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Solving the optimum communication spanning tree problem

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  • Zetina, Carlos Armando
  • Contreras, Ivan
  • Fernández, Elena
  • Luna-Mota, Carlos

Abstract

This paper presents an algorithm based on Benders decomposition to solve the optimum communication spanning tree problem. The algorithm integrates within a branch-and-cut framework a stronger reformulation of the problem, combinatorial lower bounds, in-tree heuristics, fast separation algorithms, and a tailored branching rule. Computational experiments show solution time savings of up to three orders of magnitude compared to state-of-the-art exact algorithms. In addition, our algorithm is able to prove optimality for five unsolved instances in the literature and four from a new set of larger instances.

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  • Zetina, Carlos Armando & Contreras, Ivan & Fernández, Elena & Luna-Mota, Carlos, 2019. "Solving the optimum communication spanning tree problem," European Journal of Operational Research, Elsevier, vol. 273(1), pages 108-117.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:1:p:108-117
    DOI: 10.1016/j.ejor.2018.07.055
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    References listed on IDEAS

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    1. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    2. Franz Rothlauf, 2009. "On Optimal Solutions for the Optimal Communication Spanning Tree Problem," Operations Research, INFORMS, vol. 57(2), pages 413-425, April.
    3. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, February.
    4. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    5. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2001. "Simultaneous Assignment of Locomotives and Cars to Passenger Trains," Operations Research, INFORMS, vol. 49(4), pages 531-548, August.
    6. Prabha Sharma, 2006. "Algorithms for the optimum communication spanning tree problem," Annals of Operations Research, Springer, vol. 143(1), pages 203-209, March.
    7. C.D. Randazzo & H.P.L. Luna, 2001. "A Comparison of Optimal Methods for Local Access Uncapacitated Network Design," Annals of Operations Research, Springer, vol. 106(1), pages 263-286, September.
    8. R. K. Ahuja & V. V. S. Murty, 1987. "Exact and Heuristic Algorithms for the Optimum Communication Spanning Tree Problem," Transportation Science, INFORMS, vol. 21(3), pages 163-170, August.
    9. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    10. Ivan Contreras & Elena Fernández & Alfredo Marín, 2010. "Lagrangean bounds for the optimum communication spanning tree problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 140-157, July.
    11. Alysson Costa & Jean-François Cordeau & Bernard Gendron, 2009. "Benders, metric and cutset inequalities for multicommodity capacitated network design," Computational Optimization and Applications, Springer, vol. 42(3), pages 371-392, April.
    12. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2000. "A Benders Decomposition Approach for the Locomotive and Car Assignment Problem," Transportation Science, INFORMS, vol. 34(2), pages 133-149, May.
    13. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2011. "Benders Decomposition for Large-Scale Uncapacitated Hub Location," Operations Research, INFORMS, vol. 59(6), pages 1477-1490, December.
    14. Ricardo Saraiva de Camargo & Gilberto de Miranda & Henrique Pacca L. Luna, 2009. "Benders Decomposition for Hub Location Problems with Economies of Scale," Transportation Science, INFORMS, vol. 43(1), pages 86-97, February.
    15. Contreras, Ivan & Fernández, Elena & Marín, Alfredo, 2010. "The Tree of Hubs Location Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 390-400, April.
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    Cited by:

    1. Yu Yang & An Wang & Hua Wang & Wei-Ting Zhao & Dao-Qiang Sun, 2019. "On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution," Mathematics, MDPI, vol. 7(5), pages 1-19, May.

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