A fast many-objective hypervolume algorithm using iterated incremental calculations

Three fast algorithms have been proposed for calculating hypervolume exactly: the Hypervolume by Slicing Objectives algorithm (HSO) optimised with heuristics designed to improve the average case; an adaptation of the Overmars and Yap algorithm for solving the Klee´s measure problem; and a recent algorithm by Fonseca et al. We propose a fourth algorithm IIHSO based largely on the Incremental HSO algorithm, a version of HSO adapted to calculate the exclusive hypervolume contribution of a point to a front. We give a comprehensive analysis of IIHSO and performance comparison between three state of the art algorithms, and conclude that IIHSO outperforms the others on most important and representative data in many objectives.