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Multi-objective optimization problems with fuzzy relation equation constraints. (English) Zbl 0994.90130
Summary: 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.

90C29 Multi-objective and goal programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C59 Approximation methods and heuristics in mathematical programming
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