On the behaviour of evolution strategies optimising cigar functions

  • Authors:
  • Dirk V. Arnold;Hans-Georg Beyer

  • Affiliations:
  • Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 1W5 dirk@cs.dal.ca;Department of Computer Science, Vorarlberg University of Applied Sciences, Hochschulstrasse 1, A-6850 Dornbirn, Austria hgb@fhv.at

  • Venue:
  • Evolutionary Computation
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper studies the performance of multi-recombinative evolution strategies using isotropically distributed mutations with cumulative step length adaptation when applied to optimising cigar functions. Cigar functions are convex-quadratic objective functions that are characterised by the presence of only two distinct eigenvalues of their Hessian, the smaller one of which occurs with multiplicity one. A simplified model of the strategy's behaviour is developed. Using it, expressions that approximately describe the stationary state that is attained when the mutation strength is adapted are derived. The performance achieved by cumulative step length adaptation is compared with that obtained when using optimally adapted step lengths.