A general noise model and its effects on evolution strategy performance

Most studies concerned with the effects of noise on the performance of optimization strategies, in general, and on evolutionary approaches, in particular, have assumed a Gaussian noise model. However, practical optimization strategies frequently face situations where the noise is not Gaussian. Noise distributions may be skew or biased, and outliers may be present. The effects of non-Gaussian noise are largely unexplored, and it is unclear whether the insights gained and the recommendations with regard to the sizing of strategy parameters that have been made under the assumption of Gaussian noise bear relevance to more general situations. In this paper, the behavior of a powerful class of recombinative evolution strategies is studied on the sphere model under the assumption of a very general noise model. A performance law is derived, its implications are studied both analytically and numerically, and comparisons with the case of Gaussian noise are drawn. It is seen that while overall, the assumption of Gaussian noise in previous studies is less severe than might have been expected, some significant differences do arise when considering noise that is of unbounded variance, skew, or biased.