Comparing Evolutionary Algorithms to the (1+1)-EA by Means of Stochastic Ordering

In this paper, we study the conditions in which the (1+1)-EA compares favorably to other evolutionary algorithms (EAs) in terms of tness distribution function at given iteration and 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 exampled on the sorting problem with HAM landscape and the exchange mutation operator. Also we consider several cases where the (1+1)-EA is the best possible search strategy in the class of the EAs.