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

Harvard

Igel, C, Hansen, N & Roth, S 2007, 'Covariance matrix adaptation for multi-objective optimization', Evolutionary Computation, bind 15, nr. 1, s. 1-28. https://doi.org/10.1162/evco.2007.15.1.1

APA

Igel, C., Hansen, N., & Roth, S. (2007). Covariance matrix adaptation for multi-objective optimization. Evolutionary Computation, 15(1), 1-28. https://doi.org/10.1162/evco.2007.15.1.1

Vancouver

Igel C, Hansen N, Roth S. Covariance matrix adaptation for multi-objective optimization. Evolutionary Computation. 2007;15(1):1-28. https://doi.org/10.1162/evco.2007.15.1.1

Author

Igel, Christian ; Hansen, Nikolaus ; Roth, Stefan. / Covariance matrix adaptation for multi-objective optimization. I: Evolutionary Computation. 2007 ; Bind 15, Nr. 1. s. 1-28.

Bibtex

@article{5d0de0b554a84bc1ae782c459a7f4017,
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.",
author = "Christian Igel and Nikolaus Hansen and Stefan Roth",
year = "2007",
doi = "10.1162/evco.2007.15.1.1",
language = "English",
volume = "15",
pages = "1--28",
journal = "Evolutionary Computation",
issn = "1063-6560",
publisher = "M I T Press",
number = "1",

}

RIS

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