A rigorous complexity analysis of the (1+1) evolutionary algorithm for linear functions with Boolean inputs

Evolutionary algorithms (EAs) are heuristic randomized algorithms which, by many impressive experiments, have been proven to behave quite well for optimization problems of various kinds. In this paper, a rigorous complexity analysis of the (1+1) evolutionary algorithm for linear functions with Boolean inputs is given. The analysis is carried out for different mutation rates. The main contribution of the paper is not the result that the expected run time of the (1+1) evolutionary algorithm is at most /spl Theta/(n ln n) for linear functions with n variables, but the presentation of methods showing how this result can be proven rigorously.