Local performance of the (1 + 1)-ES in a noisy environment

While noise is a phenomenon present in many real world optimization problems, the understanding of its potential effects on the performance of evolutionary algorithms is still incomplete. This paper investigates the effects of fitness proportionate Gaussian noise for a (1 + 1)-ES with isotropic normal mutations on the quadratic sphere in the limit of infinite search-space dimensionality. It is demonstrated experimentally that the results provide a good approximation for finite space dimensionality. It is shown that overvaluation as a result of failure to re-evaluate parental fitness leads to both reduced success probabilities and improved performance. Implications for mutation strength adaptation rules are discussed and optimal re-sampling rates are computed.