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Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem

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  • de Souza, Mauricio C.
  • Martins, Pedro

Abstract

We develop ideas to enhance the performance of the variable neighborhood search (VNS) by guiding the search in the shaking phase, and by employing the Skewed strategy. For this purpose, Second Order algorithms and Skewed functions expressing structural differences are embedded in an efficient VNS proposed in the literature for the degree constrained minimum spanning tree problem. Given an undirected graph with weights associated with its edges, the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph, subject to constraints on node degrees. Computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date. We report results showing that the VNS with the proposed strategies improved the best known solutions for all the hardest benchmark instances. Moreover, these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature.

Suggested Citation

  • de Souza, Mauricio C. & Martins, Pedro, 2008. "Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(3), pages 677-690, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:677-690
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    References listed on IDEAS

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    1. Brimberg, J. & Urosevic, D. & Mladenovic, N., 2006. "Variable neighborhood search for the vertex weighted k-cardinality tree problem," European Journal of Operational Research, Elsevier, vol. 171(1), pages 74-84, May.
    2. Stefan Voßs & Andreas Fink & Cees Duin, 2005. "Looking Ahead with the Pilot Method," Annals of Operations Research, Springer, vol. 136(1), pages 285-302, April.
    3. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
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    1. Cerrone, C. & Cerulli, R. & Raiconi, A., 2014. "Relations, models and a memetic approach for three degree-dependent spanning tree problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 442-453.
    2. Luis Bicalho & Alexandre Cunha & Abilio Lucena, 2016. "Branch-and-cut-and-price algorithms for the Degree Constrained Minimum Spanning Tree Problem," Computational Optimization and Applications, Springer, vol. 63(3), pages 755-792, April.
    3. S Vlah & Z Lukač & J Pacheco, 2011. "Use of VNS heuristics for scheduling of patients in hospital," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1227-1238, July.
    4. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

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