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The hop-constrained minimum cost flow spanning tree problem with nonlinear costs: an ant colony optimization approach

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Abstract

In this work we address the Hop-Constrained Minimum cost Flow Spanning Tree (HMFST) problem with nonlinear costs. The HMFST problem is an extension of the Hop-Constrained Minimum Spanning Tree problem since it considers flow requirements other than unit flows. We propose a hybrid heuristic, based on ant colony optimization and on local search, to solve this class of problems given its combinatorial nature and also that the total costs are nonlinearly flow dependent with a fixed-charge component. We solve a set of benchmark problems available online and compare the results obtained with the ones reported in the literature for a Multi-Population hybrid biased random key Genetic Algorithm (MPGA). Our algorithm proved to be able to find an optimum solution in more than 75 % of the runs, for each problem instance solved, and was also able to improve on many results reported for the MPGA. Furthermore, for every single problem instance we were able to find a feasible solution, which was not the case for the MPGA. Regarding running times, our algorithm improves upon the computational time used by CPLEX and was always lower than that of the MPGA.

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Acknowledgments

This work is partially funded by ERDF (FEDER), the COMPETE through the FCT as part of projects PTDC/EGE-GES/099741/2008 and PTDC/EEA-CRO/116014/2009 and the North Portugal Regional Operational Programme (ON.2O Novo Norte) under the National Strategic Reference Framework.

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Authors and Affiliations

  1. Faculdade de Economia and LIAAD-INESC TEC, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464 , Porto, Portugal

    Marta S. R. Monteiro & Dalila B. M. M. Fontes

  2. Faculdade de Engenharia and ISR-Porto, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 , Porto, Portugal

    Fernando A. C. C. Fontes

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  1. Marta S. R. Monteiro
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  2. Dalila B. M. M. Fontes
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  3. Fernando A. C. C. Fontes
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Correspondence to Dalila B. M. M. Fontes.

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Monteiro, M.S.R., Fontes, D.B.M.M. & Fontes, F.A.C.C. The hop-constrained minimum cost flow spanning tree problem with nonlinear costs: an ant colony optimization approach. Optim Lett 9, 451–464 (2015). https://doi.org/10.1007/s11590-014-0762-6

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