Self-Adaptive Niching CMA-ES with Mahalanobis Metric

Existing niching techniques commonly use the Euclidean distance metric in the decision space for the classification of feasible solutions to the niches under formation. This approach is likely to encounter problems in high-dimensional landscapes with non-isotropic basins of attraction. Here we consider niching with the covariance matrix adaptation evolution strategy (CMA-ES), and introduce the Mahalanobis distance metric into the niching mechanism, aiming to allow a more accurate spatial classification, based on the ellipsoids of the distribution, rather than hyper-spheres of the Euclidean metric. This is tested with the CMA-(+) routines, and compared to two niching frameworks - fixed niche radius as well as self- adaptive niche radius, which is based on the coupling to the step-size. The performance of the different variants is evaluated on a suite of theoretical test-functions. We thus present here the Mahalanobis-assisted CMA-niching as a state-of-the-art niching technique within evolution strategies (ES), and propose it as a solution to the so-called niche radius problem.