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The selective traveling salesman problem with draft limits

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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.

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References

  • 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)

    Article  MathSciNet  Google Scholar 

  • Balas, E.: The prize collecting traveling salesman problem. Networks 19(6), 621–636 (1989)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Feillet, D., Dejax, P., Gendreau, M.: Traveling salesman problems with profits. Transp. Sci. 39(2), 188–205 (2005)

    Article  Google Scholar 

  • Golden, B.L., Levy, L., Vohra, R.: The orienteering problem. Naval Res. Logist. 34(3), 307–318 (1987)

    Article  Google Scholar 

  • Hansen, P., Mladenović, N., Pérez, J.A.M.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175(1), 367–407 (2010)

    Article  MathSciNet  Google Scholar 

  • Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423–454 (2017)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  MathSciNet  Google Scholar 

  • 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 

  • Kataoka, S., Morito, S.: An algorithm for single constraint maximum collection problem. J. Oper. Res. Soc. Jpn. 31(4), 515–530 (1988)

    Article  MathSciNet  Google Scholar 

  • Laporte, G., Martello, S.: The selective travelling salesman problem. Discrete Appl. Math. 26(2), 193–207 (1990)

    Article  MathSciNet  Google Scholar 

  • Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  MathSciNet  Google Scholar 

  • Mladenović, N., Todosijević, R., Urošević, D.: Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf. Sci. 326, 160–171 (2016)

    Article  Google Scholar 

  • Rakke, J.G., Christiansen, M., Fagerholt, K., Laporte, G.: The traveling salesman problem with draft limits. Comput. Oper. Res. 39(9), 2161–2167 (2012)

    Article  MathSciNet  Google Scholar 

  • Reinelt, G.: TSPLIB: a traveling salesman problem library. ORSA J. Comput. 3, 376–384 (1991)

    Article  Google Scholar 

  • 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

  • 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

  • Vansteenwegen, P., Souffriau, W., Van Oudheusden, D.: The orienteering problem: a survey. Eur. J. Oper. Res. 209(1), 1–10 (2011)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Département Réseaux & Télécoms, IUT de Béthune, Université d’Artois, 62000, Béthune, France

    Shahin Gelareh

  2. Département d’informatique et de recherche opérationnelle et CIRRELT, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, QC, H3C 3J7, Canada

    Bernard Gendron

  3. LAMIH UMR CNRS 8201, Université Polytechnique Hauts-de-France, 59313, Valenciennes Cedex 9, France

    Saïd Hanafi & Raca Todosijević

  4. IT Innovation Center, University of Southampton, Southampton, UK

    Rahimeh Neamatian Monemi

Authors
  1. Shahin Gelareh
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  2. Bernard Gendron
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  3. Saïd Hanafi
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  4. Rahimeh Neamatian Monemi
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  5. Raca Todosijević
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Corresponding author

Correspondence to Bernard Gendron.

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Gelareh, S., Gendron, B., Hanafi, S. et al. The selective traveling salesman problem with draft limits. J Heuristics 26, 339–352 (2020). https://doi.org/10.1007/s10732-019-09406-z

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  • DOI: https://doi.org/10.1007/s10732-019-09406-z

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