Skip to main content

Advertisement

Springer Nature Link
Log in

A general variable neighborhood search for solving the multi-objective open vehicle routing problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

The multi-objective open vehicle routing problem (MO-OVRP) is a variant of the classic vehicle routing problem in which routes are not required to return to the depot after completing their service and where more than one objective is optimized. This work is intended to solve a more realistic and general version of the problem by considering three different objective functions. MO-OVRP seeks solutions that minimize the total number of routes, the total travel cost, and the longest route. For this purpose, we present a general variable neighborhood search algorithm to approximate the efficient set. The performance of the proposal is supported by an extensive computational experimentation which includes the comparison with the well-known multi-objective genetic algorithm NSGA-II.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

Notes

  1. \(a\preceq b\) means that the solution a weakly dominates the solution b, i.e., a is not worse than b in any of the objectives.

References

  • Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolut. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  • Duarte, A., Pantrigo, J., Pardo, E., Sánchez Oro, J.: Parallel variable neighbourhood search strategies for the cutwidth minimization problem. IMA J. Manag. Math. 27(1), 55 (2016)

    Article  MathSciNet  Google Scholar 

  • Eiben, A.E., Smith, J.E.: Introduction to evolutionary computing (2003)

  • Fu, Z., Eglese, R., Li, L.Y.O.: A new tabu search heuristic for the open vehicle routing problem. J. Oper. Res. Soc. 56(3), 267–274 (2005)

    Article  Google Scholar 

  • Gillett, B., Miller, L.: A heuristic algorithm for the vehicle-dispatch problem. Oper. Res. 22(2), 340–349 (1974)

    Article  Google Scholar 

  • Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449–467 (2001)

    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 

  • López Sánchez, A.D., Hernández Díaz, A.G., Vigo, D., Caballero, R., Molina, J.: A multi-start algorithm for a balanced real-world open vehicle routing problem. Eur. J. Oper. Res. 238(1), 104–113 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Norouzi, N., Tavakkoli Moghaddam, R., Ghazanfari, M., Alinaghian, M., Salamatbakhsh, A.: A new multi-objective competitive open vehicle routing problem solved by particle swarm optimization. Netw. Spat. Econ. 12(4), 609–633 (2012)

    Article  MathSciNet  Google Scholar 

  • Sánchez Oro, J., Pantrigo, J.J., Duarte, A.: Combining intensification and diversification strategies in VNS. An application to the Vertex Separation problem. Comput. Oper. Res. 52(Part B), 209–219 (2014). Recent advances in Variable neighborhood search

    Article  MathSciNet  Google Scholar 

  • Sánchez Oro, J., Sevaux, M., Rossi, A., Martí, R., Duarte, A.: Solving dynamic memory allocation problems in embedded systems with parallel variable neighborhood search strategies. Electron. Notes Discret. Math. 47, 85–92 (2015)

    Article  MathSciNet  Google Scholar 

  • Schrage, L.: Formulation and structure of more complex/realistic routing and scheduling problems. Networks 11(2), 229–232 (1981)

    Article  Google Scholar 

  • Tarantilis, C.D., Ioannou, G., Kiranoudis, C.T., Prastacos, G.P.: Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm. J. Oper. Res. Soc. 56(5), 588–596 (2005)

    Article  Google Scholar 

  • Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2002)

  • We, Z., Tingxin, S., Fei, H., Xi, L.: Multiobjective Vehicle Routing Problem with Route Balance Based on Genetic Algorithm. Discrete Dynamics in Nature and Society 2013(Article ID 325686), 9 (2013)

  • Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. PhD Thesis, Swiss Federal Institute of Technology Zurich (1999)

  • Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms—A comparative case study, pp. 292–301. Springer, Berlin, Heidelberg (1998)

    Google Scholar 

  • Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. Trans. Evol. Comp 7(2), 117–132 (2003)

    Article  Google Scholar 

Download references

Acknowledgements

J. M. Colmenar and J. Sánchez-Oro are supported by the Spanish Ministry of “Economía y Competitividad”, Grant Refs. TIN2015-65460-C2-2-P and TIN2014-54806-R. A.D. López-Sánchez acknowledge support from the Spanish Ministry of Science and Innovation through Projects ECO2013-47129-C4-1-R and ECO2016-76567-C4-1-R.

Author information

Authors and Affiliations

  1. Rey Juan Carlos University, C/Tulipán, s/n, 28933, Móstoles, Madrid, Spain

    Jesús Sánchez-Oro & J. Manuel Colmenar

  2. Pablo de Olavide University, Ctra. Utrera Km 1, 41013, Sevilla, Spain

    Ana D. López-Sánchez

Authors
  1. Jesús Sánchez-Oro
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Ana D. López-Sánchez
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. J. Manuel Colmenar
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jesús Sánchez-Oro.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sánchez-Oro, J., López-Sánchez, A.D. & Colmenar, J.M. A general variable neighborhood search for solving the multi-objective open vehicle routing problem. J Heuristics 26, 423–452 (2020). https://doi.org/10.1007/s10732-017-9363-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-017-9363-8

Keywords