An interactive fuzzy satisficing method for multiobjective nonconvex programming problems through floating-point genetic algorithms
Masatoshi Sakawa, Katsuhiro Yauchi · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 2000
This article focuses on the multiobjective nonconvex nonlinear programming problem. The following interactive fuzzy satisficing method is proposed using the floating-point genetic algorithm. The fuzzy goal of the decision-maker for each objective function is specified by the membership function. The Pareto optimal solution is derived, which is close to the reference membership value set by the decision-maker, in the sense of the augmented min–max criterion. If the decision-maker is not satisfied with the solution, the reference membership value is interactively updated to derive the satisficing solution for the decision-maker from the set of Pareto optimal solutions. In the derivation of the Pareto optimal solution for the augmented min–max problem, GENOCOP III proposed by Michalewicz and colleagues is not used. Instead, a more efficient method is proposed, where the improved GENOCOP III is applied to cope with the problems in GENOCOP III, by introducing the efficient search of the initial feasible solution, and the search of the feasible solution by bisection method. The validity of the proposed method is shown through numerical examples. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(6): 10–18, 2000