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A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs

Article

Abstract

We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level problems. In particular, we consider MIBLPs with upper-level constraints that involve lower-level variables. We assume that the inducible region is nonempty and all variables are bounded. By using the reformulation and decomposition scheme, an MIBLP is first converted into its equivalent single-level formulation, then computed by a column-and-constraint generation based decomposition algorithm. The solution procedure is enhanced by a projection strategy that does not require the relatively complete response property. To ensure its performance, we prove that our new method converges to the global optimal solution in a finite number of iterations. A large-scale computational study on random instances and instances of hierarchical supply chain planning are presented to demonstrate the effectiveness of the algorithm.

Keywords

Mixed-integer bilevel linear program Global optimization Single-level reformulation Reformulation and decomposition method Projection Hierarchical supply chain planning 

Notes

Acknowledgements

We greatly appreciate the helpful discussions with Professor Andreas Wächter at Department of Industrial Engineering and Management Sciences at Northwestern University. The paper has been greatly improved by the insightful and constructive feedback from the associate editor and three anonymous reviewers. The authors acknowledge financial support from National Science Foundation (NSF) CAREER Award (CBET-1643244).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Northwestern UniversityEvanstonUSA
  2. 2.Cornell UniversityIthacaUSA
  3. 3.University of PittsburghPittsburghUSA

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