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RAMP for the capacitated minimum spanning tree problem

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  • Cesar Rego
  • Frank Mathew
  • Fred Glover

Abstract

This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated minimum spanning tree problem (CMST). A surrogate constraint relaxation incorporating cutting planes is proposed to explore the dual solution space. In the dual RAMP approach, primal-feasible solutions are obtained by simple tabu searches that project dual solutions onto primal feasible space. A primal-dual approach is achieved by including a scatter search procedure that further exploits the adaptive memory framework. Computational results from applying the methods to a standard set of benchmark problems disclose that the dual RAMP algorithm finds high quality solutions very efficiently and that its primal-dual enhancement is still more effective. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Cesar Rego & Frank Mathew & Fred Glover, 2010. "RAMP for the capacitated minimum spanning tree problem," Annals of Operations Research, Springer, vol. 181(1), pages 661-681, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:661-681:10.1007/s10479-010-0800-4
    DOI: 10.1007/s10479-010-0800-4
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    References listed on IDEAS

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    1. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    2. Luis Gouveia, 1995. "A 2n Constraint Formulation for the Capacitated Minimal Spanning Tree Problem," Operations Research, INFORMS, vol. 43(1), pages 130-141, February.
    3. Mark H. Karwan & Ronald L. Rardin, 1984. "Surrogate Dual Multiplier Search Procedures in Integer Programming," Operations Research, INFORMS, vol. 32(1), pages 52-69, February.
    4. Yagiura, Mutsunori & Kishida, Masahiro & Ibaraki, Toshihide, 2006. "A 3-flip neighborhood local search for the set covering problem," European Journal of Operational Research, Elsevier, vol. 172(2), pages 472-499, July.
    5. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
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    Cited by:

    1. R. Christopher L. Riley & Cesar Rego, 2019. "Intensification, diversification, and learning via relaxation adaptive memory programming: a case study on resource constrained project scheduling," Journal of Heuristics, Springer, vol. 25(4), pages 793-807, October.
    2. M. Kritikos & G. Ioannou, 2017. "A greedy heuristic for the capacitated minimum spanning tree problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1223-1235, October.
    3. Zhixing Luo & Hu Qin & T. C. E. Cheng & Qinghua Wu & Andrew Lim, 2021. "A Branch-and-Price-and-Cut Algorithm for the Cable-Routing Problem in Solar Power Plants," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 452-476, May.

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