Self-adaptation on the Ridge Function Class: First Results for the Sharp Ridge

This paper presents first results of an analysis of the σ-self-adaptation mechanism on the sharp ridge for non-recombinative (1,λ) evolution strategies (ES). To analyze the ES's evolution, we consider the so-called evolution equations which describe the one-generation change. Neglecting stochastic perturbations and considering only the mean value dynamics, we will investigate possible causes why self-adaptation can fail on the sharp ridge.

[1]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[2]  Dirk V. Arnold,et al.  Hierarchically organised evolution strategies on the parabolic ridge , 2006, GECCO '06.

[3]  Ahmet Irfan Oyman,et al.  Convergence behavior of evolution strategies on ridge functions , 1999 .

[4]  B. Arnold,et al.  A first course in order statistics , 1994 .

[5]  Mikhail A. Semenov.  Convergence Velocity Of Evolutionary Algorithm With Self-adaptation , 2002, GECCO.

[6]  Hans-Georg Beyer,et al.  On the performance of (1, Lambda)-evolution strategies for the ridge function class , 2001, IEEE Trans. Evol. Comput..

[7]  D. Farnsworth.  A First Course in Order Statistics , 1993 .

[8]  Michael Herdy,et al.  Reproductive Isolation as Strategy Parameter in Hierarichally Organized Evolution Strategies , 1992, PPSN.

[9]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[10]  Hans-Georg Beyer,et al.  On the performance of (1,l)-Evolution Strategies at the ridge function class , 2001 .

[11]  Hans-Georg Beyer,et al.  Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge , 2008, Natural Computing.

[12]  Anne Auger,et al.  Convergence results for the (1, lambda)-SA-ES using the theory of phi-irreducible Markov chains , 2005, Theor. Comput. Sci..

[13]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[14]  A. Auger.  Convergence results for the ( 1 , )-SA-ES using the theory of-irreducible Markov chains , 2005 .