A Convergence Analysis of Unconstrained and Bound Constrained Evolutionary Pattern Search

Abstract

We present and analyze a class of evolutionary algorithms for unconstrained and bound constrained optimization on Rn: evolutionary pattern search algorithms (EPSAs). EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. We show that EPSAs can be cast as stochastic pattern search methods, and we use this observation to prove that EPSAs have a probabilistic, weak stationary point convergence theory. This convergence theory is distinguished by the fact that the analysis does not approximate the stochastic process of EP-SAs, and hence it exactly characterizes their convergence properties.