Heuristics for Optimising the Calculation of Hypervolume for Multi-objective Optimisation Problems

The fastest known algorithm for calculating the hypervolume of a set of solutions to a multiobjective optimisation problem is the HSO algorithm (Hypervolume by Slicing Objectives). However, the performance of HSO for a given front varies a lot depending on the order in which it processes the objectives in that front. We present and evaluate two alternative heuristics that each attempt to identify a good order for processing the objectives of a given front. We show that both heuristics make a substantial difference to the performance of HSO for randomly-generated and benchmark data in 5–9 objectives, and that they both enable HSO to reliably avoid the worst-case performance for those fronts. The enhanced HSO will enable the use of hypervolume with larger populations in more objectives.