Skip to main content

A Population-Based Local Search for Solving a Bi-objective Vehicle Routing Problem

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4446))

Abstract

In this paper we present a population-based local search for solving a bi-objective vehicle routing problem. The objectives of the problem are minimization of the tour length and balancing the routes. The algorithm repeatedly generates a pool of good initial solutions by using a randomized savings algorithm followed by local search. The local search uses three neighborhood structures and evaluates the fitness of candidate solutions using dominance relation. Several test instances are used to assess the performance of the new approach. Computational results show that the population-based local search outperforms the best known algorithm for this problem.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dantzig, G., Ramsey, J.: The truck dispatching problem. Management Science 6, 80–91 (1959)

    MATH  MathSciNet  Google Scholar 

  2. Baldacci, R., Mingozzi, A., Hadjiconstantinou, E.: An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Operations Research 52(5), 723–738 (2004)

    Article  MathSciNet  Google Scholar 

  3. Fukasawa, R., Longo, H., Lysgaard, J., Poggi de Aragão, M., Reis, M., Uchoa, E., Werneck, R.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical Programming 106(3), 491–511 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lenstra, J., Kan, A.: Complexity of vehicle routing and scheduling problem. Networks 11, 221–227 (1981)

    Google Scholar 

  5. Clarke, G., Wright, J.: Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12, 568–581 (1964)

    Article  Google Scholar 

  6. Cordeau, J., Gendreau, M., Laporte, G., Potvin, J., Semet, F.: A guide to vehicle routing heuristics. Journal of the Operational Research Society 53, 512–522 (2002)

    Article  MATH  Google Scholar 

  7. Ehrgott, M., Gandibleux, X.: A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22, 425–460 (2000)

    MATH  MathSciNet  Google Scholar 

  8. Rochat, Y., Taillard, E.: Probabilistic diversification and intensification in local search for vehicle routing. Journal of Heuristics 1, 147–167 (1995)

    Article  MATH  Google Scholar 

  9. Doerner, K., Gronalt, M., Hartl, R.F., Reimann, M., Strauss, C., Stummer, M.: SavingsAnts for the vehicle routing problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 11–20. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  10. Jozefowiez, N., Semet, F., Talbi, E.G.: Enhancements of NSGA-II and its application to the vehicle routing problem with route balancing. In: Talbi, E.-G., Liardet, P., Collet, P., Lutton, E., Schoenauer, M. (eds.) EA 2005. LNCS, vol. 3871, pp. 131–142. Springer, Berlin Heidelberg New York (2006)

    Chapter  Google Scholar 

  11. Jozefowiez, N., Semet, F., Talbi, E.G.: Parallel and hybrid models for multi-objective optimization: Application to the vehicle routing problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN VII. LNCS, vol. 2439, pp. 271–280. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  12. Haubelt, C., Gamenik, J., Teich, J.: Initial population construction for convergence improvement of moeas. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 191–205. Springer, Heidelberg (2005)

    Google Scholar 

  13. Gandibleux, X., Morita, H., Katoh, N.: The supported solutions used as a genetic information in a population heuristic. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 429–442. Springer, Berlin Heidelberg New York (2001)

    Google Scholar 

  14. Morita, H., Gandibleux, X., Katoh, N.: Experimental feedback on biobjective permutation scheduling problems solved with a population heuristic. Foundations of Computing and Decision Sciences 26(1), 23–50 (2001)

    Google Scholar 

  15. Arroyo, J., Armentano, V.: Genetic local search for multi-objective flowshop scheduling problems. European Journal of Operational Research 167, 717–738 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Basseur, M., Seynhaeve, F., Talbi, E.: Path relinking in pareto multi-objective genetic algorithms. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 120–134. Springer, Berlin Heidelberg New York (2005)

    Google Scholar 

  17. Reimann, M., Doerner, K., Hartl, R.: D-ants: Savings based ants divide and conquer the vehicle routing problem. Computers & Operations Research 31(4), 563–591 (2004)

    Article  MATH  Google Scholar 

  18. Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.) Cominbatorial Optimization, John Wiley and Sons, New York, NY (1979)

    Google Scholar 

  19. Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical Report TIK-Report No. 214, Computer Engineering and Networks Laboratory, ETH Zurich, Gloriastrasse 35, ETH-Zentrum, 8092 Zurich, Switzerland (2006)

    Google Scholar 

  20. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Trans. Evolutionary Computation 3(4), 257–271 (1999)

    Article  Google Scholar 

  21. Hansen, M., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Technical Report Technical Report IMM-REP-1998-7, Technical University of Denmark (1998)

    Google Scholar 

  22. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimisation: NSGA-II. In: PPSN, pp. 849–858 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Carlos Cotta Jano van Hemert

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Pasia, J.M., Doerner, K.F., Hartl, R.F., Reimann, M. (2007). A Population-Based Local Search for Solving a Bi-objective Vehicle Routing Problem. In: Cotta, C., van Hemert, J. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2007. Lecture Notes in Computer Science, vol 4446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71615-0_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71615-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71614-3

  • Online ISBN: 978-3-540-71615-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics