Recombination for learning strategy parameters in the MO-CMA-ES

Abstract

The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) is a variable-metric algorithm for real-valued vector optimization. It maintains a parent population of candidate solutions, which are varied by additive, zero-mean Gaussian mutations. Each individual learns its own covariance matrix for the mutation distribution considering only its parent and offspring. However, the optimal mutation distribution of individuals that are close in decision space are likely to be similar if we presume some notion of continuity of the optimization problem. Therefore, we propose a lateral (inter-individual) transfer of information in the MO-CMA-ES considering also successful mutations of neighboring individuals for the covariance matrix adaptation. We evaluate this idea on common bi-criteria objective functions. The preliminary results show that the new adaptation rule significantly improves the performance of the MO-CMA-ES. © Springer-Verlag 2009.