Information Dimension of a Population’s Attractor a Binary Genetic Algorithm

  • Paweł Kieś


The tools for a description of chaotic dynamics are applied to investigate the work of a binary genetic algorithm (BGA). The method for determining strange attractors from BGA’s populations is shown. Attractor’s information dimension is taken as a measure of the state of BGA’s activity. The equivalence between the information dimension of a population’s attractor and the entropy of related bit positions for a given population is shown and confirmed experimentally.


Genetic Algorithm Search Space Strange Attractor Information Dimension Poincare Section 
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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  1. [1]
    Bäck T,: “The Interaction of Mutation Rate, Selection, and Self-Adaptation within a Genetic Algorithm”, Parallel Problem Solving from Nature, Vol. 2, pp. 85–94, Amsterdam, North Holland, 1992.Google Scholar
  2. [2]
    Baker G.L., Gollub J,P.: Chaotic Dynamies: an Introduction, Cambridge Univ. Press, Cambridge, 1996.CrossRefMATHGoogle Scholar
  3. [3]
    De Jong K,A., Spears W.M.: “A Formal Analysis of the Role of Multi-point Crossover in Genetic Algorithms”, Annals of Math. and AI Journal, Vol. 5, No, 1, pp. 1–26. J,C. Baltzer AG Scientific Publishing Co., 1992.MATHGoogle Scholar
  4. [4]
    Falconer K,J,: “Fractal geometry”, Math. Found. Appl., John Wiley, Chichester, pp.15–25, 1990.Google Scholar
  5. [5]
    Kieś P.: “Dimension of attractors generated by a genetic algorithm”, Procs. of the IX-th Intern. Symposium on Intelligent Information Systems, pp. 40–45, Bystra, Poland, June 2000.Google Scholar
  6. [6]
    Kieś P.: “Meaning of the information dimension of a population’s attractor in a binary GA”, IEEE Trans. on Evolutionary Computation, 2001 (sent to print).Google Scholar
  7. [7]
    Kolonko M.: “A Generalized Crossover Operation for Genetic Algorithms”, Complex Systems, pp. 177–191, Vol. 9, 1995.MathSciNetMATHGoogle Scholar
  8. [8]
    Michalewicz Z.: Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1996.CrossRefMATHGoogle Scholar
  9. [9]
    Ott E.: Chaos in Dynamical Systems, Cambridge Univ. Press, Cambridge, 1996.Google Scholar
  10. [10]
    Qi T., Palmieri F.: “Theoretical Analysis of Evolutionary Algorithms with an Infinite Population Size in Continuous Space, Part II: Analysis of the Diversification Role of Crossover”, IEEE Trans. of Neural Networks, Vol. 5, No. 1, 1994Google Scholar
  11. [11]
    Rudolph G.: “Convergence analysis of canonical genetic algorithms”, IEEE Trans. on Neural Networks, Special Issue on Evolutionary Computation, Vol. 5, No, 1, 1994Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Paweł Kieś
    • 1
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

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