A Generalized Stationary Point Convergence Theory for Evolutionary Algorithms
William E. Hart · University of North Texas Digital Library (University of North Texas) · 1997
This paper presents a convergence theory for evolutionary pattern search algorithms (EPSAs) . EPSAs are self-adapting evolutionary algorithms that modify the step size of the mutation operator in response to the success of previous optimization steps. Previously, we have proven a stationary point convergence theory for EPSAs for which the step size is not allowed to increase. The present analysis generalizes this analysis to prove a convergence theory for EPSAs that are allowed to both increase and decrease the step size. This convergence theory is based on an extension of the convergence theory for generalized pattern search methods. 1 INTRODUCTION This paper concerns the application of evolutionary search algorithms to solve an unconstrained minimization problem to find x 2 D such that f(x ) = min x2D f(x); where D is a compact subset of R n and f : D ! R. In particular, we consider the convergence properties of evolutionary pattern search algorithms (EPSAs), which were ...