超卷指标：问题与算法
The Hypervolume Indicator: Problems and Algorithms
摘要：
超体积指标是随机多目标优化器评估以及进化多目标优化算法选择中最常用的集合质量指标之一。它的理论性质证明了它的广泛接受，特别是严格的单调性方面的优势，这仍然是唯一的超体积为基础的指标。本文讨论了超体积相关问题的计算，突出了它们之间的关系，提供了所使用的范例和技术的概述，每个问题的主要算法的描述，以及关于渐近复杂性和运行时间的最快算法的概要。通过提供与超容积指标相关的计算问题的完整概述，本文可作为开发新算法的起点，并支持用户确定可用于每个问题的最合适的实施方案。
英文摘要：
The hypervolume indicator is one of the most used set-quality indicators for the assessment of stochastic multiobjective optimizers, as well as for selection in evolutionary multiobjective optimization algorithms. Its theoretical properties justify its wide acceptance, particularly the strict monotonicity with respect to set dominance which is still unique of hypervolume-based indicators. This paper discusses the computation of hypervolume-related problems, highlighting the relations between them, providing an overview of the paradigms and techniques used, a description of the main algorithms for each problem, and a rundown of the fastest algorithms regarding asymptotic complexity and runtime. By providing a complete overview of the computational problems associated to the hypervolume indicator, this paper serves as the starting point for the development of new algorithms, and supports users in the identification of the most appropriate implementations available for each problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
