Proceedings Article10.1109/CEC45853.2021.9504725
Hypervolume by Slicing Objective Algorithm: An Improved Version
Sumit Mishra,Srinibas Swain,Sangita Sarmah,Carlos A. Coello Coello +3 more
- 28 Jun 2021
- pp 2451-2458
TL;DR: In this paper, the authors show that the worst-case time complexity of the HSO algorithm, as obtained by its authors, is incorrect and provide an efficient implementation of the algorithm, which guarantees that unique slices are generated to compute the hypervolume.
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Abstract: The hypervolume remains a popular performance indicator in evolutionary multi-objective, mainly because of its nice mathematical properties (i.e., it’s the only performance indicator known to be Pareto-compliant). However, its high computational cost (which grows polynomially on the population size but exponentially on the number of objectives) has severely limited its use in many-objective optimization. This has motivated a variety of proposals that attempt to overcome this limitation. One of the most popular proposals currently available is the so-called Hypervolume by Slicing Objectives (HSO) algorithm. Here, we show that the worst-case time complexity of the HSO algorithm, as obtained by its authors, is incorrect. Then, we provide an efficient implementation of the HSO algorithm, which guarantees that unique slices are generated to compute the hypervolume.
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A faster algorithm for calculating hypervolume
TL;DR: An algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published and increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.