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.

中文翻译：

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进化多目标优化中超量指标的综述

超卷被广泛用作进化多目标优化（EMO）领域的性能指标。它不仅用于评估EMO算法（EMOA）的性能，而且还用于基于指标的EMOA，以指导搜索。自1990年代后期提出初始建议以来，已针对各种主题进行了广泛的研究，包括超量计算，最优 $ \亩$ -分布，子集选择，基于超量的EMOA以及超量指标的扩展。但是，目前还没有系统地调查这些主题的超量指标的工作，而该指标已在EMO领域中频繁使用。本文旨在填补这一空白，并提供有关超量指标的全面调查。我们希望这项调查将有助于EMO研究人员更深入，更深入地了解超量指标，并促进EMO领域对超量指标的进一步利用。