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On Numerical Stability and Statistical Consistency of the Balanced Minimum Evolution Problem

Author

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  • 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 affected by numerical instabilities that may preclude its use on practical instances. In this article, we investigate the impact of rescaling the objective function of the problem to overcome numerical instabilities and we show how this strategy may affect the statistical consistency of the optimal solution. In particular, we show that the numerical instabilities at the core of the BMEP cannot be overcome by any kind of rescaling of the objective function. As an extension of this negative result, we also characterize the class of the input distance matrices that may give rise to numerical instabilities for large scale instances.

Suggested Citation

  • Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2021. "On Numerical Stability and Statistical Consistency of the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2021026
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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 & 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.
    6. 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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    Keywords

    Combinatorial optimization ; network design ; balanced minimum evolution problem;
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