Searching for Balance: Understanding Self-adaptation on Ridge Functions

  • Monte Lunacek
  • Darrell Whitley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)


The progress rate of a self-adaptive evolution strategy is sub-optimal on ridge functions because the global step-size, denoted σ, becomes too small. On the parabolic ridge we conjecture that σ will stabilize when selection is unbiased towards larger or smaller step-sizes. On the sharp ridge, where the bias in selection is constant, σ will continue to decrease. We show that this is of practical interest because ridges can cause even the best solutions found by self-adaptation to be of little value on ridge problems where spatially close parameters tend to have similar values.


Search Space Evolution Strategy Strategy Parameter Progress Rate Object 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.


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  1. 1.
    Arnold, D.V., Beyer, H.-G.: Evolution strategies with cumulative step-length adaptation on the noisy parabolic ridge. Technical report, Dalhousie University (2006)Google Scholar
  2. 2.
    Bäck, T.: Evolutonary Algorithms in Theory and Practice. Oxford University Press, New York (1996)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., Schwefel, H.-P.: Evolution strategies - a comprehensive introduction. Natural Computing: an international journal 1(1), 3–52 (2002)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Englen, R., Denning, A., Gurney, K., Stephens, G.: Global observations of the carbon budget: I. expected satellite capabilities for emission spectroscopy in the eos and npoess eras. Journal of Geophysical Research 106(20), 055–20,068 (2001)Google Scholar
  6. 6.
    Hansen, N.: Invariance, self-adaptation and correlated mutations in evolution strategies. In: Proceedings of Parallel Problem Solving from Nature, pp. 355–364 (2000)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: Proceedings of Parallel Problem Solving from Nature, pp. 207–217 (1992)Google Scholar
  9. 9.
    Ostermeier, A., Gawelczyk, A., Hansen, N.: A derandomized approach to self-adaptation of evolution strategies. Evolutionary Computation 2(4), 369–380 (1994)CrossRefGoogle Scholar
  10. 10.
    Oyman, A.I., Beyer, H., Schwefel, H.: Where elitists start limping evolution strategies at ridge functions. In: Parallel Problem Solving from Nature – PPSN VGoogle Scholar
  11. 11.
    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
  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.
    Salomon, R.: Applying evolutionary algorithms to real-world-inspired problems with physical smoothness constraints. In: Proceedings of the Congress on Evolutionary ComputationGoogle Scholar
  14. 14.
    Salomon, R.: The curse of high dimensional search spaces: Observing premature convergence in unimodal functions. In: Proceedings of the Congress on Evolutionary Computation, pp. 918–923. IEEE Press, Los Alamitos (2004)Google Scholar
  15. 15.
    Whitley, D., Lunacek, M., Knight, J.: Ruffled by ridges: How evolutionary algorithms can fail. In: Proceedings of GECCO (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Monte Lunacek
    • 1
  • Darrell Whitley
    • 1
  1. 1.Colorado State UniversityFort CollinsUSA

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