Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms

• Published in: IEEE transactions on evolutionary computation Vol. 18; no. 2; pp. 269 - 285
• Main Authors: He, Zhenan, Yen, Gary G., Zhang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Benchmark testing; Computer science; control theory; systems; Convergence; Evolutionary algorithms; Evolutionary computation; Exact sciences and technology; Fitness; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; multiobjective evolutionary algorithm; NSGA-II; Object recognition; Optimization; Pareto optimality; Pareto optimization; Search problems; SPEA2; Theoretical computing; Vectors; NSGA-II; Pareto optimum; Evolutionary algorithm; Multiobjective programming; Dominance; SPEA2; multiobjective evolutionary algorithm; Fuzzy logic; Experimental result; Genetic algorithm; Classification; Fuzzy relation; Pareto optimality; Optimality principle; Mathematical programming
• ISSN: 1089-778X; 1941-0026
• DOI: 10.1109/TEVC.2013.2258025

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.