Genetic Algorithms in Problem Space for Sequencing Problems
Abstract
In this paper, genetic algorithms will be developed for sequencing type problems of importance in manufacturing systems. The proposed algorithms are based on an auxiliary problem domain called “problem space” [15, 17]. Problem space provides a framework in which problem-specific information can be incorporated explicitly into local search heuristics. The proposed space has been found to be well suited for search by genetic algorithms perhaps because standard crossover can be used. In this paper, properties of problem space will be discussed, then three test cases will be presented which illustrate the usefulness of the method. The test problems we present are 1) the number partitioning problem, 2) the classic job shop scheduling problem (JSP) with minimum makespan as the objective, and 3) the “standard cell placement problem” which arises in the design of VLSI circuits.
Keywords
Genetic Algorithm Local Search Simulated Annealing Problem Space Local Search HeuristicPreview
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References
- 1.Adams, J., E. Balas and D. Zawack, (1988). “The Shifting Bottleneck Procedure for Job Shop Scheduling”, Management Science, 34(3), 391–401.CrossRefGoogle Scholar
- 2.Applegate, D. and Cook, W. (1991). “A Computational Study of the Job-Shop Scheduling Problem”, ORSA Journal on Computing, 3(2), 149–156.Google Scholar
- 3.Bartholdi, J. J., and Platzman, L. K., (1985). “Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidian Space”, Management Science, 34(3), 291–305.CrossRefGoogle Scholar
- 1.Carlier, J. and E. Pinson, (1989). “An Algorithm for Solving the Job-Shop Problem,” Management Science, 35 164–176.CrossRefGoogle Scholar
- 2.Committee On the Next Decade of Operations Research (CONDOR), (1988). “Operations Research: The Next Decade,” Operations Research, 36(4).Google Scholar
- 3.Goldberg, D. E., and Lingle, R. (1985). “Alleles, Loci, and the Traveling Salesman Problem”, In J. Greffenstette (ed.) Proceedings of an International Conference on Genetic Algorithms and Their Applications, Carnegie Mellon University.Google Scholar
- 4.Greffenstette, J. J., Gopal, R., Rosmaita, B., and Van Gucht, D. (1985). “Genetic Algorithms for the Traveling Salesman Problem”, In J. Greffenstette (ed.) Proceedings of an International Conference on Genetic Algorithms and Their Applications, Carnegie Mellon University.Google Scholar
- 5.Johnson, D.S., Papadimitriou, H., and Yannnakakis, M. (1988). “How Easy is Local Search?”, Journal of Computer and System Science. 37(1). 79–100.CrossRefGoogle Scholar
- 6.Johnson, D.S., Aragon, C.R., McGeoch, L.A., and Schevon, C. (1991). “Optimization by Simulated Annealing: an Experimental Evaluation; Part II Graph Coloring and Number Partitioning”, Operations Research 39(3), 378–406.CrossRefGoogle Scholar
- 7.Kang, S., (1983). “Linear Ordering and Application to Placement”, Proceedings of the 20th Design Automation Conference, pp 457–464.Google Scholar
- 8.Karmarkar, N. and Karp, R.M., (1982). “The Differencing Method of Set Partitioning”. Report No. UCB/CSD 82/113, Computer Science Division, University of California, Berkeley.Google Scholar
- 9.Muth, J.F., P. Thompson and P. Winters (eds.), (1963). Industrial Scheduling, Prentice-Hall, Englewood Cliffs New Jersey.Google Scholar
- 10.Papadimitriou, C.H. and K. Steiglitz, (1982). Combinatorial Optimization Algorithms and Complexity, Prentice Hall Inc., Englewood Cliffs, New Jersey.Google Scholar
- 11.Sechen, C. and Sangiovanni-Vincentelli, A. (1985). “The TimberWolf Placement and Routing Package”, IEEE Journal of Solid-State Circuits, 20(2). 510–522.CrossRefGoogle Scholar
- 12.Storer, R.H., Wu, S.D. and Vaccari, R. (1990). “New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling”, to appear, Management Science .Google Scholar
- 13.Storer, R.H., Wu, S.D. and Vaccari, R. (1991). “Local Search in Problem and Heuristic Space for Job Shop Scheduling”, Working Paper, Dept. of Industrial Engineering, Lehigh University, Bethlehem, PA.Google Scholar
- 14.Storer, R.H. and Wu, S.D. (1991). “Local Search in Problem and Heuristic Space for Job Shop Scheduling Genetic Algorithms”, to appear in Proc. Joint US-German Conf. on New Directions of OR in Manufacturing.Google Scholar
- 15.Whitley, D., Starkweather, T. and Fuquay, D. (1989). “Scheduling Problems and Traveling Salesmen: The Genetic Edge Recombination Operator” Proceedings of the Third International Conference on Genetic Algorithms. George Mason University, Morgan Kaufman Publishers, San Mateo CA.Google Scholar