Skip to main content
SpringerLink
Log in

Self-adaptation of evolution strategies under noisy fitness evaluations

  • Original article
  • Published:
Genetic Programming and Evolvable Machines Aims and scope Submit manuscript

Abstract

This paper investigates the self-adaptation behavior of (\(1,\lambda \))-evolution strategies (ES) on the noisy sphere model. To this end, the stochastic system dynamics is approximated on the level of the mean value dynamics. Being based on this “microscopic” analysis, the steady state behavior of the ES for the scaled noise scenario and the constant noise strength scenario will be theoretically analyzed and compared with real ES runs. An explanation will be given for the random walk like behavior of the mutation strength in the vicinity of the steady state. It will be shown that this is a peculiarity of the \((1,\lambda)\)-ES and that intermediate recombination strategies do not suffer from such behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, in A First Course in Order Statistics, Wiley: New York, 1992.

  2. A. Auger, “Convergence results for \((1,\lambda)\)-SA-ES using the theory of φ-irreducible Markov chains,” in Workshop on Evolutionary Algorithms - ICALP-2003, Eindhoven: The Netherlands, 2003.

  3. H.-G. Beyer, “Toward a theory of evolution strategies: Self-Adaptation,” Evolutionary Computation, vol. 3, pp. 311–347, 1996.

  4. H.-G. Beyer, The Theory of Evolution Strategies. Natural Computing Series. Springer: Heidelberg, 2001.

  5. H.-G. Beyer and K. Deb, “On self-adaptive features in real-parameter evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, vol. 5, pp. 250–270, 2001.

  6. H.-G. Beyer and H.-P. Schwefel, “Evolution strategies: A comprehensive introduction,” Natural Computing, vol. 1, pp. 3–52, 2002.

  7. A. Bienvenüe and O. François, “Global convergence for evolution strategies in spherical problems: Some simple proofs and difficulties,” Theoretical Computer Science, vol. 308, pp. 269–289, 2003.

  8. W. E. Hart, J. M. DeLaurentis, and L. A. Ferguson, “On the convergence of an implicitly self-adaptive evolutionary algorithm on one-dimensional unimodal problems,” IEEE Transactions on Evolutionary Computation, To appear.

  9. Y. Jin and J. Branke, “Evolutionary optimization in uncertain environments–A survey,” IEEE Transactions on Evolutionary Computation, vol. 9, pp. 303–317, 2005.

  10. D. G. Luenberger, in Introduction to Dynamic Systems, Wiley: Chichester, 1979.

  11. A. Ostermeier, A. Gawelczyk, and N. Hansen, “A derandomized approach to self-adaptation of evolution strategies,” Evolutionary Computation, vol. 2, pp. 369–380, 1995.

  12. I. Rechenberg, in Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Frommann-Holzboog Verlag: Stuttgart, 1973.

  13. I. Rechenberg, Evolutionsstrategie '94, Frommann-Holzboog Verlag: Stuttgart, 1994.

  14. H.-P. Schwefel, Adaptive Mechanismen in der biologischen Evolution und ihr Einfluß auf die Evolutionsgeschwindigkeit, Technical report, Technical University of Berlin, 1974, Abschlußbericht zum DFG-Vorhaben Re 215/2.

  15. M. A. Semenov, “Convergence velocity of evolutionary algorithm with self-adaptation,” in GECCO 2002: Proc. of the Genetic and Evolutionary Computation Conference, New York, USA, W. B. Langdon et al. (eds.), Morgan Kaufman Publishers: San Francisco, CA, 2002, pp. 210–213.

  16. M. A. Semenov and D. A. Terkel, “Analysis of convergence of an evolutionary algorithm with self-adaptation using a stochastic Lyapunov function,” Evolutionary Computation, vol. 11, pp. 363–379, 2003.

Download references

Acknowledgments

This work was supported by the Research Center for Process- and Product-Engineering at the Vorarlberg University of Applied Sciences and by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center SFB 531 at the University of Dortmund.

Author information

Authors and Affiliations

  1. Department of Computer Science, Vorarlberg University of Applied Sciences, Hochschulstr. 1, A-6850, Dornbirn, Austria

    Hans-Georg Beyer

  2. Department of Computer Science, Universität der Bundeswehr München, D-85577, Neubiberg, Germany

    Silja Meyer-Nieberg

Authors
  1. Hans-Georg Beyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silja Meyer-Nieberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hans-Georg Beyer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beyer, HG., Meyer-Nieberg, S. Self-adaptation of evolution strategies under noisy fitness evaluations. Genet Program Evolvable Mach 7, 295–328 (2006). https://doi.org/10.1007/s10710-006-9017-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10710-006-9017-3

Keywords

Search

Navigation