Adaptive Niche Radii and Niche Shapes Approaches for Niching with the CMA-ES

While the motivation and usefulness of niching methods is beyond doubt, the relaxation of assumptions and limitations concerning the hypothetical search landscape is much needed if niching is to be valid in a broader range of applications. Upon the introduction of radii-based niching methods with derandomized evolution strategies (ES), the purpose of this study is to address the so-called niche radius problem. A new concept of an adaptive individual niche radius is applied to niching with the covariance matrix adaptation evolution strategy (CMA-ES). Two approaches are considered. The first approach couples the radius to the step size mechanism, while the second approach employs the Mahalanobis distance metric with the covariance matrix mechanism for the distance calculation, for obtaining niches with more complex geometrical shapes. The proposed approaches are described in detail, and then tested on high-dimensional artificial landscapes at several levels of difficulty. They are shown to be robust and to achieve satisfying results.