A Survey on the Hypervolume Indicator in Evolutionary Multiobjective Optimization

Hypervolume is widely used as a performance indicator in the field of evolutionary multiobjective optimization (EMO). It is used not only for performance evaluation of EMO algorithms (EMOAs) but also in indicator-based EMOAs to guide the search. Since its initial proposal in the late 1990s, a wide v...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation Vol. 25; no. 1; pp. 1 - 20
Main Authors: Shang, Ke, Ishibuchi, Hisao, He, Linjun, Pang, Lie Meng
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation methods
Convergence
Evolutionary algorithms
hypervolume contribution
hypervolume indicator
many-objective optimization
multiobjective optimization
Multiple objective analysis
Optimization
Performance evaluation
Proposals
Sociology
Statistics
ISSN:1089-778X, 1941-0026
Online Access:Get full text
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Summary:Hypervolume is widely used as a performance indicator in the field of evolutionary multiobjective optimization (EMO). It is used not only for performance evaluation of EMO algorithms (EMOAs) but also in indicator-based EMOAs to guide the search. Since its initial proposal in the late 1990s, a wide variety of studies have been done on various topics, including hypervolume calculation, optimal μ-distribution, subset selection, hypervolume-based EMOAs, and extensions of the hypervolume indicator. However, currently there is no work to systematically survey the hypervolume indicator for these topics whereas it has been frequently used in the EMO field. This article aims to fill this gap and provide a comprehensive survey on the hypervolume indicator. We expect that this survey will help EMO researchers to understand the hypervolume indicator more deeply and thoroughly, and promote further utilization of the hypervolume indicator in the EMO field.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2020.3013290