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Relations, models and a memetic approach for three degree-dependent spanning tree problems

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  • Cerrone, C.
  • Cerulli, R.
  • Raiconi, A.

Abstract

In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the classical Minimum Leaves Spanning Tree problem as a relevant problem in this field and show its relations with the Minimum Branch Vertices and the Minimum Degree Sum Problems. We present a unified memetic algorithm for the three problems and show its effectiveness on a wide range of test instances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:3:p:442-453
    DOI: 10.1016/j.ejor.2013.07.029
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    References listed on IDEAS

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    1. 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.
    2. R. Cerulli & M. Gentili & A. Iossa, 2009. "Bounded-degree spanning tree problems: models and new algorithms," Computational Optimization and Applications, Springer, vol. 42(3), pages 353-370, April.
    3. Francesco Carrabs & Raffaele Cerulli & Manlio Gaudioso & Monica Gentili, 2013. "Lower and upper bounds for the spanning tree with minimum branch vertices," Computational Optimization and Applications, Springer, vol. 56(2), pages 405-438, October.
    4. Neumann, Frank, 2007. "Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1620-1629, September.
    5. Fernandes, Lucinda Matos & Gouveia, Luis, 1998. "Minimal spanning trees with a constraint on the number of leaves," European Journal of Operational Research, Elsevier, vol. 104(1), pages 250-261, January.
    6. Zhou, Gengui & Gen, Mitsuo, 1999. "Genetic algorithm approach on multi-criteria minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 114(1), pages 141-152, April.
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    Cited by:

    1. Mercedes Landete & Alfredo Marín & José Luis Sainz-Pardo, 2017. "Decomposition methods based on articulation vertices for degree-dependent spanning tree problems," Computational Optimization and Applications, Springer, vol. 68(3), pages 749-773, December.
    2. Weinand, Jann Michael & Kleinebrahm, Max & McKenna, Russell & Mainzer, Kai & Fichtner, Wolf, 2019. "Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    3. Marín, Alfredo, 2015. "Exact and heuristic solutions for the Minimum Number of Branch Vertices Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 680-689.
    4. Singh, Kavita & Sundar, Shyam, 2019. "A hybrid steady-state genetic algorithm for the min-degree constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 276(1), pages 88-105.
    5. Rafael A. Melo & Phillippe Samer & Sebastián Urrutia, 2016. "An effective decomposition approach and heuristics to generate spanning trees with a small number of branch vertices," Computational Optimization and Applications, Springer, vol. 65(3), pages 821-844, December.

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