On the Norm of Dominant Difference for Many-Objective Particle Swarm Optimization.

Recent studies in multiobjective particle swarm optimization (PSO) have the tendency to employ Pareto-based technique, which has a certain effect. However, they will encounter difficulties in their scalability upon many-objective optimization problems (MaOPs) due to the poor discriminability of Pareto optimality, which will affect the selection of leaders, thereby deteriorating the effectiveness of the algorithm. This paper presents a new scheme of discriminating the solutions in objective space. Based on the properties of Pareto optimality, we propose the dominant difference of a solution, which can demonstrate its dominance in every dimension. By investigating the norm of dominant difference among the entire population, the discriminability between the candidates that are difficult to obtain in the objective space is obtained indirectly. By integrating it into PSO, we gained a novel algorithm named many-objective PSO based on the norm of dominant difference (MOPSO/DD) for dealing with MaOPs. Moreover, we design a L -norm-based density estimator which makes MOPSO/DD not only have good convergence and diversity but also have lower complexity. Experiments on benchmark problems demonstrate that our proposal is competitive with respect to the state-of-the-art MOPSOs and multiobjective evolutionary algorithms.