A comparison of evolution strategies with other direct search methods in the presence of noise

Evolution strategies are general, nature-inspired heuristics for search and optimization. Due to their use of populations of candidate solutions and their advanced adaptation schemes, there is a common belief that evolution strategies are especially useful for optimization in the presence of noise. Empirical evidence as well as a number of theoretical findings with respect to the performance of evolution strategies on a class of spherical objective functions disturbed by Gaussian noise support that belief. However, little is known with respect to the capabilities in the presence of noise of evolution strategies relative to those of other direct optimization strategies. In the present paper, theoretical results with respect to the performance of evolution strategies in the presence of Gaussian noise are summarized and discussed. Then, the performance of evolution strategies is compared empirically with that of several other direct optimization strategies in the noisy, spherical environment that the theoretical results have been obtained in. Due to the simplicity of that environment, the results are easily interpretable and can serve to reveal the respective strengths and weaknesses of the algorithms. It is seen that for low levels of noise, most of the strategies exhibit similar degrees of efficiency. For higher levels of noise, their step length adaptation scheme affords evolution strategies a greater degree of robustness than the other algorithms tested.