  Mixed strategy EAs aim to integrate several mutation operators into a single
algorithm. However few theoretical analysis has been made to answer the
question whether and when the performance of mixed strategy EAs is better than
that of pure strategy EAs. In theory, the performance of EAs can be measured by
asymptotic convergence rate and asymptotic hitting time. In this paper, it is
proven that given a mixed strategy (1+1) EAs consisting of several mutation
operators, its performance (asymptotic convergence rate and asymptotic hitting
time)is not worse than that of the worst pure strategy (1+1) EA using one
mutation operator; 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 one mutation operator.
