Abstract

This paper analyzes the Self-Adaptation (SA) algorithm widely used to adapt strategy parameters of the Evolution Strategy (ES) in order to obtain maximal ES-performance. The investigations are concentrated on the adaptation of one general mutation strength  (called  SA) in  ESs. The hypersphere serves as the fitness model.

Starting from an introduction into the basic concept of self-adaptation, a framework for the analysis of  SA is developed on two levels: a microscopic level concerning the description of the stochastic changes from one generation to the next, and a macroscopic level describing the evolutionary dynamics of the  SA over the time (generations). The  -SA requires the fixing of a new strategy parameter, the so-called learning parameter. The influence of this parameter on the ES performance is investigated and rules for its tuning are presented and discussed. The results of the theoretical analysis are compared with ES experiments and it will be shown that applying Schwefel's  -scaling rule guarantees the linear convergence order of the ES.

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