An interactive fuzzy satisficing method for large scale multiobjective 0–1 programming problems with fuzzy parameters through genetic algorithms

In this paper, by considering the experts’ imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective block angular 0–1 programming problems involving fuzzy numbers are formulated. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-multiobjective 0–1 programming problem is introduced and an extended Pareto optimality concept is defined. For the α-multiobjective 0–1 programming problem, the fuzzy goal of the decision maker for each objective function quantified by eliciting the corresponding membership function is considered. Since the decision maker must select a compromise or satisficing solution from the extended Pareto optimal solution set including an infinite number of elements in general, an interactive fuzzy satisficing method through genetic algorithms for deriving a satisficing solution for the decision maker from an extended Pareto optimal solution set is presented. Then, for fixed α and reference membership levels, the corresponding extended Pareto optimal solution can be obtained by solving a minimax problem with block angular structure. In order to solve the minimax problem efficiently, we adopt a genetic algorithm with decomposition procedures. Finally, both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments.