Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework

Cheikh Touré; Anne Auger; Nikolaus Hansen; Dimo Brockhoff

doi:10.1145/3321707.3321852

Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework

Cheikh Touré
, Anne Auger
, Nikolaus Hansen
, Dimo Brockhoff

INRIA Institut National de Recherche en Informatique et en Automatique

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the p × n-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given p − 1 fixed solutions. Crucially, dominated solutions minimize their distance to the empirical Pareto front defined by these p − 1 solutions. We instantiate the framework with CMA-ES as single-objective optimizer. The new algorithm, COMO-CMA-ES, is empirically shown to converge linearly on bi-objective convex-quadratic problems and is compared to MO-CMA-ES, NSGA-II and SMS-EMOA.

Original language	English
Title of host publication	GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference
Publisher	Association for Computing Machinery, Inc
Pages	638-646
Number of pages	9
ISBN (Electronic)	9781450361118
DOIs	https://doi.org/10.1145/3321707.3321852
Publication status	Published - 13 Jul 2019
Event	2019 Genetic and Evolutionary Computation Conference, GECCO 2019 - Prague, Czech Republic Duration: 13 Jul 2019 → 17 Jul 2019

Publication series

Name	GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference

Conference

Conference	2019 Genetic and Evolutionary Computation Conference, GECCO 2019
Country/Territory	Czech Republic
City	Prague
Period	13/07/19 → 17/07/19

Keywords

Hypervolume
Hypervolume contribution
Hypervolume improvement
Multiobjective optimization
Quality indicator
Single-objective optimization

Access to Document

10.1145/3321707.3321852

Cite this

Touré, C., Auger, A., Hansen, N., & Brockhoff, D. (2019). Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework. In GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference (pp. 638-646). (GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference). Association for Computing Machinery, Inc. https://doi.org/10.1145/3321707.3321852

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title = "Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework",

abstract = "We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the p × n-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given p − 1 fixed solutions. Crucially, dominated solutions minimize their distance to the empirical Pareto front defined by these p − 1 solutions. We instantiate the framework with CMA-ES as single-objective optimizer. The new algorithm, COMO-CMA-ES, is empirically shown to converge linearly on bi-objective convex-quadratic problems and is compared to MO-CMA-ES, NSGA-II and SMS-EMOA.",

keywords = "Hypervolume, Hypervolume contribution, Hypervolume improvement, Multiobjective optimization, Quality indicator, Single-objective optimization",

author = "Cheikh Tour{\'e} and Anne Auger and Nikolaus Hansen and Dimo Brockhoff",

note = "Publisher Copyright: {\textcopyright} 2019 Copyright held by the owner/author(s). Publication rights licensed to the Association for Computing Machinery.; 2019 Genetic and Evolutionary Computation Conference, GECCO 2019 ; Conference date: 13-07-2019 Through 17-07-2019",

year = "2019",

month = jul,

day = "13",

doi = "10.1145/3321707.3321852",

language = "English",

series = "GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference",

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}

Touré, C, Auger, A, Hansen, N & Brockhoff, D 2019, Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework. in GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference. GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference, Association for Computing Machinery, Inc, pp. 638-646, 2019 Genetic and Evolutionary Computation Conference, GECCO 2019, Prague, Czech Republic, 13/07/19. https://doi.org/10.1145/3321707.3321852

Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework. / Touré, Cheikh; Auger, Anne; Hansen, Nikolaus et al.
GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc, 2019. p. 638-646 (GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the p × n-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given p − 1 fixed solutions. Crucially, dominated solutions minimize their distance to the empirical Pareto front defined by these p − 1 solutions. We instantiate the framework with CMA-ES as single-objective optimizer. The new algorithm, COMO-CMA-ES, is empirically shown to converge linearly on bi-objective convex-quadratic problems and is compared to MO-CMA-ES, NSGA-II and SMS-EMOA.

KW - Hypervolume

KW - Hypervolume contribution

KW - Hypervolume improvement

KW - Multiobjective optimization

KW - Quality indicator

KW - Single-objective optimization

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M3 - Conference contribution

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Touré C, Auger A, Hansen N , Brockhoff D. Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework. In GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc. 2019. p. 638-646. (GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference). doi: 10.1145/3321707.3321852

Uncrowded hypervolume improvement: COMO-CMA-ES and the Sofomore framework

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