Resampling versus Repair in Evolution Strategies Applied to a Constrained Linear Problem

Abstract

We study the behaviour of multi-recombination evolution strategies for the problem of maximising a linear function with a single linear constraint. Two variants of the algorithm are considered: a strategy that resamples infeasible candidate solutions and one that applies a simple repair mechanism. Integral expressions that describe the strategies’ one-generation behaviour are derived and used in a simple zeroth order model for the steady state attained when operating with constant step size. Applied to the analysis of cumulative step size adaptation, the approach provides an intuitive explanation for the qualitative difference in the algorithm variants’ behaviour. The findings have implications for the design of constraint handling techniques to be used in connection with cumulative step size adaptation.