Rigorous analyses of fitness-proportional selection for optimizing linear functions

Abstract

Rigorous runtime analyses of evolutionary algorithms (EAs) mainly investigate algorithms that use elitist selection methods. Two algorithms commonly studied are Randomized Local Search (RLS) and the (1+1) EA and it is well known that both optimize any linear pseudo-Boolean function on n bits within an expected number of O(n log n) fitness evaluations. In this paper, we analyze variants of these algorithms that use fitness proportional selection.