This article considers bilevel linear programming problems where the coefficients of the objective functions in the problem are given as a possibilistic variable characterized by a quadratic membership function. An extended Stackelberg solution is defined by incorporating the notions of possibility theory into the original concept of Stackelberg solutions. The characteristic of the proposed mod...

The bilevel programming problems are useful tools for solving the hierarchy decision problems. In this paper, a genetic algorithm based on the simplexmethod is constructed to solve the linear-quadratic bilevel programming problem (LQBP). By use of Kuhn–Tucker conditions of the lower level programming, the LQBP is transformed into a single level programming which can be simplified to a linear pr...

This paper deals with bilevel programming programs with convex lower level problems. New necessary and sufficient optimality conditions that involve a single-level mathematical program satisfying the linear independence constraint qualification are introduced. These conditions are solved by an interior point technique for nonlinear programming. Neither the optimality conditions nor the algorith...

#Electrical, Electronic & Computer Engineering The University of Southern Queensland Toowoomba, Queensland 4350, Australia [email protected] Abstract In a real world bilevel decision-making, the lower level of a bilevel decision usually involves multiple decision units. This paper proposes the Kth-best approach for linear bilevel multifollower programming problems with shared variables among fol...

Bilevel programming, a tool for modeling decentralized decision problems, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be an Np-hard problem. Numerous algorithms have been developed for solving bilevel programming problems. These algorithms lack the required efficiency for solving a real problem. ...

———————————————————————————————Abstract In sciences and industries such as signal optimization, traffic assignment, economic market and etc, many problems have been modeled by bilevel programming (BLP) problems, where in each level one must optimize some objective functions. There are so many algorithms in order to find the global optimum of the linear version of BLP problems. This paper addres...

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem ...