A Stationary Point Convergence Theory for Evolutionary Algorithms

William E. Hart
Massively Parallel Computing Research Laboratory
P. O. Box 5800
Sandia National Laboratories
Albuquerque, NM 87185-1110


This paper defines a class of evolutionary algorithms called evolutionary pattern search algorithms (EPSAs) and analyzes their convergence properties. This class of algorithms is closely related to evolutionary programming, evolution strategie and real-coded genetic algorithms. EPSAs are self-adapting evolutionary algorithms that modify the step size of the mutation operator in response to the success of previous optimization steps. The rule used to adapt the step size can be used to provide a stationary point convergence theory for EPSAs on any continuous function. This convergence theory is based on an extension of the convergence theory for generalized pattern search methods.