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Efficient lower and upper bounds for the weight-constrained minimum spanning tree problem using simple Lagrangian based algorithms

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  • Cristina Requejo

    (University of Aveiro)

  • Eulália Santos

    (ISLA-Higher Institute of Leiria and Santarém)

Abstract

The weight-constrained minimum spanning tree problem (WMST) is a combinatorial optimization problem for which simple but effective Lagrangian based algorithms have been used to compute lower and upper bounds. In this work we present several Lagrangian based algorithms for the WMST and propose two new algorithms, one incorporates cover inequalities. A uniform framework for deriving approximate solutions to the WMST is presented. We undertake an extensive computational experience comparing these Lagrangian based algorithms and show that these algorithms are fast and present small integrality gap values. The two proposed algorithms obtain good upper bounds and one of the proposed algorithms obtains the best lower bounds to the WMST.

Suggested Citation

  • Cristina Requejo & Eulália Santos, 2020. "Efficient lower and upper bounds for the weight-constrained minimum spanning tree problem using simple Lagrangian based algorithms," Operational Research, Springer, vol. 20(4), pages 2467-2495, December.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:4:d:10.1007_s12351-018-0426-x
    DOI: 10.1007/s12351-018-0426-x
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    References listed on IDEAS

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    1. Agostinho Agra & Cristina Requejo & Eulália Santos, 2016. "Implicit cover inequalities," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1111-1129, April.
    2. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    3. Ramos, R. M. & Alonso, S. & Sicilia, J. & Gonzalez, C., 1998. "The problem of the optimal biobjective spanning tree," European Journal of Operational Research, Elsevier, vol. 111(3), pages 617-628, December.
    4. Amado, Ligia & Barcia, Paulo, 1996. "New polynomial bounds for matroidal knapsacks," European Journal of Operational Research, Elsevier, vol. 95(1), pages 201-210, November.
    5. Kaitala, V. & Wolsey, L. A., 1995. "Optimal trees. In M. O. Ball et al (eds.)," LIDAM Reprints CORE 1148, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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