Covariance matrix adaptation for multi-objective optimization
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Covariance matrix adaptation for multi-objective optimization. / Igel, Christian; Hansen, Nikolaus; Roth, Stefan.
I: Evolutionary Computation, Bind 15, Nr. 1, 2007, s. 1-28.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Covariance matrix adaptation for multi-objective optimization
AU - Igel, Christian
AU - Hansen, Nikolaus
AU - Roth, Stefan
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
U2 - 10.1162/evco.2007.15.1.1
DO - 10.1162/evco.2007.15.1.1
M3 - Journal article
C2 - 17388777
VL - 15
SP - 1
EP - 28
JO - Evolutionary Computation
JF - Evolutionary Computation
SN - 1063-6560
IS - 1
ER -
ID: 32645811