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Empirical study of exact algorithms for the multi-objective spanning tree

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Abstract

The multi-objective spanning tree (MoST) is an extension of the minimum spanning tree problem (MST) that, as well as its single-objective counterpart, arises in several practical applications. However, unlike the MST, for which there are polynomial-time algorithms that solve it, the MoST is NP-hard. Several researchers proposed techniques to solve the MoST, each of those methods with specific potentialities and limitations. In this study, we examine those methods and divide them into two categories regarding their outcomes: Pareto optimal sets and Pareto optimal fronts. To compare the techniques from the two groups, we investigated their behavior on 2, 3 and 4-objective instances from different classes. We report the results of a computational experiment on 8100 complete and grid graphs in which we analyze specific features of each algorithm as well as the computational effort required to solve the instances.

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Acknowledgements

We thank Francis Sourd and Olivier Spanjaard who kindly provided the code of their algorithm. This research was partially supported by the NPAD/UFRN (High Performance Computing Center at Universidade Federal do Rio Grande do Norte) and by the CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, under Grants 301845/2013-1, 308062/2014-0 and 130286/2017-6.

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  1. Department of Informatics and Applied Mathematics, Universidade Federal do Rio Grande do Norte, Campus Universitário Lagoa Nova, Natal, Brazil

    I. F. C. Fernandes, E. F. G. Goldbarg, S. M. D. M. Maia & M. C. Goldbarg

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  1. I. F. C. Fernandes
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Fernandes, I.F.C., Goldbarg, E.F.G., Maia, S.M.D.M. et al. Empirical study of exact algorithms for the multi-objective spanning tree. Comput Optim Appl 75, 561–605 (2020). https://doi.org/10.1007/s10589-019-00154-1

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