Evolutionary Optimization with Cumulative Step Length Adaptation

Abstract

Iterative algorithms for numerical optimization in continuous spaces typically need to adapt their step lengths in the course of the search. While some strategies employ fixed schedules for reducing the step lengths over time, others attempt to adapt interactively in response to either the outcome of trial steps or to the history of the search process. Evolutionary algorithms are of the latter kind. One of the control strategies that is commonly used in evolution strategies is the cumulative step length adaptation approach. This paper presents a first theoretical analysis of that adaptation strategy by considering the algorithm as a dynamical system. The analysis includes the practically relevant case of noise interfering in the optimization process. Recommendations are made with respect to the problem of choosing appropriate population sizes.