Solving nonlinear optimization problems with fuzzy relation equation constraints

• Published in: Fuzzy sets and systems Vol. 119; no. 1; pp. 1 - 20
• Main Authors: Lu, Jianjun, Fang, Shu-Cherng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2001
• Subjects: Fuzzy relation equations; Genetic algorithms; Nonlinear optimization; Fuzzy relation equations; Nonlinear optimization; Genetic algorithms
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/S0165-0114(98)00471-0

An optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented. Since the solution set of the fuzzy relation equations is in general a non-convex set, when it is not empty, conventional nonlinear programming methods are not ideal for solving such a problem. In this paper, a genetic algorithm (GA) is proposed. This GA is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations. The individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations. The construction of test problems is also developed to evaluate the performance of the proposed algorithm.