E Volut Ion Strateg Ies

Evolutionary algorithms (EAs) are general stochastic search heuristics often used to solve complex optimization problems. Unfortunately, EA theory is still somewhat weak with respect to providing a deeper understanding of EAs and guidance for the practitioner. In this paper we improve this situation by extending existing theory on the wellknown (1+1) EA to cover the (1 + ) EA, an EA that maintains an o spring population of size . Our goal is to understand how the value of a ects expected optimization time. We compare the (1 + ) EA with the (1+1) EA and prove that on simple unimodal functions no improvements are obtained for > 1. By contrast there are more complex functions for which sensible values of can decrease the optimization time from exponential to a polynomial of small degree with overwhelming probability. These results shed light on the role of and provide some guidelines for the practitioner.