Pure Strategy or Mixed Strategy?

Mixed strategy evolutionary algorithms (EAs) aim at integrating several mutation operators into a single algorithm. However no analysis has been made to answer the theoretical question: whether and when is the performance of mixed strategy EAs better than that of pure strategy EAs? In this paper, asymptotic convergence rate and asymptotic hitting time are proposed to measure the performance of EAs. It is proven that the asymptotic convergence rate and asymptotic hitting time of any mixed strategy (1+1) EA consisting of several mutation operators is not worse than that of the worst pure strategy (1+1) EA using only one mutation operator. Furthermore it is proven that if these mutation operators are mutually complementary, then it is possible to design a mixed strategy (1+1) EA whose performance is better than that of any pure strategy (1+1) EA using only one mutation operator.