Evolution Strategies with Cumulative Step Length Adaptation on the Noisy Parabolic Ridge

Authors: 

Dirk V. Arnold
Hans-Georg Beyer

Author Addresses: 

Faculty of Computer Science
Dalhousie University
6050 University Ave.
PO Box 15000
Halifax, Nova Scotia, Canada
B3H 4R2

Hans-Georg Beyer
Department of Computer Science
Research Center Process and Product Engineering
Vorarlberg University of Applied Sciences
Hochschulstr. 1
A-6850 Dornbirn, Austria

Abstract: 

This paper presents an analysis of the performance of the (mu/mu,lambda)-ES with isotropic mutations and cumulative step length adaptation on the noisy parabolic ridge. Several forms of dependency of the noise strength on the distance from the ridge axis are considered. Closed form expressions are derived that describe the mutation strength and the progress rate of the strategy in high-dimensional search spaces. It is seen that as for the sphere model, larger levels of noise present lead to cumulative step length adaptation generating increasingly inadequate mutation strengths, and that the problem can be ameliorated to some degree by working with larger populations.

Tech Report Number: 
CS-2006-02
Report Date: 
January 16, 2006
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