Hypervolume-Based Cooperative Coevolution with Two Reference Points for Multi-Objective Optimization

Abstract

An important issue in hypervolume-based evolutionary multi-objective optimization (EMO) algorithms is the specification of a reference point for hypervolume calculation. However, its appropriate specification has not been carefully studied in the literature. Some recent studies have pointed out the importance and difficulty of the reference point specification. Its appropriate specification depends on problem characteristics such as the Pareto front shape and the number of objectives. In this paper, the difficulty of the reference point specification in hypervolume-based EMO algorithms is circumvented by using two reference points. Instead of using only a single reference point, we propose a new hypervolume-based EMO algorithm that can effectively utilize two reference points cooperatively. Experimental results show that the proposed algorithm has good and robust performance on a wide range of test problems. In comparison to hypervolume-based EMO algorithms with only a single reference point, the proposed algorithm can find a wider and more uniformly distributed solution set. On a recently proposed real-world problem suite, the proposed algorithm shows competitive performance in comparison to state-of-the-art algorithms.