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Compressing branch-and-bound trees

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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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Funding

G. Muñoz was supported by the Chilean National Agency of Research and Development through ANID PIA/PUENTE AFB230002. 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.

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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

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  1. Gonzalo Muñoz
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  2. Joseph Paat
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Correspondence to Joseph Paat.

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A short version of this article was accepted for publication at IPCO 2023 [28]. This extended version contains more detailed discussions and proofs, and new computational contributions and experiments.

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Muñoz, G., Paat, J. & Xavier, Á.S. Compressing branch-and-bound trees. Math. Program. (2024). https://doi.org/10.1007/s10107-024-02080-5

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