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.