Hierarchically organised evolution strategies on the parabolic ridge

Abstract

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 selfadaptation. 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.

Step Length Adaptation on Ridge Functions

“…Introducing isolation decreases the likelihood of opportunistic individuals that make short steps being rewarded. Arnold and MacLeod (2006) analytically study the performance of hierarchically organized strategies on parabolic ridges and derive expressions that describe the dependence of the strategies' performance on the length of the isolation periods. The derivation presented here generalizes those results by considering ridge topologies other than parabolic ones, and by including the effects of noise in the calculations.…”

“…In that reference, it is seen in experiments that mutative self-adaptation performs unsatisfactorily on some ridges, and hierarchically organized strategies are proposed as an alternative. A first analytical investigation of the behavior of hierarchically organized evolution strategies on parabolic ridges has recently been presented by Arnold and MacLeod (2006). Mutative self-adaptation on ridge functions is the subject of the analysis presented by Beyer and Meyer-Nieberg (Beyer and Meyer-Nieberg, 2006;Meyer-Nieberg and Beyer, 2007a).…”

“…The approach to the analyses of mutative selfadaptation and two-point adaptation is new and will conceivably prove useful in other fitness environments in the future. The treatment of hierarchically organized evolution strategies generalizes that in Arnold and MacLeod (2006), both by considering ridges other than parabolic ones and by including the effects of noise. Section 7 contrasts and compares the properties of the different adaptation algorithms, and the paper concludes with suggestions for future work.…”

Multi-Level Evolution Strategies for High-Resolution Black-Box Control

“…In what follows, we restrict the usage of multi-level to the MG context. Also, the term Hierarchically Organised ESs has been used [2] in a different context of parameter tuning by means of a bi-level meta-evolution treatment. Despite the terminology resemblance, the latter studies are not relevant to the current work.…”