HVC-Net: Deep learning based hypervolume contribution approximation

Ke Shang; Weiduo Liao; Hisao Ishibuchi

doi:10.1007/978-3-031-14714-2_29

HVC-Net: Deep learning based hypervolume contribution approximation

Ke Shang
, Weiduo Liao
, Hisao Ishibuchi^*

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

8 Citations (Scopus)

Abstract

In this paper, we propose HVC-Net, a deep learning based hypervolume contribution approximation method for evolutionary multi-objective optimization. The basic idea of HVC-Net is to use a deep neural network to approximate the hypervolume contribution of each solution in a non-dominated solution set. HVC-Net has two characteristics: (1) It is permutation equivalent to the order of solutions in the input solution set, and (2) a single HVC-Net can handle solution sets of various size (e.g., solution sets with 20, 50 and 100 solutions). The performance of HVC-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume contribution approximation methods (i.e., point-based method and line-based method). Our experimental results show that HVC-Net outperforms the other two methods in terms of both the runtime and the ability to identify the smallest (largest) hypervolume contributor in a solution set, which shows the superiority of HVC-Net for hypervolume contribution approximation. © 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG.

Original language	English
Title of host publication	Parallel Problem Solving from Nature – PPSN XVII
Subtitle of host publication	17th International Conference, PPSN 2022 - Proceedings
Editors	Günter Rudolph, Anna V. Kononova, Hernán Aguirre, Pascal Kerschke, Gabriela Ochoa, Tea Tušar
Publisher	Springer, Cham
Pages	414-426
Volume	Part I
ISBN (Electronic)	978-3-031-14714-2
ISBN (Print)	978-3-031-14713-5
DOIs	https://doi.org/10.1007/978-3-031-14714-2_29
Publication status	Published - 2022
Externally published	Yes
Event	17th International Conference on Parallel Problem Solving from Nature (PPSN 2022) - Dortmund, Germany Duration: 10 Sept 2022 → 14 Sept 2022 https://engineering.esteco.com/events/international-conference-on-parallel-problem-solving-from-nature-ppsn-xvii/#:~:text=International%20Conference%20on%20Parallel%20Problem%20Solving%20from%20Nature%20(PPSN%20XVII),-10%20%2D%2014%20Sep&text=The%20seventeenth%20International%20Conference%20on,10%20to%2014%20September%202022.

Publication series

Name	Lecture Notes in Computer Science
Volume	13398
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Parallel Problem Solving from Nature (PPSN 2022)
Abbreviated title	PPSN XVII
Place	Germany
City	Dortmund
Period	10/09/22 → 14/09/22
Internet address	https://engineering.esteco.com/events/international-conference-on-parallel-problem-solving-from-nature-ppsn-xvii/#:~:text=International%20Conference%20on%20Parallel%20Problem%20Solving%20from%20Nature%20(PPSN%20XVII),-10%20%2D%2014%20Sep&text=The%20seventeenth%20International%20Conference%20on,10%20to%2014%20September%202022.

Research Keywords

Hypervolume contribution
Approximation
Evolutionary multi-objective optimization · Deep learning
Deep learning

Access Output

10.1007/978-3-031-14714-2_29

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Shang, K., Liao, W., & Ishibuchi, H. (2022). HVC-Net: Deep learning based hypervolume contribution approximation. In G. Rudolph, A. V. Kononova, H. Aguirre, P. Kerschke, G. Ochoa, & T. Tušar (Eds.), Parallel Problem Solving from Nature – PPSN XVII: 17th International Conference, PPSN 2022 - Proceedings (Vol. Part I, pp. 414-426). (Lecture Notes in Computer Science; Vol. 13398). Springer, Cham. https://doi.org/10.1007/978-3-031-14714-2_29

Shang, Ke ; Liao, Weiduo ; Ishibuchi, Hisao. / HVC-Net : Deep learning based hypervolume contribution approximation. Parallel Problem Solving from Nature – PPSN XVII: 17th International Conference, PPSN 2022 - Proceedings. editor / Günter Rudolph ; Anna V. Kononova ; Hernán Aguirre ; Pascal Kerschke ; Gabriela Ochoa ; Tea Tušar. Vol. Part I Springer, Cham, 2022. pp. 414-426 (Lecture Notes in Computer Science).

@inproceedings{89c24201a10a4992ac0b8bc4553473ef,

title = "HVC-Net: Deep learning based hypervolume contribution approximation",

abstract = "In this paper, we propose HVC-Net, a deep learning based hypervolume contribution approximation method for evolutionary multi-objective optimization. The basic idea of HVC-Net is to use a deep neural network to approximate the hypervolume contribution of each solution in a non-dominated solution set. HVC-Net has two characteristics: (1) It is permutation equivalent to the order of solutions in the input solution set, and (2) a single HVC-Net can handle solution sets of various size (e.g., solution sets with 20, 50 and 100 solutions). The performance of HVC-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume contribution approximation methods (i.e., point-based method and line-based method). Our experimental results show that HVC-Net outperforms the other two methods in terms of both the runtime and the ability to identify the smallest (largest) hypervolume contributor in a solution set, which shows the superiority of HVC-Net for hypervolume contribution approximation. {\textcopyright} 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG.",

keywords = "Hypervolume contribution, Approximation, Evolutionary multi-objective optimization · Deep learning, Deep learning",

author = "Ke Shang and Weiduo Liao and Hisao Ishibuchi",

year = "2022",

doi = "10.1007/978-3-031-14714-2\_29",

language = "English",

isbn = "978-3-031-14713-5",

volume = "Part I",

series = "Lecture Notes in Computer Science",

publisher = "Springer, Cham",

pages = "414--426",

editor = "G{\"u}nter Rudolph and Kononova, \{Anna V.\} and Hern{\'a}n Aguirre and Pascal Kerschke and Gabriela Ochoa and Tea Tu{\v s}ar",

booktitle = "Parallel Problem Solving from Nature – PPSN XVII",

note = "17th International Conference on Parallel Problem Solving from Nature (PPSN 2022), PPSN XVII ; Conference date: 10-09-2022 Through 14-09-2022",

url = "https://engineering.esteco.com/events/international-conference-on-parallel-problem-solving-from-nature-ppsn-xvii/\#:\textasciitilde{}:text=International\%20Conference\%20on\%20Parallel\%20Problem\%20Solving\%20from\%20Nature\%20(PPSN\%20XVII),-10\%20\%2D\%2014\%20Sep\&text=The\%20seventeenth\%20International\%20Conference\%20on,10\%20to\%2014\%20September\%202022.",

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Shang, K, Liao, W & Ishibuchi, H 2022, HVC-Net: Deep learning based hypervolume contribution approximation. in G Rudolph, AV Kononova, H Aguirre, P Kerschke, G Ochoa & T Tušar (eds), Parallel Problem Solving from Nature – PPSN XVII: 17th International Conference, PPSN 2022 - Proceedings. vol. Part I, Lecture Notes in Computer Science, vol. 13398, Springer, Cham, pp. 414-426, 17th International Conference on Parallel Problem Solving from Nature (PPSN 2022), Dortmund, Germany, 10/09/22. https://doi.org/10.1007/978-3-031-14714-2_29

HVC-Net: Deep learning based hypervolume contribution approximation. / Shang, Ke; Liao, Weiduo; Ishibuchi, Hisao.
Parallel Problem Solving from Nature – PPSN XVII: 17th International Conference, PPSN 2022 - Proceedings. ed. / Günter Rudolph; Anna V. Kononova; Hernán Aguirre; Pascal Kerschke; Gabriela Ochoa; Tea Tušar. Vol. Part I Springer, Cham, 2022. p. 414-426 (Lecture Notes in Computer Science; Vol. 13398).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - HVC-Net

T2 - 17th International Conference on Parallel Problem Solving from Nature (PPSN 2022)

AU - Shang, Ke

AU - Liao, Weiduo

AU - Ishibuchi, Hisao

PY - 2022

Y1 - 2022

N2 - In this paper, we propose HVC-Net, a deep learning based hypervolume contribution approximation method for evolutionary multi-objective optimization. The basic idea of HVC-Net is to use a deep neural network to approximate the hypervolume contribution of each solution in a non-dominated solution set. HVC-Net has two characteristics: (1) It is permutation equivalent to the order of solutions in the input solution set, and (2) a single HVC-Net can handle solution sets of various size (e.g., solution sets with 20, 50 and 100 solutions). The performance of HVC-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume contribution approximation methods (i.e., point-based method and line-based method). Our experimental results show that HVC-Net outperforms the other two methods in terms of both the runtime and the ability to identify the smallest (largest) hypervolume contributor in a solution set, which shows the superiority of HVC-Net for hypervolume contribution approximation. © 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG.

AB - In this paper, we propose HVC-Net, a deep learning based hypervolume contribution approximation method for evolutionary multi-objective optimization. The basic idea of HVC-Net is to use a deep neural network to approximate the hypervolume contribution of each solution in a non-dominated solution set. HVC-Net has two characteristics: (1) It is permutation equivalent to the order of solutions in the input solution set, and (2) a single HVC-Net can handle solution sets of various size (e.g., solution sets with 20, 50 and 100 solutions). The performance of HVC-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume contribution approximation methods (i.e., point-based method and line-based method). Our experimental results show that HVC-Net outperforms the other two methods in terms of both the runtime and the ability to identify the smallest (largest) hypervolume contributor in a solution set, which shows the superiority of HVC-Net for hypervolume contribution approximation. © 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG.

KW - Hypervolume contribution

KW - Approximation

KW - Evolutionary multi-objective optimization · Deep learning

KW - Deep learning

UR - https://www.scopus.com/pages/publications/85136924801

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85136924801&origin=recordpage

U2 - 10.1007/978-3-031-14714-2_29

DO - 10.1007/978-3-031-14714-2_29

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 978-3-031-14713-5

VL - Part I

T3 - Lecture Notes in Computer Science

SP - 414

EP - 426

BT - Parallel Problem Solving from Nature – PPSN XVII

A2 - Rudolph, Günter

A2 - Kononova, Anna V.

A2 - Aguirre, Hernán

A2 - Kerschke, Pascal

A2 - Ochoa, Gabriela

A2 - Tušar, Tea

PB - Springer, Cham

Y2 - 10 September 2022 through 14 September 2022

ER -

Shang K, Liao W, Ishibuchi H. HVC-Net: Deep learning based hypervolume contribution approximation. In Rudolph G, Kononova AV, Aguirre H, Kerschke P, Ochoa G, Tušar T, editors, Parallel Problem Solving from Nature – PPSN XVII: 17th International Conference, PPSN 2022 - Proceedings. Vol. Part I. Springer, Cham. 2022. p. 414-426. (Lecture Notes in Computer Science). Epub 2022 Aug 14. doi: 10.1007/978-3-031-14714-2_29

HVC-Net: Deep learning based hypervolume contribution approximation

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