Comparing evolutionary algorithms to the (1+1) -EA

In this paper, we study the conditions in which the random hill-climbing algorithm (1 + 1)-EA compares favorably to other evolutionary algorithms (EAs) in terms of fitness function distribution at a given iteration and with respect to the average optimization time. Our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the (1 + 1)-EA. In this case one can extend the lower bounds obtained for the expected optimization time of the (1 + 1)-EA to other EAs based on the dominated reproduction operator. This method is demonstrated on the sorting problem with HAM landscape and the exchange mutation operator. We consider several simple examples where the (1 + 1)-EA is the best possible search strategy in the class of the EAs.