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A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation

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In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range of bilevel optimization problems. The framework has been fully implemented in the open-source solver MibS. The paper describes the algorithmic options offered by MibS and presents computational results evaluating the effectiveness of the various options for the solution of a number of classes of bilevel optimization problems from the literature.

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Acknowledgements

This research was made possible with support from National Science Foundation Grants CMMI-1435453, CMMI-0728011, and ACI-0102687.

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Authors and Affiliations

  1. Department of Industrial and System Engineering, Lehigh University, Bethlehem, PA, USA

    Sahar Tahernejad & Ted K. Ralphs

  2. Hospital for Special Surgery, New York, NY, USA

    Scott T. DeNegre

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  1. Sahar Tahernejad
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  2. Ted K. Ralphs
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  3. Scott T. DeNegre
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Correspondence to Ted K. Ralphs.

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Tahernejad, S., Ralphs, T.K. & DeNegre, S.T. A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation. Math. Prog. Comp. 12, 529–568 (2020). https://doi.org/10.1007/s12532-020-00183-6

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