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Compressing Branch-and-Bound Trees

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Integer Programming and Combinatorial Optimization (IPCO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13904))

Abstract

A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same (or stronger) bound by either (1) applying a different disjunction at some node in T or (2) removing leaves from T? We believe such post-hoc analysis of BB trees may assist in identifying helpful general disjunctions in BB algorithms. We initiate our study by considering computational complexity and limitations of TCP. We then conduct experiments to evaluate the compressibility of realistic branch-and-bound trees generated by commonly-used branching strategies, using both an exact and a heuristic compression algorithm.

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Acknowledgements

J. Paat was supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant [RGPIN-2021-02475]. Á.S. Xavier was partially supported by the U.S. Department of Energy Office of Electricity. The authors want to thank the referees, whose comments improved the overall presentation of the paper, led to better bounds in Theorem 2, and identified directions of future work.

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Authors and Affiliations

  1. Institute of Engineering Sciences, Universidad de O’Higgins, Rancagua, Chile

    Gonzalo Muñoz

  2. Sauder School of Business, University of British Columbia, Vancouver, BC, Canada

    Joseph Paat

  3. Energy Systems and Infrastructure Analysis Division, Argonne National Laboratory, Lemont, IL, USA

    Álinson S. Xavier

Authors
  1. Gonzalo Muñoz
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  2. Joseph Paat
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  3. Álinson S. Xavier
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Correspondence to Joseph Paat .

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Editors and Affiliations

  1. University of Wisconsin-Madison, Madison, WI, USA

    Alberto Del Pia

  2. Otto-von-Guericke-Universität, Magdeburg, Sachsen-Anhalt, Germany

    Volker Kaibel

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Muñoz, G., Paat, J., Xavier, Á.S. (2023). Compressing Branch-and-Bound Trees. In: Del Pia, A., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2023. Lecture Notes in Computer Science, vol 13904. Springer, Cham. https://doi.org/10.1007/978-3-031-32726-1_25

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  • DOI: https://doi.org/10.1007/978-3-031-32726-1_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32725-4

  • Online ISBN: 978-3-031-32726-1

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