A Convergence Analysis of Unconstrained and Bound Constrained Evolutionary Pattern Search

The authors present and analyze a class of evolutionary algorithms for unconstrained and bound constrained optimization on R{sup n}: 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. They show that EPSAs can be cast as stochastic pattern search methods, and they use this observation to prove that EpSAs have a probabilistic weak stationary point convergence theory. This work provides the first convergence analysis for a class of evolutionary algorithms that guarantees convergence almost surely to a stationary point of a nonconvex objective function