Improve Performance of Pareto Corner Search-based Objective Reduction in Many-Objective Optimization

Multi-objective optimization evolutionary algorithms (MOEAs) is one of the most well-known approaches for solving the multi-objective optimization problems (MOPs). When the number of objectives is greater than three, the MOPs are considered as many-objective optimization problem (MaOPs), and many-objective optimization evolutionary algorithms (MaOEAs) are proposed to solve MaOPs. However, MaOPs often contain redundant objectives which do not conflict to any other objectives or even correlate positively to some other. These redundant objectives seriously degrade the efficiency of MOEAs/MaOEAs, so they should be removed to help MaOEAs work better. Therefore, this paper proposes new objective reduction algorithms which uses a Pareto corner search algorithm (PCSEA) to generate non-dominated solutions at corners of Pareto front (PF), and then applies machine learning techniques to remove redundant objectives. The proposed methods not only promote the strengths of PCSEA in finding non-dominated solutions but also promote the strengths of machine learning algorithms in automatically finding the optimal set of objectives. The experiments on 36 instances of DTLZ5(I,M) and 10 instances of WFG3(M) show that the proposed methods can more often find the right set of objectives than six other benchmark methods, respectively about 80% success compared to about 62% success of the other methods.