Selection Strategy Based on Proper Pareto Optimality in Evolutionary Multi-objective Optimization

On the multi-objective optimization problems (MOP), the dominance-resistant solution (DRS) refers to the solution that has inferior objective values but is difficult to dominate by other solutions. Prior studies have affirmed that DRSs are prevalent across MOPs and difficult to eliminate, leading to substantial performance deterioration in many multi-objective evolutionary algorithms (MOEAs). In this paper, we propose a metric inspired by proper Pareto optimality and then develop a selection strategy based on this metric (SPP) to mitigate the negative impact of DRSs. Furthermore, we implement SPP on multi-objective evolutionary algorithm based on decomposition (MOEA/D) and call the new algorithm MOEA/D-SPP. Specifically, the algorithm employs the penalty-based boundary intersection method to scalarize the MOP. Subsequently, SPP is integrated into the environmental selection. The strategy measures and sorts a set of solutions such that DRSs can be identified and removed. Finally, weight vectors are adjusted, thereby enhancing the population diversity. In experimental studies, MOEA/D-SPP outperforms five state-of-the-art MOEAs on DRS-MOPs, demonstrating the promising application of SPP.