Self-adaptation on the Ridge Function Class: First Results for the Sharp Ridge

  • Hans-Georg Beyer
  • Silja Meyer-Nieberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)


This paper presents first results of an analysis of the σ-self-adaptation mechanism on the sharp ridge for non-recombinative (1,λ) evolution strategies (ES). To analyze the ES’s evolution, we consider the so-called evolution equations which describe the one-generation change. Neglecting stochastic perturbations and considering only the mean value dynamics, we will investigate possible causes why self-adaptation can fail on the sharp ridge.


Taylor Series Evolution Strategy Sphere Model Progress Rate Learning Parameter 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A First Course in Order Statistics. Wiley, New York (1992)MATHGoogle Scholar
  2. 2.
    Arnold, D.V., Beyer, H.-G.: Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge. Technical Report CS-2006-02 CS-2006-02, Dalhousie University, Faculty of Computer Science (January 2006)Google Scholar
  3. 3.
    Arnold, D.V., MacLeod, A.: Hierarchically organised evolution strategies on the parabolic ridge. Technical Report CS-2006-03 CS-2006-03, Dalhousie University, Faculty of Computer Science (January 2006)Google Scholar
  4. 4.
    Auger, A.: Convergence results for the (1,λ)-SA-ES using the theory of φ-irreducible Markov chains. Theoretical Computer Science 334, 35–69 (2005)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Beyer, H.-G.: On the performance of (1,λ)-evolution strategies for the ridge function class. IEEE Transactions on Evolutionary Computation 5(3), 218–235 (2001)CrossRefGoogle Scholar
  6. 6.
    Beyer, H.-G.: The Theory of Evolution Strategies. Natural Computing Series. Springer, Heidelberg (2001)Google Scholar
  7. 7.
    Herdy, M.: Reproductive isolation as strategy parameter in hierarchically organized evolution strategies. In: Männer, R., Manderick, B. (eds.) Parallel Problem Solving from Nature, vol. 2, pp. 207–217. Elsevier, Amsterdam (1992)Google Scholar
  8. 8.
    Oyman, A.I.: Convergence Behavior of Evolution Strategies on Ridge Functions. Ph.d. thesis, University of Dortmund, Department of Computer Science (1999)Google Scholar
  9. 9.
    Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog Verlag, Stuttgart (1973)Google Scholar
  10. 10.
    Schwefel, H.-P.: Adaptive Mechanismen in der biologischen Evolution und ihr Einfluß auf die Evolutionsgeschwindigkeit. Technical report, Technical University of Berlin, Abschlußbericht zum DFG-Vorhaben Re 215/2 (1974)Google Scholar
  11. 11.
    Semenov, M.A.: Convergence velocity of evolutionary algorithm with self-adaptation. In: GECCO 2002, pp. 210–213 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hans-Georg Beyer
    • 1
  • Silja Meyer-Nieberg
    • 2
  1. 1.Department of Computer ScienceVorarlberg University of Applied SciencesDornbirnAustria
  2. 2.Department of Computer ScienceUniversität der Bundeswehr MünchenNeubibergGermany

Personalised recommendations