Hypervolume Maximization: A Geometric View of Pareto Set Learning

Xiaoyuan Zhang; Xi Lin; Bo Xue; Yifan Chen; Qingfu Zhang

Hypervolume Maximization: A Geometric View of Pareto Set Learning

Xiaoyuan Zhang, Xi Lin, Bo Xue, Yifan Chen^*, Qingfu Zhang^*

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

6 Citations (Scopus)

Abstract

This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms. Code is available at https://github.com/xzhang2523/hvpsl/tree/master.

Original language	English
Title of host publication	37th Conference on Neural Information Processing Systems, NeurIPS 2023
Editors	A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, S. Levine
Publisher	Neural Information Processing Systems Foundation
Pages	1-28
Number of pages	28
ISBN (Print)	9781713899921
Publication status	Published - Dec 2023
Event	37th Conference on Neural Information Processing Systems, NeurIPS 2023 - Ernest N. Morial Convention Center, New Orleans, United States Duration: 10 Dec 2023 → 16 Dec 2023 https://proceedings.neurips.cc/paper_files/paper/2023 (conference paper search) https://openreview.net/group?id=NeurIPS.cc/2023/Conference#tab-accept-oral (conference paper search) https://neurips.cc/Conferences/2023 (conference website)

Publication series

Name	Advances in Neural Information Processing Systems
Volume	36
ISSN (Print)	1049-5258

Name	NeurIPS Proceedings

Conference

Conference	37th Conference on Neural Information Processing Systems, NeurIPS 2023
Country/Territory	United States
City	New Orleans
Period	10/12/23 → 16/12/23
Internet address	https://proceedings.neurips.cc/paper_files/paper/2023 (conference paper search) https://openreview.net/group?id=NeurIPS.cc/2023/Conference#tab-accept-oral (conference paper search) https://neurips.cc/Conferences/2023 (conference website)

Scopus Subject Areas

Computer Networks and Communications
Information Systems
Signal Processing

Access to Document

https://proceedings.neurips.cc/paper_files/paper/2023/file/7a7f6cc5dc2a84fb4edf0feb8e5cfd50-Paper-Conference.pdf

Cite this

Zhang, X., Lin, X., Xue, B., Chen, Y., & Zhang, Q. (2023). Hypervolume Maximization: A Geometric View of Pareto Set Learning. In A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, & S. Levine (Eds.), 37th Conference on Neural Information Processing Systems, NeurIPS 2023 (pp. 1-28). (Advances in Neural Information Processing Systems; Vol. 36), (NeurIPS Proceedings). Neural Information Processing Systems Foundation. https://proceedings.neurips.cc/paper_files/paper/2023/file/7a7f6cc5dc2a84fb4edf0feb8e5cfd50-Paper-Conference.pdf

Zhang, Xiaoyuan ; Lin, Xi ; Xue, Bo et al. / Hypervolume Maximization : A Geometric View of Pareto Set Learning. 37th Conference on Neural Information Processing Systems, NeurIPS 2023. editor / A. Oh ; T. Naumann ; A. Globerson ; K. Saenko ; M. Hardt ; S. Levine. Neural Information Processing Systems Foundation, 2023. pp. 1-28 (Advances in Neural Information Processing Systems). (NeurIPS Proceedings).

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title = "Hypervolume Maximization: A Geometric View of Pareto Set Learning",

abstract = "This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms. Code is available at https://github.com/xzhang2523/hvpsl/tree/master.",

author = "Xiaoyuan Zhang and Xi Lin and Bo Xue and Yifan Chen and Qingfu Zhang",

note = "This paper is supported by the Research Grants Council of the Hong Kong Special Administrative Region, China [GRF Project No: CityU 11215622] and by Natural Science Foundation of China [Project No: 62276223]. In the last, we sincerely appreciate the helpful insights and feedbacks provided by Liang Zhao;Dake Bu;Yingying Yu (CityU Hong Kong) and Dr. Jingda Deng (XJTU). Publisher Copyright: {\textcopyright} 2023 Neural information processing systems foundation. All rights reserved.; 37th Conference on Neural Information Processing Systems, NeurIPS 2023 ; Conference date: 10-12-2023 Through 16-12-2023",

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series = "Advances in Neural Information Processing Systems",

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booktitle = "37th Conference on Neural Information Processing Systems, NeurIPS 2023",

url = "https://proceedings.neurips.cc/paper_files/paper/2023, https://openreview.net/group?id=NeurIPS.cc/2023/Conference#tab-accept-oral, https://neurips.cc/Conferences/2023",

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Zhang, X, Lin, X, Xue, B, Chen, Y & Zhang, Q 2023, Hypervolume Maximization: A Geometric View of Pareto Set Learning. in A Oh, T Naumann, A Globerson, K Saenko, M Hardt & S Levine (eds), 37th Conference on Neural Information Processing Systems, NeurIPS 2023. Advances in Neural Information Processing Systems, vol. 36, NeurIPS Proceedings, Neural Information Processing Systems Foundation, pp. 1-28, 37th Conference on Neural Information Processing Systems, NeurIPS 2023, New Orleans, Louisiana, United States, 10/12/23. <https://proceedings.neurips.cc/paper_files/paper/2023/file/7a7f6cc5dc2a84fb4edf0feb8e5cfd50-Paper-Conference.pdf>

Hypervolume Maximization: A Geometric View of Pareto Set Learning. / Zhang, Xiaoyuan; Lin, Xi; Xue, Bo et al.
37th Conference on Neural Information Processing Systems, NeurIPS 2023. ed. / A. Oh; T. Naumann; A. Globerson; K. Saenko; M. Hardt; S. Levine. Neural Information Processing Systems Foundation, 2023. p. 1-28 (Advances in Neural Information Processing Systems; Vol. 36), (NeurIPS Proceedings).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

TY - GEN

T1 - Hypervolume Maximization

T2 - 37th Conference on Neural Information Processing Systems, NeurIPS 2023

AU - Zhang, Xiaoyuan

AU - Lin, Xi

AU - Xue, Bo

AU - Chen, Yifan

AU - Zhang, Qingfu

N1 - This paper is supported by the Research Grants Council of the Hong Kong Special Administrative Region, China [GRF Project No: CityU 11215622] and by Natural Science Foundation of China [Project No: 62276223]. In the last, we sincerely appreciate the helpful insights and feedbacks provided by Liang Zhao;Dake Bu;Yingying Yu (CityU Hong Kong) and Dr. Jingda Deng (XJTU). Publisher Copyright: © 2023 Neural information processing systems foundation. All rights reserved.

PY - 2023/12

Y1 - 2023/12

N2 - This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms. Code is available at https://github.com/xzhang2523/hvpsl/tree/master.

AB - This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms. Code is available at https://github.com/xzhang2523/hvpsl/tree/master.

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SN - 9781713899921

T3 - Advances in Neural Information Processing Systems

SP - 1

EP - 28

BT - 37th Conference on Neural Information Processing Systems, NeurIPS 2023

A2 - Oh, A.

A2 - Naumann, T.

A2 - Globerson, A.

A2 - Saenko, K.

A2 - Hardt, M.

A2 - Levine, S.

PB - Neural Information Processing Systems Foundation

Y2 - 10 December 2023 through 16 December 2023

ER -

Zhang X, Lin X, Xue B, Chen Y, Zhang Q. Hypervolume Maximization: A Geometric View of Pareto Set Learning. In Oh A, Naumann T, Globerson A, Saenko K, Hardt M, Levine S, editors, 37th Conference on Neural Information Processing Systems, NeurIPS 2023. Neural Information Processing Systems Foundation. 2023. p. 1-28. (Advances in Neural Information Processing Systems). (NeurIPS Proceedings).

Hypervolume Maximization: A Geometric View of Pareto Set Learning

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