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A tabu search heuristic for the generalized minimum spanning tree problem

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  • Öncan, Temel
  • Cordeau, Jean-François
  • Laporte, Gilbert

Abstract

This paper describes an attribute based tabu search heuristic for the generalized minimum spanning tree problem (GMSTP) known to be NP-hard. Given a graph whose vertex set is partitioned into clusters, the GMSTP consists of designing a minimum cost tree spanning all clusters. An attribute based tabu search heuristic employing new neighborhoods is proposed. An extended set of TSPLIB test instances for the GMSTP is generated and the heuristic is compared with recently proposed genetic algorithms. The proposed heuristic yields the best results for all instances. Moreover, an adaptation of the tabu search algorithm is proposed for a variation of the GMSTP in which each cluster must be spanned at least once.

Suggested Citation

  • Öncan, Temel & Cordeau, Jean-François & Laporte, Gilbert, 2008. "A tabu search heuristic for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 306-319, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:2:p:306-319
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    References listed on IDEAS

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    2. Haouari, Mohamed & Chaouachi, Jouhaina Siala, 2006. "Upper and lower bounding strategies for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 171(2), pages 632-647, June.
    3. Pop, Petrica C. & Kern, W. & Still, G., 2006. "A new relaxation method for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 170(3), pages 900-908, May.
    4. M Haouari & J Chaouachi & M Dror, 2005. "Solving the generalized minimum spanning tree problem by a branch-and-bound algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 382-389, April.
    5. Bruce Golden & S. Raghavan & Daliborka Stanojević, 2005. "Heuristic Search for the Generalized Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 290-304, August.
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    10. Duin, C. W. & Volgenant, A. & Vo[ss], S., 2004. "Solving group Steiner problems as Steiner problems," European Journal of Operational Research, Elsevier, vol. 154(1), pages 323-329, April.
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    Cited by:

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    4. Pop, Petrică C. & Matei, Oliviu & Sabo, Cosmin & Petrovan, Adrian, 2018. "A two-level solution approach for solving the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 478-487.
    5. Masoumeh Zojaji & Mohammad Reza Mollakhalili Meybodi & Kamal Mirzaie, 0. "A rapid learning automata-based approach for generalized minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-24.
    6. Masoumeh Zojaji & Mohammad Reza Mollakhalili Meybodi & Kamal Mirzaie, 2020. "A rapid learning automata-based approach for generalized minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 636-659, October.
    7. Mehmet Berkehan Akçay & Hüseyin Akcan & Cem Evrendilek, 2018. "All Colors Shortest Path problem on trees," Journal of Heuristics, Springer, vol. 24(4), pages 617-644, August.
    8. Pop, Petrică C., 2020. "The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances," European Journal of Operational Research, Elsevier, vol. 283(1), pages 1-15.

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