LS-CMA-ES: A second-order algorithm for covariance matrix adaptation

Abstract

Evolution Strategies, a class of Evolutionary Algorithms based on Gaussian mutation and deterministic selection, are today considered the best choice as far as parameter optimization is concerned. However, there are multiple ways to tune the covariance matrix of the Gaussian mutation. After reviewing the state of the art in covariance matrix adaptation, a new approach is proposed, in which the update of the covariance matrix is based on a quadratic approximation of the target function, obtained by some Least-Square minimization. A dynamic criterion is designed to detect situations where the approximation is not accurate enough, and original Covariance Matrix Adaptation (CMA) should rather be directly used. The resulting algorithm is experimentally validated on benchmark functions, outperforming CMA-ES on a large class of problems. © Springer-Verlag 2004.