Interactive decision making for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms

In this paper, by considering the experts' fuzzy understanding of the natur e of the parameters in the problem-formulation process, multiobjective nonc onvex nonlinear programming problems with fuzzy numbers are formulated. Usi ng the level sets of fuzzy numbers, the corresponding nonfuzzy programming problems together with an extended Pareto optimality concept are introduced , For deriving a satisficing solution for the decision maker from an extend ed Pareto optimal solution set, an interactive decision making method is pr esented. In the proposed interactive decision making method, if the decisio n maker specifies the degree of the level sets of fuzzy numbers and the ref erence objective values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems for which the co evolutionary genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, the revised GENOCOP III is propo sed by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Illustrat ive numerical examples demonstrate the feasibility and efficiency of the pr oposed method. (C) 2000 Elsevier Science B.V. All rights reserved.