Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms

Evolutionary algorithms have been effectively used to solve multiobjective optimization problems with a small number of objectives, two or three in general. However, when problems with many objectives are encountered, nearly all algorithms perform poorly due to loss of selection pressure in fitness evaluation solely based upon the Pareto optimality principle. In this paper, we introduce a new fitness evaluation mechanism to continuously differentiate individuals into different degrees of optimality beyond the classification of the original Pareto dominance. The concept of fuzzy logic is adopted to define a fuzzy Pareto domination relation. As a case study, the fuzzy concept is incorporated into the designs of NSGA-II and SPEA2. Experimental results show that the proposed methods exhibit better performance in both convergence and diversity than the original ones for solving many-objective optimization problems.