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Evolutionary Computation

Fall 2000, Vol. 8, No. 3, Pages 267-289
Posted Online March 13, 2006.
(doi:10.1162/106365600750078781)
© 2000 Massachusetts Institute of Technology
Analysis of the (μ/μ, λ)-ES on the Parabolic Ridge

A. Irfan Oyman

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

Hans-Georg Beyer

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

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The progress behavior of evolution strategies (ES) using recombination is analyzed in this paper on the parabolic ridge. This test function represents landscapes far from the optimum. The ES algorithms with intermediate and dominant recombination are considered in the analysis. The derivations are presented for intermediate recombination. Thereafter, the formulae for dominant recombination are obtained using the so-called surrogate mutation model. In the analysis, the formulae are derived for the progress rate and for the stationary distance R(∞) to the ridge axis. As a result, it will be shown that the progress rate can increase if recombination is applied. Simulations are used to show the appropriateness of the formulae derived.

Cited by

Dirk V. Arnold, Hans-Georg Beyer. (2009) Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge. Natural Computing 7:4, 555-587
Online publication date: 1-Jan-2009.
CrossRef
Dirk V. Arnold, Alexander MacLeod. (2008) Step Length Adaptation on Ridge Functions. Evolutionary Computation 16:2, 151-184
Online publication date: 1-Jun-2008.
Abstract | PDF (454 KB) | PDF Plus (461 KB) 
H.G. Beyer. (2001) On the performance of (1, λ)-evolution strategies for the ridge function class. IEEE Transactions on Evolutionary Computation 5:3, 218-235
Online publication date: 1-Jul-2001.
CrossRef
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