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 e ects on the performance of evolutionary algorithms is still incomplete. This paper investigates the e ects of noise for the in nite-dimensional quadratic sphere and a (1+1)-ES with isotropic normal mutations. It is shown that overvaluation as a result of failure to reevaluate parental tness leads to both reduced success probabilities and improved performance. Implications for mutation strength adaptation rules are discussed and optimal resampling rates are computed.