The (μ/μ, λ) Strategies — or Why “Sex” May be Good

  • Hans-Georg Beyer
Part of the Natural Computing Series book series (NCS)


Two special cases of multirecombination will be investigated — the intermediate (μ/μ I) recombination and the dominant (μ/μ D) recombination. The first section deals mainly with the (μ/μ I, λ)-ES. The N-dependent φ will be derived for the sphere model. Thereafter, the reasons for the higher performance of the recombinative strategies are investigated. This higher performance compared to the nonrecombinative strategies will be explained by the genetic repair hypothesis (GR). The second part of the chapter is devoted to the (μ/μ D, λ)-ES. In contrast to the theory of the (μ/μ I, λ)-ES, the analysis of the (μ/μ D, λ)-ES is still in its infancy. A simple model with surrogate mutations will be introduced in Sect. 6.2. This model describes the fundamental aspects of dominant recombination for N → ∞. The dominant recombination generates offspring populations reminiscent of a species. Therefore, the MISR principle (mutation-induced speciation by recombination) is postulated. The asymptotic behavior of the recombinative strategies will be investigated in Sect. 6.3. It will be shown that the (μ/μ, λ)-ES attains in the asymptotic limit case a progress rate which is a times larger than that of the (1 + 1)-ES.


Progress Rate Fitness Landscape Offspring Distribution Residual Distance Intermediate Recombination 
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  1. 22.
    The analytical derivation of the progress rate of the (A + A)-ES and therefore also of the fitness efficiency is still an unsolved problem. However, it seems very plausible that for A 1 the inequality 4 +a (a*) yoi +a (a*) should hold.Google Scholar
  2. 23.
    Naturally, from the pragmatic point of view, one would not choose ‘8 arbitrarily, as is done here. Instead, one would choose t9 = i9, so that one has = 7),,µ,a and therefore the most fitness-efficient strategy in the application.Google Scholar
  3. 24.
    Recently, first results on the noisy (µhµ A)-ES have been reported in Arnold and Beyer (2001).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hans-Georg Beyer
    • 1
  1. 1.Department of Computer ScienceUniversity of DortmundDortmundGermany

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