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

Daniele Catanzaro, Martin Frohn and Raffaele Pesenti
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Daniele Catanzaro: Université catholique de Louvain, LIDAM/CORE, Belgium
Martin Frohn: Université catholique de Louvain, LIDAM/CORE, Belgium

No 2021026, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: Combinatorial optimization; network design; balanced minimum evolution problem (search for similar items in EconPapers)
Pages: 5
Date: 2021-01-01
New Economics Papers: this item is included in nep-net and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2021026

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