Journal ArticleDOI
New branch-and-bound rules for linear bilevel programming
TLDR
In this paper, a branch-and-bound algorithm for linear bilevel programming is proposed, where necessary optimality conditions expressed in terms of tightness of the follower's constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to those used in mixed-integer programming.Abstract:
A new branch-and-bound algorithm for linear bilevel programming is proposed. Necessary optimality conditions expressed in terms of tightness of the follower’s constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to those used in mixed-integer programming. Computational results are reported and compare favorably to those of previous methods. Problems with up to 150 constraints, 250 variables controlled by the leader, and 150 variables controlled by the follower have been solved.read more
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Journal ArticleDOI
An overview of bilevel optimization
TL;DR: This paper presents fields of application, focus on solution approaches, and makes the connection with MPECs (Mathematical Programs with Equilibrium Constraints), a branch of mathematical programming of both practical and theoretical interest.
Journal ArticleDOI
Bilevel and multilevel programming: A bibliography review
TL;DR: This paper contains a bibliography of all references central to bilevel and multilevel programming that the authors know of and it is hoped that this bibliography facilitates and encourages their research.
Journal ArticleDOI
Shortest‐path network interdiction
Eitan Israeli,R. Kevin Wood +1 more
TL;DR: Computational results demonstrate orders‐of‐magnitude improvements of the decomposition algorithms over direct solution of the MIP and show that SVIs also help solve the original MIP faster.
Journal ArticleDOI
Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
TL;DR: In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized.
Journal ArticleDOI
A bilevel mixed-integer program for critical infrastructure protection planning
TL;DR: This paper presents a bilevel formulation of the r-interdiction median problem with fortification (RIMF), which identifies the most cost-effective way of allocating protective resources among the facilities of an existing but vulnerable system so that the impact of the most disruptive attack to r unprotected facilities is minimized.