Pareto optimal set approximation by models: A linear case

Aimin Zhou; Haoying Zhao; Hu Zhang; Guixu Zhang

doi:10.1007/978-3-030-12598-1_36

Pareto optimal set approximation by models: A linear case

Aimin Zhou^*, Haoying Zhao, Hu Zhang, Guixu Zhang

^*Corresponding author for this work

School of Computer Science and Technology

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

2 Scopus citations

Abstract

The optimum of a multiobjective optimization problem (MOP) usually consists of a set of tradeoff solutions, called Pareto optimal set, that balances different objectives. In the community of evolutionary computation, an internal or external population with a limited size is usually used to approximate the Pareto optimal set. Since the Pareto optimal set forms a manifold in both the decision and objective spaces under mild conditions, it is possible to use a model as well as a population of solutions to approximate the Pareto optimal set. Following this idea, the paper proposes to use a set of linear models to approximate the Pareto optimal set in the decision space. The basic idea is to partition the manifold into different segments and use a linear model to approximate each segment in a local area. To implement the algorithm, the models are incorporated in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. The proposed algorithm is applied to a test suite, and the comparison study demonstrates that models can help to improve the performance of algorithms that only use solutions to approximate the Pareto optimal set.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings
Editors	Carlos A. Coello Coello, Patrick Reed, Kalyanmoy Deb, Erik Goodman, Kathrin Klamroth, Sanaz Mostaghim, Kaisa Miettinen
Publisher	Springer Verlag
Pages	451-462
Number of pages	12
ISBN (Print)	9783030125974
DOIs	https://doi.org/10.1007/978-3-030-12598-1_36
State	Published - 2019
Event	10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 - East Lansing, United States Duration: 10 Mar 2019 → 13 Mar 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11411 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019
Country/Territory	United States
City	East Lansing
Period	10/03/19 → 13/03/19

Keywords

Evolutionary multiobjective optimization
MOEA/D
Regularity model

Access to Document

10.1007/978-3-030-12598-1_36

Cite this

Zhou, A., Zhao, H., Zhang, H., & Zhang, G. (2019). Pareto optimal set approximation by models: A linear case. In C. A. Coello Coello, P. Reed, K. Deb, E. Goodman, K. Klamroth, S. Mostaghim, & K. Miettinen (Eds.), Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings (pp. 451-462). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-12598-1_36

Zhou, Aimin ; Zhao, Haoying ; Zhang, Hu et al. / Pareto optimal set approximation by models : A linear case. Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. editor / Carlos A. Coello Coello ; Patrick Reed ; Kalyanmoy Deb ; Erik Goodman ; Kathrin Klamroth ; Sanaz Mostaghim ; Kaisa Miettinen. Springer Verlag, 2019. pp. 451-462 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Pareto optimal set approximation by models: A linear case",

abstract = "The optimum of a multiobjective optimization problem (MOP) usually consists of a set of tradeoff solutions, called Pareto optimal set, that balances different objectives. In the community of evolutionary computation, an internal or external population with a limited size is usually used to approximate the Pareto optimal set. Since the Pareto optimal set forms a manifold in both the decision and objective spaces under mild conditions, it is possible to use a model as well as a population of solutions to approximate the Pareto optimal set. Following this idea, the paper proposes to use a set of linear models to approximate the Pareto optimal set in the decision space. The basic idea is to partition the manifold into different segments and use a linear model to approximate each segment in a local area. To implement the algorithm, the models are incorporated in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. The proposed algorithm is applied to a test suite, and the comparison study demonstrates that models can help to improve the performance of algorithms that only use solutions to approximate the Pareto optimal set.",

keywords = "Evolutionary multiobjective optimization, MOEA/D, Regularity model",

author = "Aimin Zhou and Haoying Zhao and Hu Zhang and Guixu Zhang",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 ; Conference date: 10-03-2019 Through 13-03-2019",

year = "2019",

doi = "10.1007/978-3-030-12598-1\_36",

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Zhou, A, Zhao, H, Zhang, H & Zhang, G 2019, Pareto optimal set approximation by models: A linear case. in CA Coello Coello, P Reed, K Deb, E Goodman, K Klamroth, S Mostaghim & K Miettinen (eds), Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11411 LNCS, Springer Verlag, pp. 451-462, 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019, East Lansing, United States, 10/03/19. https://doi.org/10.1007/978-3-030-12598-1_36

Pareto optimal set approximation by models: A linear case. / Zhou, Aimin; Zhao, Haoying; Zhang, Hu et al.
Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. ed. / Carlos A. Coello Coello; Patrick Reed; Kalyanmoy Deb; Erik Goodman; Kathrin Klamroth; Sanaz Mostaghim; Kaisa Miettinen. Springer Verlag, 2019. p. 451-462 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS).

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

TY - GEN

T1 - Pareto optimal set approximation by models

T2 - 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019

AU - Zhou, Aimin

AU - Zhao, Haoying

AU - Zhang, Hu

AU - Zhang, Guixu

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2019.

PY - 2019

Y1 - 2019

N2 - The optimum of a multiobjective optimization problem (MOP) usually consists of a set of tradeoff solutions, called Pareto optimal set, that balances different objectives. In the community of evolutionary computation, an internal or external population with a limited size is usually used to approximate the Pareto optimal set. Since the Pareto optimal set forms a manifold in both the decision and objective spaces under mild conditions, it is possible to use a model as well as a population of solutions to approximate the Pareto optimal set. Following this idea, the paper proposes to use a set of linear models to approximate the Pareto optimal set in the decision space. The basic idea is to partition the manifold into different segments and use a linear model to approximate each segment in a local area. To implement the algorithm, the models are incorporated in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. The proposed algorithm is applied to a test suite, and the comparison study demonstrates that models can help to improve the performance of algorithms that only use solutions to approximate the Pareto optimal set.

AB - The optimum of a multiobjective optimization problem (MOP) usually consists of a set of tradeoff solutions, called Pareto optimal set, that balances different objectives. In the community of evolutionary computation, an internal or external population with a limited size is usually used to approximate the Pareto optimal set. Since the Pareto optimal set forms a manifold in both the decision and objective spaces under mild conditions, it is possible to use a model as well as a population of solutions to approximate the Pareto optimal set. Following this idea, the paper proposes to use a set of linear models to approximate the Pareto optimal set in the decision space. The basic idea is to partition the manifold into different segments and use a linear model to approximate each segment in a local area. To implement the algorithm, the models are incorporated in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. The proposed algorithm is applied to a test suite, and the comparison study demonstrates that models can help to improve the performance of algorithms that only use solutions to approximate the Pareto optimal set.

KW - Evolutionary multiobjective optimization

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KW - Regularity model

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SN - 9783030125974

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BT - Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings

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A2 - Reed, Patrick

A2 - Deb, Kalyanmoy

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A2 - Klamroth, Kathrin

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Zhou A, Zhao H, Zhang H, Zhang G. Pareto optimal set approximation by models: A linear case. In Coello Coello CA, Reed P, Deb K, Goodman E, Klamroth K, Mostaghim S, Miettinen K, editors, Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. Springer Verlag. 2019. p. 451-462. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-12598-1_36

Pareto optimal set approximation by models: A linear case

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