The (M-1)+1 Framework of Relaxed Pareto Dominance for Evolutionary Many-Objective Optimization.

In the past several years, it has become apparent that the effectiveness of Pareto dominance-based multiobjective evolutionary algorithms degrades dramatically when solving many-objective optimization problems (MaOPs). Instead, research efforts have been driven toward developing evolutionary algorithms (EAs) that do not rely on Pareto dominance (e.g., decomposition-based techniques) to solve MaOPs. However, it is still a non-trivial issue for many existing non-Pareto-dominance-based EAs to deal with unknown irregular Pareto front shapes. In this paper, we develop the novel “(M-1)+1" framework of relaxed Pareto dominance to address MaOPs, which can simultaneously promote both convergence and diversity. To be specific, we apply M symmetrical cases of relaxed Pareto dominance during the environmental selection step, where each enhances the selection pressure of M-1 objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed method is very competitive with or outperforms state-of-the-art methods on a variety of scalable test problems.