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Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

Author

Listed:
  • Uchoa, Eduardo

    (Departamento de Engenharia de Producão)

  • Fukasawa, Ricardo

    (School of Industrial and Systems Engineering)

  • Lysgaard, Jens

    (Department of Accounting, Aarhus School of Business)

  • Pessoa, Artur

    (Departamento de Engenharia de Producão)

  • Poggi de Aragão, Marcus

    (Departamento de Informática)

  • Andrade, Diogo

    (RUTCOR)

Abstract

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimality

Suggested Citation

  • Uchoa, Eduardo & Fukasawa, Ricardo & Lysgaard, Jens & Pessoa, Artur & Poggi de Aragão, Marcus & Andrade, Diogo, 2006. "Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation," CORAL Working Papers L-2006-08, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbls:2006-008
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    File URL: http://www.hha.dk/bs/wp/log/L_2006_08.pdf
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    References listed on IDEAS

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    5. Leslie Hall, 1996. "Experience with a Cutting Plane Algorithm for the Capacitated Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 219-234, August.
    6. Gouveia, Luis & Joao Lopes, Maria, 2005. "The capacitated minimum spanning tree problem: On improved multistar constraints," European Journal of Operational Research, Elsevier, vol. 160(1), pages 47-62, January.
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    Cited by:

    1. Kjeldsen, Karina Hjortshøj, 2008. "Classification of routing and scheduling problems in liner shipping," CORAL Working Papers L-2008-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    2. Lysgaard, Jens & Løber, Janni, 2008. "Scheduling participants of Assessment Centres," CORAL Working Papers L-2008-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.

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