A fuzzy goal programming procedure for solving quadratic bilevel programming problems

Abstract

This article presents a fuzzy goal programming (FGP) procedure for solving quadratic bilevel programming problems (QBLPP). In the proposed approach, the membership functions for the defined fuzzy objective goals of the decision makers (DM) at both the levels are developed first. Then, a quadratic programming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming (NLGP) model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then, at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach.

Mixed 0−1 Goal Programming Approach to Interval-Valued Bilevel Programming Problems Via Bio-Inspired Computational Algorithm

“…Finally, the executable GP model appears as: (20) subject to the constraints sets defined in (15) and (19) Now, since GA is a goal satisfier [9] rather than optimizer, the defined GA scheme can be employed here to minimize the regret function 'Z' in (20) and thereby to reach a satisfactory decision by minimizing the regrets of both the DMs.…”

“…Using the expressions of Z in (20) and following the procedure, the executable GP model in the form of mixed 0-1 programming problem appears as: Find X(x 1 , x 2 ) so as to…”

“…The GAs [9,17] as prominent tools to optimization of multiobjective decision making (MODM) problems [15,16] have also been introduced to solve BLPPs [12,18]. The GA based fuzzy goal programming (FGP) approaches [20,24] to linear as well fractional BLPPs and MLPPs have been studied by Pal et al [29,30] in the recent past. However, the extensive study in this area is at an early stage.…”

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

“…In fuzzy environment, Pal and Moitra [35] proposed fuzzy goal programming (FGP) procedure for solving QBLPP in 2003. In [35], Pal and Moitra formulated QBLPP in two phases by using the notion of distance function.…”

“…In fuzzy environment, Pal and Moitra [35] proposed fuzzy goal programming (FGP) procedure for solving QBLPP in 2003. In [35], Pal and Moitra formulated QBLPP in two phases by using the notion of distance function. At the first phase of the solution process, Pal and Moitra transform QBLPP model into nonlinear goal programming model in order to maximize the membership value of each of the fuzzy objective goals based on their priorities in the decision context.…”