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Cumulative Step Length Adaptation on Ridge Functions

  • Dirk V. Arnold
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)

Abstract

The ridge function class is a parameterised family of test functions that is often used to evaluate the capabilities and limitations of optimisation strategies. Past research with the goal of analytically determining the performance of evolution strategies on the ridge has focused either on the parabolic case or on simple one-parent strategies without step length adaptation. This paper extends that research by studying the performance of multirecombination evolution strategies with cumulative step length adaptation for a wide range of ridge topologies.

Keywords

Evolution Strategy Step Length Candidate Solution Progress Rate Search Point 
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.
    Arnold, D.V., Beyer, H.-G.: Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge. Technical Report CS-2006-02, Faculty of Computer Science, Dalhousie University (2006), Available at: http://www.cs.dal.ca/research/techreports/2006/CS-2006-02.shtml
  2. 2.
    Arnold, D.V., MacLeod, A.: Hierarchically organised evolution strategies on the parabolic ridge. In: Keijzer, M., et al. (eds.) Proceedings of the 2006 Genetic and Evolutionary Computation Conference, ACM Press, New York (2006)Google Scholar
  3. 3.
    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
  4. 4.
    Beyer, H.-G.: The Theory of Evolution Strategies. Springer, Heidelberg (2001)Google Scholar
  5. 5.
    Beyer, H.-G., Schwefel, H.-P.: Evolution strategies — A comprehensive introduction. Natural Computing 1(1), 3–52 (2002)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    David, H.A., Nagaraja, H.N.: Concomitants of order statistics. In: Balakrishnan, N., Rao, C.R. (eds.) Handbook of Statistics, vol. 16, pp. 487–513. Elsevier, Amsterdam (1998)Google Scholar
  7. 7.
    Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)CrossRefGoogle Scholar
  8. 8.
    Herdy, M.: Reproductive isolation as strategy parameter in hierarchically organized evolution strategies. In: Männer, R., et al. (eds.) Parallel Problem Solving from Nature — PPSN II, pp. 207–217. Elsevier, Amsterdam (1992)Google Scholar
  9. 9.
    Ostermeier, A., Gawelczyk, A., Hansen, N.: Step-size adaptation based on non-local use of selection information. In: Davidor, Y., et al. (eds.) Parallel Problem Solving from Nature — PPSN III, pp. 189–198. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Oyman, A.I., Beyer, H.-G.: Analysis of the (μ/μ,λ)-ES on the parabolic ridge. Evolutionary Computation 8(3), 267–289 (2000)CrossRefGoogle Scholar
  11. 11.
    Oyman, A.I., Beyer, H.-G., Schwefel, H.-P.: Where elitists start limping: Evolution strategies at ridge functions. In: Eiben, A.E., et al. (eds.) Parallel Problem Solving from Nature — PPSN V, pp. 109–118. Springer, Heidelberg (1998)Google Scholar
  12. 12.
    Oyman, A.I., Beyer, H.-G., Schwefel, H.-P.: Analysis of the (1,λ)-ES on the parabolic ridge. Evolutionary Computation 8(3), 249–265 (2000)CrossRefGoogle Scholar
  13. 13.
    Whitley, D., Lunacek, M., Knight, J.: Ruffled by ridges: How evolutionary algorithms can fail. In: Deb, K., et al. (eds.) Genetic and Evolutionary Computation — GECCO 2004, pp. 294–306. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dirk V. Arnold
    • 1
  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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