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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
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.
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.
Garey, M. R., & Johnson, D. S. (1979). Computers and Intractability- A Guide to the Theory of NP-completeness, W.H.Freeman.
Goldberg, D. E . (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wessley.
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.
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.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor.
Jones, D. R., & Beltramo, M. A. (1991). Solving Partitioning Problems with Genetic Algorithms. In Belew and Booker (1991). pp. 442–449.
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.
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.
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.
Radcliffe, N. J . (1991). Forma Analysis and Random Respectful Recombination. In Belew and Booker (1991). pp. 222–229.
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.
Schaffer, D. J . (Ed.) (1989). Proceedings of the Third International Conference on Genetic Algorithms, George Mason University, June 4–7, 1989, Morgan Kaufmann.
Smith, D . (1985). Bin Packing with Adaptive Search. In Grefenstette (1985). pp. 202–207.
Syswerda, G . (1989). Uniform Crossover in Genetic Algorithms. In Schaffer (1989). pp. 2–9.
Van Driessche, R., & Piessens, R. (1992). Load Balancing with Genetic Algorithms. In Männer and Manderick (1992). pp. 341–350.
Von Laszewski, G . (1991). Intelligent Structural Operators for the k-way Graph Partitioning Problem. In Belew and Booker ( 1991 ). pp. 45–52.
van Vliet, A . (1993): Private communication. Econometric Institute, Erasmus University Rotterdam, The Netherlands.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Falkenauer, E. (1996). The Grouping Genetic Algorithm. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_17
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3437-8_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3439-2
Online ISBN: 978-1-4613-3437-8
eBook Packages: Springer Book Archive