Abstract: In multi-objective evolutionary algorithms, the majority of researches are Pareto-based. However, the efficiency of Pareto optimality in objective space will deteriorate when there are numerous weak dominance relations. Aiming at this problem, this paper presents a framework of grid-based ranking. By integrating gird strategy, which features both convergence and distribution, with the particle swarm optimization (PSO), we propose a novel grid-based ranking multi-objective particle swarm optimization (MOPSO). Unlike the strategy of Pareto-based dominance which conducts a pairwise comparison between individuals, the grid-based ranking mechanism combines the individual dominance information in the entire solution space, and takes advantage of this information to sort. As a result, we gain the merits of the relationship between individuals in the population effectively and efficiently. By incorporating the distance between particles and approximate optimal front, we reinforce the judgement of the merits of the relationship among particles in the solution space. The experimental assessment indicates that the proposed method in this paper has relative advantages in both convergence and distribution. On this basis, we discuss the influence of grid partition on efficiency in terms of the distribution of ranks over the process of evolutionary, which verifies the efficiency of the algorithm from the other aspect.

Key words: multi-objective optimization, evolutionary algorithm, particle swarm optimization (PSO), grid, ranking