An interactive fuzzy satisficing method for multiobjective 0–1 programming problems with block angular structure through genetic algorithms

In this paper, we focus on a multiobjective 0–1 programming problem with block angular structure and propose an interactive fuzzy satisficing method to derive a satisficing solution of the decision maker in consideration of fuzzy goals for the objective functions. After a membership function with respect to each objective function has been elicited by interaction, the nearest Pareto solution in the minimax sense to the reference point given by the decision maker in the membership function value space is obtained and if the decision maker is not satisfied with this solution, the reference point is updated. By iterating this process, the satisficing solution of the decision maker is finally derived. In the proposed method, a genetic algorithm with decomposition procedures to take good advantage of the special structure of the problem is adopted. Through simple numerical experiments, both feasibility and effectiveness of the proposed method are demonstrated.