Journal of Heuristics

, Volume 19, Issue 5, pp 757–795 | Cite as

A three-phase matheuristic for capacitated multi-commodity fixed-cost network design with design-balance constraints

  • Duc Minh Vu
  • Teodor Gabriel Crainic
  • Michel Toulouse
Article

Abstract

This paper proposes a three-phase matheuristic solution strategy for the capacitated multi-commodity fixed-cost network design problem with design-balance constraints. The proposed matheuristic combines exact and neighbourhood-based methods. Tabu search and restricted path relinking meta-heuristics cooperate to generate as many feasible solutions as possible. The two meta-heuristics incorporate new neighbourhoods, and computationally efficient exploration procedures. The feasible solutions generated by the two procedures are then used to identify an appropriate part of the solution space where an exact solver intensifies the search. Computational experiments on benchmark instances show that the proposed algorithm finds good solutions to large-scale problems in a reasonable amount of time.

Keywords

Network design Design-balance constraints Tabu search  Path relinking Matheuristic 

References

  1. Andersen, J., Crainic, T.G., Christiansen, M.: Service network design with management and coordination of multiple fleets. Eur. J. Oper. Res. 193(2), 377–389 (2009a)MathSciNetCrossRefMATHGoogle Scholar
  2. Andersen, J., Crainic, T.G., Christiansen, M.: Service network design with asset management: formulations and comparative analyzes. Transp. Res. C. 17(2), 207–397 (2009b)MathSciNetCrossRefGoogle Scholar
  3. Andersen, J., Christiansen, M., Crainic, T.G., Grønhaug, R.: Branch-and-price for service network design with asset management constraints. Transp. Sci. 46(1), 33–49 (2011)CrossRefGoogle Scholar
  4. Armacost, A.P., Barnhart, C., Ware, K.A.: Composite variable formulations for express shipment service network design. Transport. Sci. 36(1), 1–20 (2002)CrossRefMATHGoogle Scholar
  5. Balakrishnan, A., Magnanti, T.L., Mirchandani, P.: Network design. In: Dell’Amico, M., Maffioli, F., Martello, S. (eds.) Annotated Bibliographies in Combinatorial Optimization, pp. 311–334. Wiley, New York (1997)Google Scholar
  6. Barnhart, C., Krishnan, N., Kim, D., Ware, K.: Network design for express shipment delivery. Comput. Optim. Appl. 21(3), 239–262 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. Chouman, M., Crainic, T.G.: A MIP-Tabu Search Hybrid Framework for Multicommodity Capacitated Fixed-Charge Network Design. Technical Report CIRRELT-2010-31. Centre interuniversitaire de recherche sur les réseaux d’entreprise, la logistique et les transports, Université de Montréal, Montréal (2010)Google Scholar
  8. Christiansen, M., Fagerholt, K., Nygreen, B., Ronen, D.: Maritime transportation. In: Barnhart, C., Laporte, G. (eds.) Transportation. Handbooks in Operations Research and Management Science, vol. 14, pp. 189–284. North-Holland, Amsterdam (2007)Google Scholar
  9. Cordeau, J.-F., Toth, P., Vigo, D.: A survey of optimization models for train routing and scheduling. Transp. Sci. 32(4), 380–404 (1998)CrossRefMATHGoogle Scholar
  10. Crainic, T.G.: Network design in freight transportation. Eur. J. Oper. Res. 122(2), 272–288 (2000)CrossRefMATHGoogle Scholar
  11. Crainic, T.G., Kim, K.: Intermodal transportation, Chap. 8. In: Barnhart, C., Laporte, G. (eds.) Transportation. Handbooks in Operations Research and Management Science, vol. 14, pp. 467–537. North-Holland, Amsterdam (2007)Google Scholar
  12. Ghamlouche, I., Crainic, T.G., Gendreau, M.: Cycle-based neighbourhoods for fixed-charge capacitated multicommodity network design. Oper. Res. 51(4), 655–667 (2003)MathSciNetCrossRefMATHGoogle Scholar
  13. Ghamlouche, I., Crainic, T.G., Gendreau, M.: Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Ann. Oper. Res. 131, 109–133 (2004)MathSciNetCrossRefMATHGoogle Scholar
  14. Glover, F.: Tabu search—Part I. ORSA J. Comput. 1(3), 190–206 (1989)CrossRefMATHGoogle Scholar
  15. Glover, F.: Tabu search—Part II. ORSA J. Comput. 2(1), 4–32 (1990)CrossRefMATHGoogle Scholar
  16. Glover, F.: A template for scatter search and path relinking. In: Hao, J., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds.) Artificial Evolution. Lecture Notes in Computer Science, vol. 1363, pp. 13–54. Springer, Berlin (1997)Google Scholar
  17. Glover, F., Laguna, M., Martí, R.: Fundamentals of scatter search and path relinking. Control Cybern. 39(3), 653–684 (2000)Google Scholar
  18. Kim, D., Barnhart, C., Ware, K., Reinhardt, G.: Multimodal express package delivery: a service network design application. Transp. Sci. 33(4), 391–407 (1999)CrossRefMATHGoogle Scholar
  19. Magnanti, T.L., Wong, R.: Network design and transportation planning: models and algorithms. Transp. Sci. 18(1), 1–55 (1984)CrossRefGoogle Scholar
  20. Minoux, M.: Network synthesis and optimum network design problems: models, solution methods applications. Networks 19, 313–360 (1989)MathSciNetCrossRefMATHGoogle Scholar
  21. Pedersen, M.B., Crainic, T.G., Madsen, O.B.G.: Models and Tabu search meta-heuristics for service network design with asset-balance requirements. Transp. Sci. 43(2), 158–177 (2009)CrossRefGoogle Scholar
  22. Smilowitz, K.R., Atamtürk, A., Daganzo, C.F.: Deferred item and vehicle routing within integrated networks. Transp. Res. E 39, 305–323 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Duc Minh Vu
    • 1
    • 2
  • Teodor Gabriel Crainic
    • 3
    • 4
  • Michel Toulouse
    • 2
    • 5
  1. 1.Département d’informatique et de recherche opérationnelleUniversité de MontréalMontrealCanada
  2. 2.Centre Interuniversitaire de Recherche sur les Réseaux d’Entreprise, la Logistique et le Transport (CIRRELT)Université de MontréalMontrealCanada
  3. 3.Département management et technologie, École des sciences de la gestionUniversité du Québec à MontréalMontrealCanada
  4. 4.Centre Interuniversitaire de Recherche sur les Réseaux d’Entreprise, la Logistique et le Transport (CIRRELT)Université du Québec à MontréalMontrealCanada
  5. 5.Department of Computer ScienceOklahoma State UniversityStillwaterUSA

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