An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions

We present an exact algorithm for the bilevel mixed integer linear programming (BMILP) problem under three simplifying assumptions. Although BMILP has been studied for decades and widely applied to various real world problems, there are only a few BMILP algorithms. Compared to these existing ones, o...

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Bibliographic Details
Published in:Computers & operations research Vol. 41; pp. 309 - 318
Main Authors: Xu, Pan, Wang, Lizhi
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.01.2014
Pergamon Press Inc
Subjects:
Algorithms
Bilevel mixed integer linear programming
Bilevel optimization
Branch-and-bound
Integer programming
Libraries
Linear programming
Mathematical analysis
Mathematical problems
Mixed integer
Online
Operations research
Optimization
Optimization algorithms
Studies
Branch-and-bound
Bilevel optimization
Bilevel mixed integer linear programming
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:We present an exact algorithm for the bilevel mixed integer linear programming (BMILP) problem under three simplifying assumptions. Although BMILP has been studied for decades and widely applied to various real world problems, there are only a few BMILP algorithms. Compared to these existing ones, our new algorithm relies on fewer and weaker assumptions, explicitly considers finite optimal, infeasible, and unbounded cases, and is proved to terminate finitely and correctly. We report results of our computational experiments on a small library of BMILP test instances, which we created and made publicly available online.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2013.07.016