research-article

What is a good direction vector set for the R2-based hypervolume contribution approximation

Authors:

Hisao IshibuchiAuthors Info & Claims

GECCO '20: Proceedings of the 2020 Genetic and Evolutionary Computation Conference

Pages 524 - 532

https://doi.org/10.1145/3377930.3390171

Published: 26 June 2020 Publication History

Abstract

The hypervolume contribution is an important concept in hypervolume-based evolutionary multi-objective optimization algorithms. It describes the loss of the hypervolume when a solution is removed from the current population. Since its calculation is #P-hard in the number of objectives, its approximation is necessary for many-objective optimization problems. Recently, an R2-based hypervolume contribution approximation method was proposed. This method relies on a set of direction vectors for the approximation. However, the influence of different direction vector generation methods on the approximation quality has not been studied yet. This paper aims to investigate this issue. Five direction vector generation methods are investigated, including Das and Dennis's method (DAS), unit normal vector method (UNV), JAS method, maximally sparse selection method with DAS (MSS-D), and maximally sparse selection method with UNV (MSS-U). Experimental results suggest that the approximation quality strongly depends on the direction vector generation method. The JAS and UNV methods show the best performance whereas the DAS method shows the worst performance. The reasons behind the results are also analyzed.

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Cited By

Liu SWang HYao WPeng W(2024)Surrogate-Assisted Environmental Selection for Fast Hypervolume-Based Many-Objective OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2023.324363228:1(132-146)Online publication date: Feb-2024
https://doi.org/10.1109/TEVC.2023.3243632
Shang KShu TIshibuchi H(2024)Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution ApproximationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.323082828:1(105-116)Online publication date: Feb-2024
https://doi.org/10.1109/TEVC.2022.3230828
Shang KChen WLiao WIshibuchi H(2023)HV-Net: Hypervolume Approximation Based on DeepSetsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.318130627:4(1154-1160)Online publication date: Aug-2023
https://doi.org/10.1109/TEVC.2022.3181306
Show More Cited By

Index Terms

What is a good direction vector set for the R2-based hypervolume contribution approximation
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization

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cover image ACM Conferences

GECCO '20: Proceedings of the 2020 Genetic and Evolutionary Computation Conference

June 2020

1349 pages

ISBN:9781450371285

DOI:10.1145/3377930

General Chair:
Carlos Artemio Coello Coello
CINVESTAV-IPN

Copyright © 2020 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 26 June 2020

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National Natural Science Foundation of China
Guangdong Provincial Key Laboratory
Program for Guangdong Introducing Innovative and Enterpreneurial Teams
Shenzhen Science and Technology Program
Program for University Key Laboratory of Guangdong Province

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GECCO '20

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SIGEVO

GECCO '20: Genetic and Evolutionary Computation Conference

July 8 - 12, 2020

Cancún, Mexico

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Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

Liu SWang HYao WPeng W(2024)Surrogate-Assisted Environmental Selection for Fast Hypervolume-Based Many-Objective OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2023.324363228:1(132-146)Online publication date: Feb-2024
https://doi.org/10.1109/TEVC.2023.3243632
Shang KShu TIshibuchi H(2024)Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution ApproximationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.323082828:1(105-116)Online publication date: Feb-2024
https://doi.org/10.1109/TEVC.2022.3230828
Shang KChen WLiao WIshibuchi H(2023)HV-Net: Hypervolume Approximation Based on DeepSetsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.318130627:4(1154-1160)Online publication date: Aug-2023
https://doi.org/10.1109/TEVC.2022.3181306
Wu GShu TShang KIshibuchi H(2023)Normalization in R2-Based Hypervolume and Hypervolume Contribution Approximation2023 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI52147.2023.10371986(449-456)Online publication date: 5-Dec-2023
https://doi.org/10.1109/SSCI52147.2023.10371986
Wu GShu TNan YShang KIshibuchi H(2023)Ensemble R2-based Hypervolume Contribution Approximation2023 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI52147.2023.10371823(1503-1510)Online publication date: 5-Dec-2023
https://doi.org/10.1109/SSCI52147.2023.10371823
Nan YIshibuchi HShu TShang K(2023)Two-Stage Greedy Approximated Hypervolume Subset Selection for Large-Scale ProblemsEvolutionary Multi-Criterion Optimization10.1007/978-3-031-27250-9_28(391-404)Online publication date: 9-Mar-2023
https://doi.org/10.1007/978-3-031-27250-9_28
Shu TShang KNan YIshibuchi H(2022)Direction Vector Selection for R2-Based Hypervolume Contribution ApproximationParallel Problem Solving from Nature – PPSN XVII10.1007/978-3-031-14721-0_8(110-123)Online publication date: 15-Aug-2022
https://doi.org/10.1007/978-3-031-14721-0_8
Nan YShang KIshibuchi HHe L(2021)A Two-stage Hypervolume Contribution Approximation Method Based on R2 Indicator2021 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC45853.2021.9504726(2468-2475)Online publication date: 28-Jun-2021
https://doi.org/10.1109/CEC45853.2021.9504726

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