GA Algorithm for FMS Genetic Algorithms are well suited for multiple-objective optimization problems. The basic feature of GA is multiple directional and global search through maintaining a population of potential solutions from generation to generation. In our implementation we have combined a Pareto-based approach with an adaptive weighted sum technique for tackling the multi-objective flexible manufacturing systems problem. One of the main issues is determining the fitness value of individuals according to multiple objectives. GECCO 2002, New York

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11 GA Main Componenets Representation Fitness Function Selection & Deletion Transformation Functions GECCO 2002, New York

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12 Chromosome Representation M1 O5 P1 P2 GECCO 2002, New York P1 O1 O2 O3 O5 P2 O2 O3O5 M1 M2M3M1M2M3 Chromosome O2O1O3 O2O5 O4 M2 M3 P1P2

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13 Fitness Function GECCO 2002, New York normalized The weights determine which of the two objectives is favored Two objectives are considered

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14 Crossover GECCO 2002, New York PARENT 1M1M2M4M3M2M4M5 PARENT 2M3 M4M5M1M2M4 PART1PART2 CHILD 1M1M2M4M3M1M2M4 ` CHILD 2M3 M4M5M2M4M5 Simple Crossover Cut points set at the part delimiter

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15 Crossover GECCO 2002, New York PARENT 1M1M2M4M3M2M4M5 PARENT 2M3 M4M5M1M2M4 PART1PART2 CHILD 1M1M3M4M5M2 M5 CHILD 2M3M2M4M3M1M4 Uniform Crossover A Cut point for each gene delimiter ` ` `` ` `

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16 Crossover GECCO 2002, New York PARENT 1M1M2M4M3M2M4M5 PARENT 2M3 M4M5M1M2M4 PART1PART2 CHILD 1M1M2M4M5M1M2M4 ` CHILD 2M3 M4M3M2M4M5 Structured Crossover Cut points Randomly set in the string

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17 GA Algorithm GECCO 2002, New York initialize pop. ; evaluate initial pop. ; while not stopping condition { select fittest parents for reproduction; apply crossover & mutation; evaluate pop.; }

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18 Benchmarks Several Benchmarks used to evaluate the performance of the GA for FMS. Randomly generated with different M/P/O. The Generator can be used for both Dynamic & Static optimization solvers. GECCO 2002, New York

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19 Benchmarks (Statistics) GECCO 2002, New York

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20 Results & Discussion The Genetic Algorithm code was developed on a Sun Sparc Ultra 10 Workstation running Solaris 8. The Code was written in C and compiled using GNU g++ version Results obtained were first run using the Genetic Algorithm by optimizing each objective function separately. The Genetic Algorithm was then run by optimizing both objective functions together. GECCO 2002, New York

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21 GA Convergence

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22 Crossover Operator

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23 Machines Involved GECCO 2002, New York

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24 Cont.. Machines Involved GECCO 2002, New York

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25 Cont.. Machines Involved GECCO 2002, New York

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26 Operations Per Machine GECCO 2002, New York

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27 Operations Per Machine GECCO 2002, New York

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28 Operations Per Machine GECCO 2002, New York

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29 Conclusions In this paper we introduced an adaptive Genetic Algorithm for Flexible Manufacturing Systems. A random benchmark generator was developed for both static and dynamic problems. Results obtained indicate that our Genetic Algorithm implementation achieves excellent results with respect to part transfer and balancing the work among the machines. Currently we are testing the Genetic Algorithm on a Dynamic version for Flexible Manufacturing where one or more machines may fail during optimization. GECCO 2002, New York

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30 Future Work Compare this Genetic Algorithm implementation with other advanced search techniques ( Tabu Search, GRASP ) for both static and dynamic problems. Incorporate local search with the Genetic Algorithm to create a Memetic Algorithm Include sequencing constraints and tools costs in the objective function. Integrating Multi Agent Systems with Genetic Algorithms for complex dynamic optimization approaches. GECCO 2002, New York

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31 All Source Code is Available at the following web site: GECCO 2002, New York

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