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The selective traveling salesman problem with draft limits

  • Shahin Gelareh
  • Bernard GendronEmail author
  • Saïd Hanafi
  • Rahimeh Neamatian Monemi
  • Raca Todosijević
Article
  • 6 Downloads

Abstract

This paper introduces the selective traveling salesman problem with draft limits, an extension of the traveling salesman problem with draft limits, wherein the goal is to design a maximum profit tour respecting draft limit constraints at the visited nodes. We propose a mixed integer linear programming (MILP) formulation for this problem. This MILP model is used to solve—to optimality—small size instances and to assess the quality of solutions obtained using a general variable neighborhood search heuristic that explores several neighborhood structures. Our extensive computational experiments confirm the efficiency of the method and the quality of the reported solutions.

Keywords

Selective traveling salesman problem with draft limits Variable neighborhood search Location neighborhood structures Traveling salesman neighborhood structures Mixed integer linear programming 

Notes

References

  1. Awerbuch, B., Azar, Y., Blum, A., Vempala, S.: New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen. SIAM J. Comput. 28(1), 254–262 (1998)MathSciNetzbMATHGoogle Scholar
  2. Balas, E.: The prize collecting traveling salesman problem. Networks 19(6), 621–636 (1989)MathSciNetzbMATHGoogle Scholar
  3. Battarra, M., Pessoa, A.A., Subramanian, A., Uchoa, E.: Exact algorithms for the traveling salesman problem with draft limits. Eur. J. Oper. Res. 235(1), 115–128 (2014)MathSciNetzbMATHGoogle Scholar
  4. Dell’Amico, M., Maffioli, F., Värbrand, P.: On prize-collecting tours and the asymmetric travelling salesman problem. Int. Trans. Oper. Res. 2(3), 297–308 (1995)zbMATHGoogle Scholar
  5. Feillet, D., Dejax, P., Gendreau, M.: Traveling salesman problems with profits. Transp. Sci. 39(2), 188–205 (2005)Google Scholar
  6. Golden, B.L., Levy, L., Vohra, R.: The orienteering problem. Naval Res. Logist. 34(3), 307–318 (1987)zbMATHGoogle Scholar
  7. Hansen, P., Mladenović, N., Pérez, J.A.M.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175(1), 367–407 (2010)MathSciNetzbMATHGoogle Scholar
  8. Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423–454 (2017)MathSciNetzbMATHGoogle Scholar
  9. Ilić, A., Urošević, D., Brimberg, J., Mladenović, N.: A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem. Eur. J. Oper. Res. 206(2), 289–300 (2010)MathSciNetzbMATHGoogle Scholar
  10. Johnson, D.S., McGeoch, L.: The traveling salesman problem: a case study in local optimization. In: Aarts, E., Lenstra, J. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. Wiley, New York (1997)Google Scholar
  11. Kataoka, S., Morito, S.: An algorithm for single constraint maximum collection problem. J. Oper. Res. Soc. Jpn. 31(4), 515–530 (1988)MathSciNetzbMATHGoogle Scholar
  12. Laporte, G., Martello, S.: The selective travelling salesman problem. Discrete Appl. Math. 26(2), 193–207 (1990)MathSciNetzbMATHGoogle Scholar
  13. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)MathSciNetzbMATHGoogle Scholar
  14. Mladenović, N., Todosijević, R., Urošević, D.: An efficient general variable neighborhood search for large travelling salesman problem with time windows. Yugosl. J. Oper. Res. 23(1), 19–30 (2013)MathSciNetzbMATHGoogle Scholar
  15. Mladenović, N., Todosijević, R., Urošević, D.: Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf. Sci. 326, 160–171 (2016)Google Scholar
  16. Rakke, J.G., Christiansen, M., Fagerholt, K., Laporte, G.: The traveling salesman problem with draft limits. Comput. Oper. Res. 39(9), 2161–2167 (2012)MathSciNetzbMATHGoogle Scholar
  17. Reinelt, G.: TSPLIB: a traveling salesman problem library. ORSA J. Comput. 3, 376–384 (1991)zbMATHGoogle Scholar
  18. Todosijević, R., Mjirda, A., Mladenović, M., Hanafi, S., Gendron, B.: A general variable neighborhood search variants for the travelling salesman problem with draft limits. Optim. Lett. (2014). https://doi.org/10.1007/s11590-014-0788-9
  19. Todosijević, R., Urošević, D., Mladenović, N., Hanafi, S.: A general variable neighborhood search for solving the uncapacitated \(r\)-allocation \(p\)-hub median problem. Optim. Lett. (2015). https://doi.org/10.1007/s11590-015-0867-6
  20. Vansteenwegen, P., Souffriau, W., Van Oudheusden, D.: The orienteering problem: a survey. Eur. J. Oper. Res. 209(1), 1–10 (2011)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Shahin Gelareh
    • 1
  • Bernard Gendron
    • 2
    Email author
  • Saïd Hanafi
    • 3
  • Rahimeh Neamatian Monemi
    • 4
  • Raca Todosijević
    • 3
  1. 1.Département Réseaux & Télécoms, IUT de BéthuneUniversité d’ArtoisBéthuneFrance
  2. 2.Département d’informatique et de recherche opérationnelle et CIRRELTUniversité de MontréalMontréalCanada
  3. 3.LAMIH UMR CNRS 8201Université Polytechnique Hauts-de-FranceValenciennes Cedex 9France
  4. 4.IT Innovation CenterUniversity of SouthamptonSouthamptonUK

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