A new fitness evaluation method based on fuzzy logic in multiobjective 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 encounter problems with many objectives (more than five), nearly all algorithms performs poorly because of loss of selection pressure in fitness evaluation solely based upon Pareto domination. In this paper, we introduce a new fitness evaluation mechanism to continuously differentiate solutions into different degrees of optimality beyond the classification of the original Pareto dominance. Here, the concept of fuzzy logic is adopted to define fuzzy-dominated relation. As a case study, the fuzzy concept is incorporated into the NSGA-II, instead of the original Pareto dominance principle. Experimental results show that the proposed method exhibits a better performance in both convergence and diversity than the original NSGA-II for solving many-objective optimization problems. More importantly, it enables a fast convergence process.