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Hypervolume-Optimal μ-Distributions on Line/Plane-Based Pareto Fronts in Three Dimensions

Hypervolume is widely used in the evolutionary multiobjective optimization (EMO) field to evaluate the quality of a solution set. For a solution set with μ solutions on a Pareto front, a larger hypervolume means a better solution set. Investigating the distribution of the solution set with the largest hypervolume is an important topic in EMO, which is the so-called hypervolume-optimal μ -distribution. Theoretical results have shown that the μ solutions are uniformly distributed on a linear Pareto front in two dimensions. However, the μ solutions are not always uniformly distributed on a single-line Pareto front in three dimensions. They are only uniform when the single-line Pareto front has one constant objective. In this article, we further investigate the hypervolume-optimal μ -distribution in three dimensions. We consider the line-based and plane-based Pareto fronts. For the line-based Pareto fronts, we extend the single-line Pareto front to two-line and three-line Pareto fronts, where each line has one constant objective. For the plane-based Pareto fronts, the linear triangular and inverted triangular Pareto fronts are considered. First, we show that the μ solutions are not always uniformly distributed on the line-based Pareto fronts. The uniformity depends on how the lines are combined. Then, we show that a uniform solution set on the plane-based Pareto front is not always optimal for hypervolume maximization. It is locally optimal with respect to a (μ+1) selection scheme. Our results can help researchers in the community to better understand and utilize the hypervolume indicator.

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Informasi Detail

Judul Seri

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION; Vol.26 No.2 April 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 349-363

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

HYPERVOLUME INDICATOR
EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION (EMO)
OPTIMAL Μ-DISTRIBUTION

Info Detail Spesifik

DOI: 10.1109/TEVC.2021.3093114

Pernyataan Tanggungjawab

Ke Shang, Hisao Ishibuchi, Weiyu Chen, Yang Nan, Weiduo Liao

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