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Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem

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Abstract

In this paper we develop, study and test new neighborhood structures for the Hop-constrained Minimum Spanning Tree Problem (HMSTP). These neighborhoods are defined by restricted versions of a new dynamic programming formulation for the problem and provide a systematic way of searching neighborhood structures based on node-level exchanges. We have also developed several local search methods that are based on the new neighborhoods. Computational experiments for a set of benchmark instances with up to 80 nodes show that the more elaborate methods produce in a quite fast way, heuristic solutions that are, for all cases, within 2% of the optimum.

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References

  • Ahuja, R., Ergun, O., Orlin, J., Punnen, A.: A survey of very large scale neighborhood search techniques. Discrete Appl. Math. 123, 75–102 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Cordeau, J.-F., Costa, A.M., Laport, G.: Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints. Eur. J. Oper. Res. 190, 68–78 (2008)

    Article  MATH  Google Scholar 

  • Dahl, G.: The 2-hop spanning tree problem. Oper. Res. Lett. 23, 21–26 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • Dahl, G., Flatberg, T., Foldnes, N., Gouveia, L.: The jump formulation for the hop-constrained minimum spanning tree problem. Working Paper no5, C.I.O. (2004)

  • Dahl, G., Gouveia, L., Requejo, C.: On formulations and methods for the hop-constrained minimum spanning tree problem. In: Pardalos, P., Resende, M. (eds.) Handbooks of Telecommunications, pp. 493–515. Springer, Berlin (2006)

    Chapter  Google Scholar 

  • Fernandes, M., Gouveia, L., Voss, S.: Determining hop-constrained heuristics with repetitive heuristics. J. Telecommun. Inf. Technol. (JTIT) 4/2007, 16–22 (2007)

    Google Scholar 

  • Gouveia, L.: Using the Miller-Tucker-Zemlin constraints to formulate a minimal spanning tree problem with hop constraints. Comput. Oper. Res. 22, 959–970 (1995)

    Article  MATH  Google Scholar 

  • Gouveia, L.: Multicommodity flow models for spanning trees with hop constraints. Eur. J. Oper. Res. 95, 178–190 (1996)

    Article  MATH  Google Scholar 

  • Gouveia, L.: Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints. INFORMS J. Comput. 10, 180–188 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • Gouveia, L., Requejo, C.: A new Lagrangian relaxation approach for the hop-constrained minimum spanning tree problem. Eur. J. Oper. Res. 132, 539–552 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Gouveia, L., Simonetti, L., Uchoa, E.: Modelling the hop-constrained minimum spanning tree problem over a layered graph. In: Proceedings of the INOC 2007 Conference, Spa, 2007

  • Gruber, M., Raidl, G.R.: Variable neighborhood search for the bounded diameter minimum spanning tree problem. In: Proceedings of 18th Mini Euro Conference on Variable Neighborhood Search, Tenerife, Spain (2005)

  • Gruber, M., van Hemert, J., Raidl, G.R.: Neighbourhood searches for the bounded diameter minimum spanning tree problem embedded in a VNS, EA and ACO. In: Proceedings of GECCO’06, Seattle Washington (2006)

  • Manyem, P., Stallmann, M.: Some approximation results in multicasting. Working paper, North Carolina State University (1996)

  • Orlin, J., Sharma, D.: Extended neighborhood: definition and characterization. Math. Program. 101, 537–559 (2005)

    Article  MathSciNet  Google Scholar 

  • Potts, C., van de Velde, S.: Dynasearch—iterative local improvement by dynamic programming—Orat 1: the traveling salesman problem. Technical Report, University of Twente (1995)

  • Voß, S.: The Steiner tree problem with hop constraints. In: Sharaiha, Y., Beasley, J. (eds.) Advances in Combinatorial Optimization Annals of Operations Research, vol. 86, pp. 321–345 (1999)

  • Woolston, K., Albin, S.: The design of centralized networks with reliability and availability constraints. Comput. Oper. Res. 15, 207–217 (1988)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculdade de Ciências, Departamento de Estatística e Investigação Operacional, Centro de Investigação Operacional, Universidade de Lisboa, Bloco C/6–Cidade Universitária, 1749-016, Lisbon, Portugal

    Luis Gouveia & Ana Paias

  2. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Dushyant Sharma

Authors
  1. Luis Gouveia
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  2. Ana Paias
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  3. Dushyant Sharma
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Correspondence to Ana Paias.

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Gouveia, L., Paias, A. & Sharma, D. Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem. J Heuristics 17, 23–37 (2011). https://doi.org/10.1007/s10732-009-9123-5

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  • DOI: https://doi.org/10.1007/s10732-009-9123-5

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