An interactive fuzzy satisficing method for multiobjective nonconvex programming problems through floating-point genetic algorithms

This article focuses on the multiobjective nonconvex nonlinear programming problem. The following interactive fuzzy satisficing method is proposed usi ng the floating-point genetic algorithm. The fuzzy goal of the decisionmake r for each objective function is specified by the membership function. The Pareto optimal solution is derived, which is close to the reference members hip value set by the decision-maker, in the sense of the augmented minmax c riterion. If the decision-maker is not satisfied with the solution, the ref erence membership value is interactively updated to derive the satisficing solution for the decisionmaker from the set of Pareto optimal solutions. In the derivation of the Pareto optimal solution for the augmented min-max pr oblem, GENOCOP III proposed by Michalewicz and colleagues is not used. Inst ead, a more efficient method is proposed, where the improved GENOCOP III is applied to cope with the problems in GENOCOP Ill, by introducing the effic ient search of the initial feasible solution, and the search of the feasibl e solution by bisection method. The validity of the proposed method is show n through numerical examples. (C) 2000 Scripta Technica.