A Rigorous Complexity Analysis of the (1 + 1) Evolutionary Algorithm for Separable 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 theoretical complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with Boolean inputs is given. Different mutation rates are compared, and the use of the crossover operator is investigated. The main contribution is not the result that the expected run time of the (1 + 1) evolutionary algorithm is Θ(
n
ln
n
) for separable functions with
n
variables but the methods by which this result can be proven rigorously.