This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficien...

#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 problems are hierarchical optimization problems where an objective function is to be minimized over the graph of the solution set mapping of a second parametric optimization problem. It is the aim of the paper to give a survey for this living research area indicating main recent approaches to solve such problems and to describe optimality conditions as well as to touch main ...

This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.

A special class of bilevel programming problems with discrete para-metric lower level problems is considered. First, necessary and suucient conditions for the existence of optimal solutions are given. Then, a pseu-dopolynomial exact and a polynomial approximate algorithms for solving the bilevel problem are proposed.

Bilevel programming is a branch of optimization where a subset of variables is constrained to lie in the optimal set of an auxiliary mathematical program. This chapter presents an overview of two specific classes of bilevel programs, and in particular their relationship to well-known combinatorial problems.