A Fast Hypervolume Contribution Strategy for Evolutionary Multi-Objective Optimization

Hypervolume indicator is one of the most classic and commonly used metrics in the field of multi-objective optimization. It is widely used to solve multi-objective optimization problems. However, as the number of objectives increases, the computational time for calculating the hypervolume contribution increases sharply. This paper introduces a simple and computationally efficient method for hypervolume contribution, referred to as pointwise Hypervolume Contribution (pHVC).This approach retains the beneficial properties of hypervolume and solves the curse of dimensionality of the hpyervolume indicator. We apply pHVC to evolutionary multi-objective optimization algorithm and propose the pHVC-EMOA. Experimental results demonstrate that pHVC-EMOA is more efficient than the other hypervolume-based EMOAs.