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 nature of the parameters in the problem-formulation process, multiobjective nonconvex nonlinear programming problems with fuzzy numbers are formulated. Using 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 extended Pareto optimal solution set, an interactive decision making method is presented. In the proposed interactive decision making method, if the decision maker specifies the degree of the level sets of fuzzy numbers and the reference objective values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems for which the coevolutionary genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, the revised GENOCOP III is proposed by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Illustrative numerical examples demonstrate the feasibility and efficiency of the proposed method. (C) 2000 Elsevier Science B.V. All rights reserved.