Genetic Algorithm for Finding the Nucleolus of Assignment Games

  • Hubert H. Chin
Part of the Theory and Decision Library book series (TDLC, volume 18)

Abstract

This paper describes a heuristic approach to finding the nucleolus of assignment games using genetic algorithms. The method consists of three steps, as follow. The first step is to maintain a set of possible solutions of the core, called population. With the concept of nucleolus, the lexicographic order is the function of fitness. The second step is to improve the population by a cyclic three-stage process consisting of a reproduction (selection), recombination (mating), and evaluation (survival of the fittest). Each cycle is called a generation. Generation by generation, the selected population will be a set of vectors with the higher fitness values. A mutation operator changes individuals that may lead to a high fitness region by performing an alternative search path. The last step is to terminate the loop by setting an acceptable condition. The highest fitness individual presents the nucleolus. The discussion includes an outline of the processing pseudocode.

Keywords

Genetic Algorithm Assignment Problem Linear Programming Problem Lexicographic Order Assignment Game 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Shapley, L. S. and M. Shubik, “The assignment Game I: The Core,” International Journal of Game Theory, 1, pp. 111–130, 1972.CrossRefGoogle Scholar
  2. Schmeidler, D., “The Nucleolus of a characteristic function game,” SIAM Journal on Applied Mathematics, 17, pp. 1163–1170, 1969.CrossRefGoogle Scholar
  3. Kuhn, H. W., “The Hungarian Method for the assignment Problem,” Naval Research Logistics Quarterly, 2, pp. 83–97, 1955.CrossRefGoogle Scholar
  4. Kohlberg, E., “The nucleolus as a solution of a Minimization Problem,” SIAM Journal on Applied Mathematics, 23, pp. 34–39, 1972.CrossRefGoogle Scholar
  5. Owen, G., “A note on the Nucleolus,” International Journal of Game Theory, 3, pp. 101–103.Google Scholar
  6. Solymosi, T. and T. E. S. Raghavan, “An Algorithm for Finding the Nucleolus of Assignment Games,” International Conference on Game Theory at Stony Brook, New York, July 1992.Google Scholar
  7. Maschler, M., B. Peleg, and L. S. Shapley, “Geometric Properties of the Kernel, Nucleolus, and Related Solution concepts,” Mathematics of Operations Research, 4, pp. 303–338, 1979.CrossRefGoogle Scholar
  8. Maschler, M, J. A. M. Potters, and S. H. Tijs, “The General Nucleolus and the Reduced Game Property,” International Journal of Game Theory, 21, pp.85–106, 1992.CrossRefGoogle Scholar
  9. Sankaran, J. K., “On Finding the Nucleolus of an N-person Cooperative Game,” International Journal of Game Theory, 19, pp. 329–338, 1991.CrossRefGoogle Scholar
  10. Holland, J. H., “Adaptation in Natural and Artificial system,” University of Michigan Press, 1975.Google Scholar
  11. DeJong, K. A., “Analysis of the Behavior of a Class of Genetic Algorithms,” University of Michigan, Ph.D. Thesis, Ann Arbor, MI., 1975.Google Scholar
  12. Brindle, A., “Genetic Algorithms for Function Optimization,” University of Alberta, Ph.D. Thesis, 1980.Google Scholar
  13. Bethke, A. D., “Genetic Algorithms as function Optimizers,” University of Michigan, Ph.D. Thesis, 1981.Google Scholar
  14. Goldberg, D., “Computer Aid Gas Pipeline Operation Using Genetic Algorithms and Rule Learning,” University of Michigan, Ph.D. Thesis, 1983.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Hubert H. Chin
    • 1
  1. 1.Computer Science DepartmentNew York Institute of TechnologyOld WestburyUSA

Personalised recommendations