Journal
IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
Volume 25, Issue 1, Pages 1-20Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TEVC.2020.3013290
Keywords
Evolutionary algorithms; hypervolume contribution; hypervolume indicator; many-objective optimization; multiobjective optimization
Funding
- National Natural Science Foundation of China [61876075]
- Guangdong Provincial Key Laboratory [2020B121201001]
- Program for Guangdong Introducing Innovative and Enterpreneurial Teams [2017ZT07X386]
- Shenzhen Science and Technology Program [KQTD2016112514355531]
- Program for University Key Laboratory of Guangdong Province [2017KSYS008]
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This article provides a comprehensive survey on the hypervolume indicator widely used in the field of evolutionary multiobjective optimization. The goal is to help researchers deepen their understanding of the principles and applications of the hypervolume indicator, and to promote further utilization of it.
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 $\mu $ -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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