Many-Objective Evolutionary Algorithm Based on Dominance Degree

For many-objective optimization problems, the comparability of non-dominated solutions is always an essential and fundamental issue. Due to the inefficiency of Pareto dominance for many-objective optimization problems, various improved dominance relations have been proposed to enhance the evolutionary pressure. However, these variants have one thing in common that they treat each solution in a static manner, and the relations between any two solutions are just defined as a kind of static spatial adjacencies, resulting in the unquantifiable comparability. Different from them, this paper proposes a dominance degree metric, which treats solutions as different stages of a dynamic motion process. The dynamic motion process represents the continuous changes of the degree of one solution from Pareto dominating others to being Pareto dominated by others. Based on the dominance degree, this paper proposes a Many-Objective Evolutionary Algorithm based on Dominance Degree, in which the mating selection and environmental update strategies are redesigned accordingly. The proposed method is comprehensively tested with several state-of-the-art optimizers on two popular test suites and practical multi-point distance minimization problems. Experimental results demonstrate its effectiveness and superiority over other optimizers in terms of the convergence, diversity and spread.