Hierarchically organised evolution strategies on the parabolic ridge

摘要

Organising evolution strategies hierarchically has been proposed as a means for adapting strategy parameters such as step lengths. Experimental research has shown that on ridge functions, hierarchically organised strategies can significantly outperform strategies that rely on mutative self-adaptation. This paper presents a first theoretical analysis of the behaviour of a hierarchically organised evolution strategy. Quantitative results are derived for the parabolic ridge that describe the dependence on the length of the isolation periods of the mutation strength and the progress rate. The issue of choosing an appropriate length of the isolation periods is discussed and comparisons with recent results for cumulative step length adaptation are drawn.