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A Dual Ascent-Based Branch-and-Bound Framework for the Prize-Collecting Steiner Tree and Related Problems

Author

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  • Markus Leitner

    (University of Vienna, Department of Statistics and Operations Research, 1090 Vienna, Austria)

  • Ivana Ljubić

    (ESSEC Business School, 95021 Cergy-Pontoise Cedex, France)

  • Martin Luipersbeck

    (University of Vienna, Department of Statistics and Operations Research, 1090 Vienna, Austria)

  • Markus Sinnl

    (University of Vienna, Department of Statistics and Operations Research, 1090 Vienna, Austria)

Abstract

We present a branch-and-bound (B&B) framework for the asymmetric prize-collecting Steiner tree problem (APCSTP). Several well-known network design problems can be transformed to the APCSTP, including the Steiner tree problem (STP), prize-collecting Steiner tree problem (PCSTP), maximum-weight connected subgraph problem (MWCS), and node-weighted Steiner tree problem (NWSTP). The main component of our framework is a new dual ascent algorithm for the rooted APCSTP, which generalizes Wong’s dual ascent algorithm for the Steiner arborescence problem. The lower bounds and dual information obtained from the algorithm are exploited within powerful bound-based reduction tests and for guiding primal heuristics. The framework is complemented by additional alternative-based reduction tests. Extensive computational results on benchmark instances for the PCSTP, MWCS, and NWSTP indicate the framework’s effectiveness, as most instances from literature are solved to optimality within seconds, including most of the (previously unsolved) largest instances from the recent DIMACS Challenge on Steiner trees. Moreover, results on new asymmetric instances for the APCSTP are reported. Since the addressed network design problems are frequently used for modeling various real-world applications (e.g., in bioinformatics), the implementation of the presented B&B framework has been made publicly available.

Suggested Citation

  • Markus Leitner & Ivana Ljubić & Martin Luipersbeck & Markus Sinnl, 2018. "A Dual Ascent-Based Branch-and-Bound Framework for the Prize-Collecting Steiner Tree and Related Problems," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 402-420, May.
  • Handle: RePEc:inm:orijoc:v:30:y:2018:i:2:p:402-420
    DOI: 10.1287/ijoc.2017.0788
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    References listed on IDEAS

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    1. A. Balakrishnan & T. L. Magnanti & R. T. Wong, 1989. "A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design," Operations Research, INFORMS, vol. 37(5), pages 716-740, October.
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    Cited by:

    1. Daniel Rehfeldt & Thorsten Koch, 2022. "On the Exact Solution of Prize-Collecting Steiner Tree Problems," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 872-889, March.
    2. Ziye Tang & Yang Jiao & R. Ravi, 2022. "Combinatorial Heuristics for Inventory Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 370-384, January.
    3. Pedersen, Jaap & Weinand, Jann Michael & Syranidou, Chloi & Rehfeldt, Daniel, 2024. "An efficient solver for large-scale onshore wind farm siting including cable routing," European Journal of Operational Research, Elsevier, vol. 317(2), pages 616-630.
    4. Ritt, Marcus & Pereira, Jordi, 2020. "Heuristic and exact algorithms for minimum-weight non-spanning arborescences," European Journal of Operational Research, Elsevier, vol. 287(1), pages 61-75.
    5. Kuzbakov, Yerlan & Ljubić, Ivana, 2024. "New formulations for two location problems with interconnected facilities," European Journal of Operational Research, Elsevier, vol. 314(1), pages 51-65.

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