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Analyses of Simple Genetic Algorithms and Island Model Parallel Genetic Algorithms

  • T. Niwa
  • M. Tanaka
Conference paper

Abstract

H. Asoh and H. Mühlenbein investigated empirically the relation among the mean convergence time, the population size, and the chromosome length of genetic algorithms (GAs). In this paper, from the mathematical point of view, the relation they revealed is convincing. Our analyses of GAs make use of the Markov chain formalism based on the Wright-Fisher model, which is a typical and well-known model in population genetics. We also give the mean convergence time under genetic drift. Genetic drift can be described by the Wright-Fisher model. We determine the stationary states of the corresponding Markov chain model and the mean convergence time to reach one of these stationary states. Furthermore, we derive the most effective mutation rate for the standard GAs and also the most effective migration rate for the island model parallel GAs with some restrictions. These rates are coincide with known empirical results.

Keywords

Genetic Algorithm Mutation Rate Genetic Drift Migration Rate Convergence Time 
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. [1]
    H. Asoh and H. Mühlenbein. On the mean convergence time of evolutionary algorithms without selection. In Parallel Problem Solving from Nature 3, 1994. to appear.Google Scholar
  2. [2]
    A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: a markov chain analysis. In Parallel Problem Solving from Nature, pages 4–12, 1990.Google Scholar
  3. [3]
    D.E. Goldberg. Genetic Algorithms in Search, Optimization & Machine Learning. Addison-Wesley, Reading, Mass., 1989.MATHGoogle Scholar
  4. [4]
    D.E. Goldberg and P. Segrest. Finite markov chain analysis of genetic algorithms. In Proceedings of the 2nd International Conference on Genetic Algorithms, pages 1–8, 1987.Google Scholar
  5. [5]
    J.H. Holland. Adaptation in Natural and Artificial Systems. Univ. of Michigan Press, Ann Arbor, Mich., 1975.Google Scholar
  6. [6]
    J. Horn. Finite markov chain analysis of genetic algorithms with niching. In Proceedings of the 5th International Conference on Genetic Algorithms, pages 110–117, 1993.Google Scholar
  7. [7]
    K.A. De Jong and W.M. Spears. A formal analysis of the role of multi-point crossover in genetic algorithms. Annals of Mathematics and Artificial Intelligence, 5:1–26, 1992.MATHCrossRefGoogle Scholar
  8. [8]
    M. Kimura. Diffusion models in population genetics. J. Appl. Prob., 1:177–232, 1964.MATHCrossRefGoogle Scholar
  9. [9]
    B. Manderick and P. Spiessens. Fine-grained parallel genetic algorithms. In Proceedings of the 3rd International Conference on Genetic Algorithms, pages 428–433, 1989.Google Scholar
  10. [10]
    T. Niwa and M. Tanaka. On the mean convergence time for simple genetic algorithms. In Proceedings of the International Conference on Evolutionary Computing’ 95, 1995.Google Scholar
  11. [11]
    G. Rudolph. Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Networks, 5(1):96–101, 1994.CrossRefGoogle Scholar
  12. [12]
    J. Suzuki. A markov chain analysis on a genetic algorithm. In Proceedings of the 5th International Conference on Genetic Algorithms, pages 146–153, 1993.Google Scholar
  13. [13]
    M. Tanaka and T. Niwa. Markov chain analysis on simple genetic algorithm. Technical Report ETL-TR-94-13, Electrotechnical Laboratory, 1994.Google Scholar
  14. [14]
    R. Tanese. Distributed genetic algorithms. In Proceedings of the 3rd International Conference on Genetic Algorithms, pages 434–439, 1989.Google Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • T. Niwa
    • 1
  • M. Tanaka
    • 1
  1. 1.Distributed Systems Section, Mathematical Informatics SectionElectrotechnical LaboratoryTsukuba-shi Ibaraki-ken 305Japan

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