A genetic algorithm approach to fuzzy quadratic bilevel programming

This article presents a genetic algorithm (GA) based fuzzy goal programming (FGP) procedure for modelling and solving quadratic bilevel programming problems (QBLPPs) of a hierarchical decision organization. In the FGP model formulation, the concept of tolerance membership functions for measuring the degree of satisfaction of the decision makers (DMs) regarding goal achievement of the fuzzy objectives and the degree of optimality of the decision vector controlled by the upper-level DM are defined in the decision making horizon. In the goal achievement function of the model, minimization of the under-deviations of the defined membership goals from the highest membership value (unity) on the basis of the assigned priorities is considered. In the solution process, sensitivity analysis on different priority structures by using an GA scheme is made to reach an ideal-point dependent solution in the decision environment. The potential use of the approach is illustrated by a numerical example.