title: Covariance matrix adaptation for multi-objective optimization.
abstract: The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most powerful evolutionary algorithms for real-valued single-objective optimization. In this paper, we develop a variant of the CMA-ES for multi-objective optimization (MOO). We first introduce a single-objective, elitist CMA-ES using plus-selection and step size control based on a success rule. This algorithm is compared to the standard CMA-ES. The elitist CMA-ES turns out to be slightly faster on unimodal functions, but is more prone to getting stuck in sub-optimal local minima. In the new multi-objective CMAES (MO-CMA-ES) a population of individuals that adapt their search strategy as in the elitist CMA-ES is maintained. These are subject to multi-objective selection. The selection is based on non-dominated sorting using either the crowding-distance or the contributing hypervolume as second sorting criterion. Both the elitist single-objective CMA-ES and the MO-CMA-ES inherit important invariance properties, in particular invariance against rotation of the search space, from the original CMA-ES. The benefits of the new MO-CMA-ES in comparison to the well-known NSGA-II and to NSDE, a multi-objective differential evolution algorithm, are experimentally shown.
authors: Institut für Neuroinformatik, Ruhr-Universität Bochum, 44780 Bochum, Germany. christian.igel@neuroinformatik.rub.de
authors: Christian
authors: C
authors: Igel
authors: Nikolaus
authors: N
authors: Hansen
authors: Stefan
authors: S
authors: Roth
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D005075:Biological Evolution; D003198:Computer Simulation; D008957:Models, Genetic