Multi-objective optimization problems with fuzzy relation equation constraints

• Published in: Fuzzy sets and systems Vol. 127; no. 2; pp. 141 - 164
• Main Authors: Loetamonphong, Jiranut, Fang, Shu-Cherng, Young, Robert E.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.04.2002; Elsevier
• Subjects: Applied sciences; Exact sciences and technology; Fuzzy relation equations; General logic; Genetic algorithm; Logic and foundations; Mathematical logic, foundations, set theory; Mathematical programming; Mathematics; Max–min composition; Multi-objective optimization; Operational research and scientific management; Operational research. Management science; Sciences and techniques of general use; Fuzzy relation equations; Multi-objective optimization; Max–min composition; Genetic algorithm; Fuzzy logic; Reproduction; Selection; Multiobjective programming; Fuzzy relation; Cluster; Feasibility; Maxmin composition; Fuzzy relation equation; Mutation
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/S0165-0114(01)00052-5

This paper studies a new class of optimization problems which have multiple objective functions subject to a set of fuzzy relation equations. Since the feasible domain of such a problem is in general non-convex and the objective functions are not necessarily linear, traditional optimization methods may become ineffective and inefficient. Taking advantage of the special structure of the solution set, a reduction procedure is developed to simplify a given problem. Moreover, a genetic-based algorithm is proposed to find the “Pareto optimal solutions”. The major components of the proposed algorithm together with some encouraging test results are reported.