Analysis of the (1 + 1) EA for a Noisy OneMax

In practical applications evaluating a fitness function is frequently subject to noise, i. e., the “true fitness” is disturbed by some random variations. Evolutionary algorithms (EAs) are often successfully applied to noisy problems, where they have turned out to be particularly robust. Theoretical results on the behavior of EAs for noisy functions are comparatively very rare, especially for discrete search spaces. Here we present an analysis of the (1 + 1) EA for a noisy variant of OneMax and compute the maximal noise strength allowing the (1 + 1) EA a polynomial runtime asymptotically exactly. The methods used in the proofs are presented in a general form with clearly stated conditions in order to simplify further applications.