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A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem

Author

Listed:
  • Catanzaro, Daniele

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Frohn, Martin

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Pesenti, Raffaele

Abstract

The Balanced Minimum Evolution Problem (BMEP) is an [APX]-hard nonlinear network design problem that consists of finding a phylogeny that minimizes the cross-entropy of the molecular sequences extracted from a given set of taxa. By combining massive parallelism with recent theoretical advances on the polyhedral combinatorics of the problem and new insights on the relationships between the BMEP and information entropy, we design a new exact solution algorithm that proves to be up to an order of magnitude faster than the current state-of-the-art sequential-version on generic instances and able to solve up to 25% more taxa within the same time limit. We also investigate some issues related to numerical stability and statistical consistency of the BMEP, arising in particular when dealing with large instances. We show, as a negative finding, that no rescaling technique may ensure numerical stability, by guaranteeing at the same time the statistical consistency of the optimal solution to the problem.

Suggested Citation

  • Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2021. "A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2021023
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    References listed on IDEAS

    as
    1. Catanzaro, Daniele & Aringhieri, Roberto & Di Summa, Marco & Pesenti, Raffaele, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 753-765.
    2. Daniele CATANZARO & Roberto ARINGHIERI & Mardo DI SUMMA & Raffaele PESENTI, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," LIDAM Reprints CORE 2767, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
    4. Catanzaro, Daniele & Pesenti, Raffaele & Wolsey, Laurence, 2020. "On the balanced minimum evolution polytope," LIDAM Reprints CORE 3096, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Daniele Catanzaro & Raffaele Pesenti, 2019. "Enumerating vertices of the balanced minimum evolution polytope," LIDAM Reprints CORE 3005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Daniele Catanzaro & Martine Labbé & Raffaele Pesenti & Juan-José Salazar-González, 2012. "The Balanced Minimum Evolution Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 276-294, May.
    7. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2020. "An information theory perspective on the balanced minimum evolution problem," LIDAM Reprints CORE 3097, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Combinatorial optimization ; network design ; balanced minimum evolution ; implicit enumeration algorithms ; parallel computing ; numerical stability;
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