A fast approximate hypervolume calculation method by a novel decomposition strategy

Abstract

In this paper, we present a new method to fast approximate the hypervolume measurement by improving the classical Monte Carlo sampling method. Hypervolume value can be used as a quality indicator or selection indicator for multiobjective evolutionary algorithms (MOEAs), and thus the efficiency of calculating this measurement is of crucial importance especially in the case of large sets or many dimensional objective spaces. To fast calculate hypervolume, we develop a new Monte Carlo sampling method by decreasing the amount of Monte Carlo sample points using a novel decomposition strategy in this paper. We first analyze the complexity of the proposed algorithm in theory, and then execute a series experiments to further test its efficiency. Both simulation experiments and theoretical analysis verify the effectiveness and efficiency of the proposed method.