Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D

Hui Li; Jianyong Sun; Qingfu Zhang; Yuxiang Shui

doi:10.1007/978-3-030-12598-1_8

Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D

Hui Li^*, Jianyong Sun, Qingfu Zhang, Yuxiang Shui

^*Corresponding author for this work

Department of Computer Science

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

10 Citations (Scopus)

Abstract

Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is one of the dominant algorithmic frameworks for multi-objective optimization in the area of evolutionary computation. The performance of multi-objective algorithms based on MOEA/D framework highly depends on how a diverse set of single objective subproblems are generated. Among all decomposition methods, the Penalty-based Boundary Intersection (PBI) method has received particular research interest in MOEA/D due to its ability for controlling the diversity of population for many-objective optimization. However, optimizing multiple PBI subproblems defined via a set of uniformly-distributed weight vectors may not be able to produce a good approximation of Pareto-optimal front when objectives have different scales. To overcome this weakness, we suggest a new strategy for adjusting weight vectors of PBI-based subproblems in this paper. Our experimental results have shown that the performance of MOEA/D-PBI with adjusted weight vectors is competitive to NSGA-III in diversity when dealing with the scaled version of some benchmark multi-objective test problems.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization
Subtitle of host publication	10th International Conference, EMO 2019, Proceedings
Editors	Kalyanmoy Deb, Erik Goodman, Carlos A., Coello Coello, Kathrin Klamroth, Kaisa Miettinen, Sanaz Mostaghim, Patrick Reed
Publisher	Springer, Cham
Pages	91-100
ISBN (Electronic)	978-3-030-12598-1
ISBN (Print)	978-3-030-12597-4
DOIs	https://doi.org/10.1007/978-3-030-12598-1_8
Publication status	Published - Mar 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
Place	United States
City	East Lansing
Period	10/03/19 → 13/03/19

Research Keywords

MOEA/D
Objective normalization
Penalty-based Boundary Intersection (PBI)

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10.1007/978-3-030-12598-1_8

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Li, H., Sun, J., Zhang, Q., & Shui, Y. (2019). Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D. In K. Deb, E. Goodman, C. A., C. Coello, K. Klamroth, K. Miettinen, S. Mostaghim, & P. Reed (Eds.), Evolutionary Multi-Criterion Optimization : 10th International Conference, EMO 2019, Proceedings (pp. 91-100). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS). Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_8

Li, Hui ; Sun, Jianyong ; Zhang, Qingfu et al. / Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D. Evolutionary Multi-Criterion Optimization : 10th International Conference, EMO 2019, Proceedings. editor / Kalyanmoy Deb ; Erik Goodman ; Carlos A. ; Coello Coello ; Kathrin Klamroth ; Kaisa Miettinen ; Sanaz Mostaghim ; Patrick Reed. Springer, Cham, 2019. pp. 91-100 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{9f89d618a0a24025956eb1f256e0b728,

title = "Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D",

abstract = "Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is one of the dominant algorithmic frameworks for multi-objective optimization in the area of evolutionary computation. The performance of multi-objective algorithms based on MOEA/D framework highly depends on how a diverse set of single objective subproblems are generated. Among all decomposition methods, the Penalty-based Boundary Intersection (PBI) method has received particular research interest in MOEA/D due to its ability for controlling the diversity of population for many-objective optimization. However, optimizing multiple PBI subproblems defined via a set of uniformly-distributed weight vectors may not be able to produce a good approximation of Pareto-optimal front when objectives have different scales. To overcome this weakness, we suggest a new strategy for adjusting weight vectors of PBI-based subproblems in this paper. Our experimental results have shown that the performance of MOEA/D-PBI with adjusted weight vectors is competitive to NSGA-III in diversity when dealing with the scaled version of some benchmark multi-objective test problems.",

keywords = "MOEA/D, Objective normalization, Penalty-based Boundary Intersection (PBI)",

author = "Hui Li and Jianyong Sun and Qingfu Zhang and Yuxiang Shui",

year = "2019",

month = mar,

doi = "10.1007/978-3-030-12598-1_8",

language = "English",

isbn = "978-3-030-12597-4",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer, Cham",

pages = "91--100",

editor = "Kalyanmoy Deb and Goodman, {Erik } and Carlos A. and Coello Coello and Kathrin Klamroth and Kaisa Miettinen and Sanaz Mostaghim and Patrick Reed",

booktitle = "Evolutionary Multi-Criterion Optimization",

note = "10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 ; Conference date: 10-03-2019 Through 13-03-2019",

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Li, H, Sun, J, Zhang, Q & Shui, Y 2019, Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D. in K Deb, E Goodman, C A., C Coello, K Klamroth, K Miettinen, S Mostaghim & P Reed (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, Cham, pp. 91-100, 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_8

Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D. / Li, Hui; Sun, Jianyong; Zhang, Qingfu et al.
Evolutionary Multi-Criterion Optimization : 10th International Conference, EMO 2019, Proceedings. ed. / Kalyanmoy Deb; Erik Goodman; Carlos A.; Coello Coello; Kathrin Klamroth; Kaisa Miettinen; Sanaz Mostaghim; Patrick Reed. Springer, Cham, 2019. p. 91-100 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS).

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

TY - GEN

T1 - Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D

AU - Li, Hui

AU - Sun, Jianyong

AU - Zhang, Qingfu

AU - Shui, Yuxiang

PY - 2019/3

Y1 - 2019/3

N2 - Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is one of the dominant algorithmic frameworks for multi-objective optimization in the area of evolutionary computation. The performance of multi-objective algorithms based on MOEA/D framework highly depends on how a diverse set of single objective subproblems are generated. Among all decomposition methods, the Penalty-based Boundary Intersection (PBI) method has received particular research interest in MOEA/D due to its ability for controlling the diversity of population for many-objective optimization. However, optimizing multiple PBI subproblems defined via a set of uniformly-distributed weight vectors may not be able to produce a good approximation of Pareto-optimal front when objectives have different scales. To overcome this weakness, we suggest a new strategy for adjusting weight vectors of PBI-based subproblems in this paper. Our experimental results have shown that the performance of MOEA/D-PBI with adjusted weight vectors is competitive to NSGA-III in diversity when dealing with the scaled version of some benchmark multi-objective test problems.

AB - Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is one of the dominant algorithmic frameworks for multi-objective optimization in the area of evolutionary computation. The performance of multi-objective algorithms based on MOEA/D framework highly depends on how a diverse set of single objective subproblems are generated. Among all decomposition methods, the Penalty-based Boundary Intersection (PBI) method has received particular research interest in MOEA/D due to its ability for controlling the diversity of population for many-objective optimization. However, optimizing multiple PBI subproblems defined via a set of uniformly-distributed weight vectors may not be able to produce a good approximation of Pareto-optimal front when objectives have different scales. To overcome this weakness, we suggest a new strategy for adjusting weight vectors of PBI-based subproblems in this paper. Our experimental results have shown that the performance of MOEA/D-PBI with adjusted weight vectors is competitive to NSGA-III in diversity when dealing with the scaled version of some benchmark multi-objective test problems.

KW - MOEA/D

KW - Objective normalization

KW - Penalty-based Boundary Intersection (PBI)

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U2 - 10.1007/978-3-030-12598-1_8

DO - 10.1007/978-3-030-12598-1_8

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

SN - 978-3-030-12597-4

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 91

EP - 100

BT - Evolutionary Multi-Criterion Optimization

A2 - Deb, Kalyanmoy

A2 - Goodman, Erik

A2 - A., Carlos

A2 - Coello, Coello

A2 - Klamroth, Kathrin

A2 - Miettinen, Kaisa

A2 - Mostaghim, Sanaz

A2 - Reed, Patrick

PB - Springer, Cham

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

Y2 - 10 March 2019 through 13 March 2019

ER -

Li H, Sun J, Zhang Q, Shui Y. Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D. In Deb K, Goodman E, A. C, Coello C, Klamroth K, Miettinen K, Mostaghim S, Reed P, editors, Evolutionary Multi-Criterion Optimization : 10th International Conference, EMO 2019, Proceedings. Springer, Cham. 2019. p. 91-100. (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_8

Adjustment of weight vectors of penalty-based boundary intersection method in MOEA/D

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