Advertisement

Random Dynamics Optimum Tracking with Evolution Strategies

  • Dirk V. Arnold
  • Hans-Georg Beyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2439)

Abstract

Dynamic optimization is frequently cited as a prime application area for evolutionary algorithms. In contrast to static optimization, the objective in dynamic optimization is to continuously adapt the solution to a changing environment– a task that evolutionary algorithms are believed to be good at. At the time being, however, almost all knowledge with regard to the performance of evolutionary algorithms in dynamic environments is of an empirical nature. In this paper, tools devised originally for the analysis in static environments are applied to study the performance of a popular type of recombinative evolution strategy with cumulative mutation strength adaptation on a dynamic problem. With relatively little effort, scaling laws that quite accurately describe the behavior of the strategy and that greatly contribute to its understanding are derived and their implications are discussed.

Keywords

Evolutionary Algorithm Evolution Strategy Candidate Solution Central Component Sphere Model 
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. 1.
    P. J. Angeline. Tracking extrema in dynamic environments. In Proc. of the Sixth International Conference on Evolutionary Programming, pages 335–345. Springer Verlag, Heidelberg, 1997.Google Scholar
  2. 2.
    D. V. Arnold and H.-G. Beyer. Local performance of the (μ/μI, λ)-ES in a noisy environment. In W. N. Martin and W. M. Spears, editors, Foundations of Genetic Algorithms 6, pages 127–141. Morgan-Kaufmann, San Francisco, 2000.Google Scholar
  3. 3.
    D. V. Arnold and H.-G. Beyer. An analysis of cumulative mutation stength adaptation. In preparation, 2002.Google Scholar
  4. 4.
    T. Bäck. On the behavior of evolutionary algorithms in dynamic environments. In Proc. of the 1998 International Conference on Evolutionary Computation, pages 446–451. IEEE Press, Piscataway, NJ, 1998.Google Scholar
  5. 5.
    H.-G. Beyer. Toward a theory of evolution strategies: Some asymptotical results from the (1 +, λ)-theory. Evolutionary Computation, 1(2):165–188, 1993.CrossRefGoogle Scholar
  6. 6.
    H.-G. Beyer. The Theory of Evolution Strategies. Natural Computing Series. Springer Verlag, Heidelberg, 2001.Google Scholar
  7. 7.
    J. Branke. Evolutionary Optimization in Dynamic Environments. Kluwer Academic Publishers, Dordrecht, 2001.Google Scholar
  8. 8.
    R. Bürger. The Mathematical Theory of Selection, Recombination, and Mutation. John Wiley & Sons, Chichester, 2000.zbMATHGoogle Scholar
  9. 9.
    S. Droste. Analysis of the (1 + 1) EA for a dynamically changing objective function. In Proc. of the 2002 Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 2002.Google Scholar
  10. 10.
    N. Hansen and A. Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159–195, 2001.CrossRefGoogle Scholar
  11. 11.
    N. Hansen. Verallgemeinerte individuelle Schrittweitenregelung in der Evolutionsstrategie. Mensch & Buch Verlag, Berlin, 1998.Google Scholar
  12. 12.
    I. Rechenberg. Evolutionsstrategie’ 94. Frommann-Holzboog, Stuttgart, 1994.Google Scholar
  13. 13.
    R. Salomon and P. Eggenberger. Adaptation on the evolutionary time scale: A working hypothesis and basic experiments. In Proc. of the Third Conference on Artificial Evolution, pages 251–262. Springer Verlag, Heidelberg, 1997.Google Scholar
  14. 14.
    K. Weicker and N. Weicker. On evolution strategy optimization in dynamic environments. In Proc. of the 1999 Congress on Evolutionary Computation, pages 2039–2046. IEEE Press, Piscataway, NJ, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dirk V. Arnold
    • 1
  • Hans-Georg Beyer
    • 1
  1. 1.Department of Computer Science XIUniversity of DortmundDortmundGermany

Personalised recommendations