Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES

Paul Dufossé; Nikolaus Hansen

doi:10.1145/3449639.3459340

Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES

Paul Dufossé
, Nikolaus Hansen

INRIA Institut National de Recherche en Informatique et en Automatique

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

Abstract

In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(μ/μw, λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the Augmented Lagrangian technique and show how surrogate modeling of the constraints can overcome some difficulties. Several variants of AL-CMA-ES are compared on a set of nonlinear constrained problems from the literature. Simple adaptive penalty techniques serve as a baseline for comparison.

Original language	English
Title of host publication	GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference
Publisher	Association for Computing Machinery, Inc
Pages	519-527
Number of pages	9
ISBN (Electronic)	9781450383509
DOIs	https://doi.org/10.1145/3449639.3459340
Publication status	Published - 26 Jun 2021
Event	2021 Genetic and Evolutionary Computation Conference, GECCO 2021 - Virtual, Online, France Duration: 10 Jul 2021 → 14 Jul 2021

Publication series

Name	GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference

Conference

Conference	2021 Genetic and Evolutionary Computation Conference, GECCO 2021
Country/Territory	France
City	Virtual, Online
Period	10/07/21 → 14/07/21

Keywords

Augmented lagrangian
CMA-ES
Constrained optimization
Evolution strategies
Penalty techniques

Access to Document

10.1145/3449639.3459340

Cite this

Dufossé, P., & Hansen, N. (2021). Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES. In GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference (pp. 519-527). (GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference). Association for Computing Machinery, Inc. https://doi.org/10.1145/3449639.3459340

Dufossé, Paul ; Hansen, Nikolaus. / Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES. GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc, 2021. pp. 519-527 (GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference).

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title = "Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES",

abstract = "In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(μ/μw, λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the Augmented Lagrangian technique and show how surrogate modeling of the constraints can overcome some difficulties. Several variants of AL-CMA-ES are compared on a set of nonlinear constrained problems from the literature. Simple adaptive penalty techniques serve as a baseline for comparison.",

keywords = "Augmented lagrangian, CMA-ES, Constrained optimization, Evolution strategies, Penalty techniques",

author = "Paul Dufoss{\'e} and Nikolaus Hansen",

note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 2021 Genetic and Evolutionary Computation Conference, GECCO 2021 ; Conference date: 10-07-2021 Through 14-07-2021",

year = "2021",

month = jun,

day = "26",

doi = "10.1145/3449639.3459340",

language = "English",

series = "GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference",

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}

Dufossé, P & Hansen, N 2021, Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES. in GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference. GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference, Association for Computing Machinery, Inc, pp. 519-527, 2021 Genetic and Evolutionary Computation Conference, GECCO 2021, Virtual, Online, France, 10/07/21. https://doi.org/10.1145/3449639.3459340

Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES. / Dufossé, Paul; Hansen, Nikolaus.
GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc, 2021. p. 519-527 (GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference).

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

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AU - Hansen, Nikolaus

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N2 - In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(μ/μw, λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the Augmented Lagrangian technique and show how surrogate modeling of the constraints can overcome some difficulties. Several variants of AL-CMA-ES are compared on a set of nonlinear constrained problems from the literature. Simple adaptive penalty techniques serve as a baseline for comparison.

AB - In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(μ/μw, λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the Augmented Lagrangian technique and show how surrogate modeling of the constraints can overcome some difficulties. Several variants of AL-CMA-ES are compared on a set of nonlinear constrained problems from the literature. Simple adaptive penalty techniques serve as a baseline for comparison.

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KW - CMA-ES

KW - Constrained optimization

KW - Evolution strategies

KW - Penalty techniques

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BT - GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference

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Dufossé P, Hansen N. Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES. In GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc. 2021. p. 519-527. (GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference). doi: 10.1145/3449639.3459340

Augmented lagrangian, penalty techniques and surrogate modeling for constrained optimization with CMA-ES

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