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International Conference on Parallel Problem Solving from Nature

PPSN 1996: Parallel Problem Solving from Nature — PPSN IV pp 122–133Cite as

On the asymptotic behavior of multirecombinant Evolution Strategies

  • Theoretical Foundations of Evolutionary Computation
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1141))

Abstract

The performance of (Μ/Μ, λ)-ESs (Evolution Strategies) in the asymptotic limit for N→∞ and λ→∞ is investigated. The conjecture made by Schwefel that the maximum performance of such strategies scales like Μ In(λ/Μ) will be proved. Furthermore, it will be shown that an optimally tuned Μ/Μ, λ)-ES performs exactly λ times faster than an optimally tuned (1+1)-ES, if the hyper-sphere is taken as the fitness model (using the number of generations as the performance measure). The notion of fitness efficiency will be introduced and will be used to derive the ES time complexity. The results are compared to the non-recombinant (Μ, λ)-ES.

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References

  1. M. Abramowitz and I. A. Stegun. Pocketbook of Mathematical Functions. Verlag Harri Deutsch, Thun, 1984.

    Google Scholar 

  2. H.-G. Beyer. Toward a Theory of Evolution Strategies: Some Asymptotical Results from the (1, + λ)-Theory. Evolutionary Computation, 1(2):165–188, 1993.

    Google Scholar 

  3. H.-G. Beyer. Toward a Theory of Evolution Strategies: On the Benefit of Sex — the (Μ/Μ, λ)-Theory. Evolutionary Computation, 3(1):81–111, 1995.

    Google Scholar 

  4. H.-G. Beyer. Toward a Theory of Evolution Strategies: The (Μ, λ)-Theory. Evolutionary Computation, 2(4):381–407, 1995.

    Google Scholar 

  5. H.-G. Beyer. Toward a Theory of Evolution Strategies: Self-Adaptation. Evolutionary Computation, 3(3):311–347, 1996.

    Google Scholar 

  6. A. Ostermeier, A. Gawelczyk, and N. Hansen. A Derandomized Approach to Self-Adaptation of Evolution Strategies. Evolutionary Computation, 2(4):369–380, 1995.

    Google Scholar 

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

    Google Scholar 

  8. 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.

    Google Scholar 

  9. H.-P. Schwefel. Evolution and Optimum Seeking. Wiley, New York, NY, 1995.

    Google Scholar 

  10. H.-P. Schwefel and G. Rudolph. Contemporary Evolution Strategies. In F. Morana, A. Moreno, J. J. Merelo, and P. Chacon, editors, Advances in Artificial Life. Third ECAL Proceedings, pages 893–907, Berlin, 1995. Springer-Verlag.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Systems Analysis Research Group, University of Dortmund, D-44221, Dortmund, Germany

    Hans-Georg Beyer

Authors
  1. Hans-Georg Beyer
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Editor information

Hans-Michael Voigt Werner Ebeling Ingo Rechenberg Hans-Paul Schwefel

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© 1996 Springer-Verlag Berlin Heidelberg

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Beyer, HG. (1996). On the asymptotic behavior of multirecombinant Evolution Strategies. In: Voigt, HM., Ebeling, W., Rechenberg, I., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN IV. PPSN 1996. Lecture Notes in Computer Science, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61723-X_976

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  • DOI: https://doi.org/10.1007/3-540-61723-X_976

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61723-5

  • Online ISBN: 978-3-540-70668-7

  • eBook Packages: Springer Book Archive

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