Abnormal Mutations: Evolution Strategies Don't Require Gaussianity

Genetic and Evolutionary Computation Conference (GECCO), pp. 701–709

Abstract

The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for isotropy. However, some theoretical results suggest that other distributions might lead to similar local convergence properties. This paper empirically shows that a wide range of evolutionary strategies, from the (1+1)-ES to CMA-ES, show comparable optimization performance when using a mutation distribution other than the standard Gaussian. Replacing it with, e.g., uniformly distributed mutations, does not deteriorate the performance of ES, when using the default adaptation mechanism for the strategy parameters. We observe that these results hold not only for the sphere model but also for a wider range of benchmark problems.

Authors 6

1. Jacob de Nobel Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Leiden, Netherlands

2. Diederick Vermetten Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Leiden, Netherlands

3. Hao Wang Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Leiden, Netherlands

4. Anna V. Kononova Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Leiden, Netherlands

5. Günter Rudolph

   TU Dortmund University

   Affiliation as printed

   TU Dortmund University, Dortmund, Germany

6. Thomas Bäck Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Leiden, Netherlands