Optimal Distributions of Solutions for Hypervolume Maximization on Triangular and Inverted Triangular Pareto Fronts of Four-Objective Problems

Ishibuchi，Hisao1; Matsumoto，Takashi2; Masuyama，Naoki2; Nojima，Yusuke2

10.1109/SSCI44817.2019.9003032

2019-12-01

978-1-7281-2486-5

2019 IEEE Symposium Series on Computational Intelligence, SSCI 2019

1857-1864

6-9 Dec. 2019

Xiamen, China

345 E 47TH ST, NEW YORK, NY 10017 USA

Institute of Electrical and Electronics Engineers Inc.

Hypervolume (HV) has been often employed for the comparison of evolutionary multiobjective optimization algorithms. In HV-based performance comparison, it is implicitly assumed that a uniformly distributed solution set on the whole Pareto front has a larger HV than a partially distributed solution set on a part of the Pareto front. In this study, we demonstrate that this assumption does not hold for multiobjective problems whose Pareto fronts are not triangular. When we use a reference point close to the nadir point for an inverted triangular Pareto front, the optimal solution set includes no solutions on the boundary of the Pareto front. However, a set of only boundary solutions (with no inside solutions) is optimal when the reference point is very far away from the nadir point. For a multiobjective problem with four objectives, we explain that such a biased distribution of solutions toward the boundary of the Pareto front looks a good solution set in a parallel coordinate plot. That is, misleading conclusions can be obtained even when we use both the HV-based evaluation and the parallel coordinate-based examination. Our observations in this paper suggest the necessity of projection-based examination of solutions for many-objective problems.

evolutionary multiobjective optimization (EMO) indicator-based EMO algorithms inverted triangular Pareto fronts optimal solution distribution performance indicators

第一

英语

EI ; CPCI-S

National Natural Science Foundation of China[61876075] ; Program for Guangdong Introducing Innovative and Enterpreneurial Teams[2017ZT07X386] ; Shenzhen Peacock Plan[KQTD2016112514355531] ; Science and Technology Innovation Committee Foundation of Shenzhen[ZDSYS201703031748284] ; Program for University Key Laboratory of Guangdong Province[2017KSYS008]

Computer Science

Computer Science, Artificial Intelligence

WOS:000555467201138

20201108276983

Artificial intelligence ; Evolutionary algorithms ; Optimal systems

Artificial Intelligence:723.4 ; Optimization Techniques:921.5 ; Systems Science:961

2-s2.0-85080895910

Scopus

1.Southern University of Science and Technology,Shenzhen Key Laboratory of Computational Intelligence,University Key Laboratory of Evolving,Intelligent Systems of Guangdong Province,Shenzhen,China
2.Osaka Prefecture University,Department of Computer Science and Intelligent Systems,Sakai, Osaka,599-8531,Japan

Ishibuchi，Hisao,Matsumoto，Takashi,Masuyama，Naoki,et al. Optimal Distributions of Solutions for Hypervolume Maximization on Triangular and Inverted Triangular Pareto Fronts of Four-Objective Problems[C]. 345 E 47TH ST, NEW YORK, NY 10017 USA:Institute of Electrical and Electronics Engineers Inc.,2019:1857-1864.