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The Grouping Genetic Algorithm

  • Emanuel Falkenauer
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

An important class of difficult optimization problems are grouping problems, where the aim is to group together members of a set (i.e. find a good partition of the set). In this paper we present the Grouping Genetic Algorithm (GGA), which is a Genetic Algorithm (GA) heavily modified to suit the structure of grouping problems. We first show why both the standard and the ordering GAs fare poorly in this domain, by pointing out their inherent difficulty to capture the regularities of the functional landscape of the grouping problems. We then propose a new encoding scheme and genetic operators adapted to these problems, embodied by the GGA. An experimental evaluation of the GGA on several different problems shows its superiority over standard GAs when applied to grouping problems. The potential of the algorithm is further illustrated by its application to the Bin Packing Problem, where a hybridised GGA outperforms one of the best Operations Research techniques to date.

Keywords

Genetic Algorithm Encode Scheme Crossover Operator Genetic Operator Hard Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Belew, R. K., & Booker, L. B. (Eds.) (1991). Proceedings of the Fourth International Conference on Genetic Algorithms, University of California, San Diego, July 13–16,1991, Morgan Kaufmann.Google Scholar
  2. Bhuyan, J. N., Raghavan, V. V., & Elayavalli, V. K. (1991). Genetic Algorithm for Clustering with an Ordered Representation. In Belew and Booker ( 1991 ). pp. 408–415.Google Scholar
  3. Ding, H., El-Keib, A.A., k Smith, R.E. (1992). Optimal Clustering of Power Networks Using Genetic Algorithms TCGA Report No. 92001, March 5, 1992, University of Alabama, Tuscaloosa, AL.Google Scholar
  4. Falkenauer, E., & Delchambre, A. (1992). A Genetic Algorithm for Bin Packing and Line Balancing. In Proceedings of the IEEE 1992 International Conference on Robotics and Automation (RA92), May 10–15, 1992, Nice, France, pp. 1186–1192.Google Scholar
  5. Falkenauer, E . (1994a). A Hybrid Grouping Genetic Algorithm for Bin Packing. Technical Report R0109, CRIF Industrial Management and Automation, Brussels, Belgium, October 1994. Submitted to The International Journal of Computers and Operations Research.Google Scholar
  6. Falkenauer, E. (1994b). A New Representation and Operators for Genetic Algorithms Applied to Grouping Problems. In Evolutionary Computation, Vol. 2, N. 2. pp. 123–144.Google Scholar
  7. Garey, M. R., & Johnson, D. S. (1979). Computers and Intractability- A Guide to the Theory of NP-completeness, W.H.Freeman.MATHGoogle Scholar
  8. Goldberg, D. E . (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wessley.Google Scholar
  9. Grefenstette, J. J . (Ed) (1985). Proceedings of the First International Conference on Genetic Algorithms and their Applications, Carnegie-Mellon University, Pittsburgh, PA, July 24–26, 1985, Lawrence Erlbaum Associates.Google Scholar
  10. Hinterding, R. & Juliff, K. (1993). A Genetic Algorithm for Stock Cutting: an Exploration of Mapping Schemes, Technical Report 24 COMP3 Freb 1993 CAMS, Victoria University of Technology.Google Scholar
  11. Holland, J. H. (1975). Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor.Google Scholar
  12. Jones, D. R., & Beltramo, M. A. (1991). Solving Partitioning Problems with Genetic Algorithms. In Belew and Booker (1991). pp. 442–449.Google Scholar
  13. Martello, S., & Toth, P. (1990). Lower Bounds and Reduction Procedures for the Bin Packing Problem. In “Discrete Applied Mathematics”, vol. 22, North-Holland, Elsevier Science, pp.59–70.Google Scholar
  14. Männer, R., & Manderick,B. (Eds.) (1992). Parallel Problem Solving from Nature, 2, Proceedings of the Second Conference on Parallel Problem Solving from Nature (PPSN2), Brussels, Belgium, September 28-30, 1992, North-Holland, Elsevier Science.MATHGoogle Scholar
  15. Mühlenbein, H . (1992). Parallel Genetic Algoriths in Combinatorial Optimization. In O.Balci, R.Sharda, & S.A.Zenios (Eds.), “Computer Science and Operations Research — New Developments in Their Interfaces”, Pergamon Press, pp.441–453.Google Scholar
  16. Radcliffe, N. J . (1991). Forma Analysis and Random Respectful Recombination. In Belew and Booker (1991). pp. 222–229.Google Scholar
  17. Reeves, C . (1993). Hybrid Genetic Algorithms for Bin-Packing and Related Problems, working paper, submited to Annals of OR Metaheuristics in Combinatorial Optimization, G. Laporte & I.H. Osman (Eds.), Baltzer, Bazel, 1995.Google Scholar
  18. Schaffer, D. J . (Ed.) (1989). Proceedings of the Third International Conference on Genetic Algorithms, George Mason University, June 4–7, 1989, Morgan Kaufmann.Google Scholar
  19. Smith, D . (1985). Bin Packing with Adaptive Search. In Grefenstette (1985). pp. 202–207.Google Scholar
  20. Syswerda, G . (1989). Uniform Crossover in Genetic Algorithms. In Schaffer (1989). pp. 2–9.Google Scholar
  21. Van Driessche, R., & Piessens, R. (1992). Load Balancing with Genetic Algorithms. In Männer and Manderick (1992). pp. 341–350.Google Scholar
  22. Von Laszewski, G . (1991). Intelligent Structural Operators for the k-way Graph Partitioning Problem. In Belew and Booker ( 1991 ). pp. 45–52.Google Scholar
  23. van Vliet, A . (1993): Private communication. Econometric Institute, Erasmus University Rotterdam, The Netherlands.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Emanuel Falkenauer
    • 1
  1. 1.Department of Industrial AutomationCRIF — Research Centre for Belgian Metalworking IndustryBrusselsBelgium

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