Hypervolume by Slicing Objective Algorithm: An Improved Version

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.