R2-Based Hypervolume Contribution Approximation

In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation Vol. 24; no. 1; pp. 185 - 192
Main Authors: Shang, Ke, Ishibuchi, Hisao, Ni, Xizi
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation
Approximation methods
Evolutionary multiobjective optimization (EMO)
hypervolume contribution
Indexes
Methods
Monte Carlo methods
Monte Carlo simulation
Nickel
Optimization
R2 indicator
Sociology
ISSN:1089-778X, 1941-0026
Online Access:Get full text
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Summary:In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method, and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2019.2909271