An Efficient Route Minimization Algorithm for the Vehicle Routing Problem with Time Windows Based on Agent Negotiation

  • Petr Kalina
  • Jiří Vokřínek
  • Vladimír Mařík
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8291)

Abstract

We present an efficient route minimization algorithm for the vehicle routing problem with time windows. The algorithm uses a generic agent decomposition of the problem featuring a clear separation between the local planning performed by the individual vehicles and the abstract global coordination achieved by negotiation — differentiating the presented algorithm from the traditional centralized algorithms. Novel negotiation semantics is introduced on the global coordination planning level allowing customers to be temporarily ejected from the emerging solution being constructed. This allows the algorithm to efficiently backtrack in situations when the currently processed customer cannot be feasibly allocated to the emerging solution. Over the relevant widely-used benchmarks the algorithm equals the best known solutions achieved by the centralized algorithms in 90.7% of the cases with an overall relative error of 0.3%, outperforming the previous comparable agent-based algorithms.

Keywords

multi-agent systems logistics optimization VRPTW 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bachem, A., Hochstättler, W., Malich, M.: The simulated trading heuristic for solving vehicle routing problems. Technical report, Discrete Applied Mathenatics (1996)Google Scholar
  2. 2.
    Brafman, R.I., Domshlak, C.: From one to many: Planning for loosely coupled multi-agent systems. In: Proceedings of the International Conference on Automated Planning and Scheduling (ICAPS), pp. 28–35 (2008)Google Scholar
  3. 3.
    Bräysy, O., Gendreau, M.: Vehicle routing problem with time windows, part I route construction and local search algorithms. Transportation Science 39(1), 104–118 (2005)CrossRefGoogle Scholar
  4. 4.
    Bräysy, O., Gendreau, M.: Vehicle routing problem with time windows, part II metaheuristics. Transportation Science 39(1), 119–139 (2005)CrossRefGoogle Scholar
  5. 5.
    Campbell, A.M., Savelsbergh, M.: Efficient insertion heuristics for vehicle routing and scheduling problems. Transportation Science 38, 369–378 (2004)CrossRefGoogle Scholar
  6. 6.
    Dan, Z., Cai, L., Zheng, L.: Improved multi-agent system for the vehicle routing problem with time windows. Tsinghua Science Technology 14(3), 407–412 (2009)CrossRefGoogle Scholar
  7. 7.
    Davidsson, P., Henesey, L., Ramstedt, L., Törnquist, J., Wernstedt, F.: An analysis of agent-based approaches to transport logistics. Transportation Research Part C: Emerging Technologies 13(4), 255–271 (2005)CrossRefGoogle Scholar
  8. 8.
    Davis, R., Smith, R.G.: Negotiation as a metaphor for distributed problem solving. Artificial Intelligence 20, 63–109 (1983)CrossRefGoogle Scholar
  9. 9.
    Desaulniers, G., Lessard, F., Hadjar, A.: Tabu search, partial elementarity, and generalized k-path inequalities for the vehicle routing problem with time windows. Transportation Science 42(3), 387–404 (2008)CrossRefGoogle Scholar
  10. 10.
    Fischer, K., Müller, J.P., Pischel, M.: Cooperative transportation scheduling: an application domain for dai. Journal of Applied Artificial Intelligence 10, 1–33 (1995)CrossRefGoogle Scholar
  11. 11.
    Gehring, H., Homberger, J.: A two-phase hybrid metaheuristic for the vehicle routing problem with time windows. European Journal of Operational Research 162(1), 220–238 (2005)CrossRefMATHGoogle Scholar
  12. 12.
    Kalina, P., Vokřínek, J.: Parallel solver for vehicle routing and pickup and delivery problems with time windows based on agent negotiation. In: 2012 IEEE Conference on Systems, Man, and Cybernetics (SMC), pp. 1558–1563 (2012)Google Scholar
  13. 13.
    Kalina, P., Vokřínek, J., Mařík, V.: The art of negotiation: Developing efficient agent-based algorithms for solving vehicle routing problem with time windows. In: Mařík, V., Lastra, J.L.M., Skobelev, P. (eds.) HoloMAS 2013. LNCS, vol. 8062, pp. 187–198. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Kohout, R., Erol, K.: In-time agent-based vehicle routing with a stochastic improvement heuristic. In: 11th Conference on Innovative Applications of Artificial Intelligence. AAAI/MIT Press (1999)Google Scholar
  15. 15.
    Komenda, A., Novák, P., Pěchouček, M.: Domain-independent multi-agent plan repair. Journal of Network and Computer Applications (in print, 2013)Google Scholar
  16. 16.
    Komenda, A., Vokrinek, J., Cap, M., Pechoucek, M.: Developing multiagent algorithms for tactical missions using simulation. IEEE Intelligent Systems 28(1), 42–49 (2013)CrossRefGoogle Scholar
  17. 17.
    Komenda, A., Vokřínek, J., Pěchouček, M.: Plan representation and execution in multi-actor scenarios by means of social commitments. Web Intelligence and Agent Systems 9(2), 123–133 (2011)Google Scholar
  18. 18.
    Leong, H.W., Liu, M.: A multi-agent algorithm for vehicle routing problem with time window. In: Proceedings of the 2006 ACM Symposium on Applied Computing, SAC 2006, pp. 106–111. ACM, New York (2006)Google Scholar
  19. 19.
    Lim, A., Zhang, X.: A two-stage heuristic with ejection pools and generalized ejection chains for the vehicle routing problem with time windows. INFORMS Journal on Computing 19(3), 443–457 (2007)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Liu, F.-H., Shen, S.-Y.: The fleet size and mix vehicle routing problem with time windows. Operational Research Society 50, 721–732 (1999)MATHGoogle Scholar
  21. 21.
    Lu, Q., Dessouky, M.M.: A new insertion-based construction heuristic for solving the pickup and delivery problem with hard time windows. European Journal of Operational Research 175, 672–687 (2005)CrossRefGoogle Scholar
  22. 22.
    Moscato, P.: On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms. Technical Report C3P Report 826, California Institute of Technology (1989)Google Scholar
  23. 23.
    Nagata, Y.: Edge assembly crossover for the capacitated vehicle routing problem. In: Cotta, C., van Hemert, J. (eds.) EvoCOP 2007. LNCS, vol. 4446, pp. 142–153. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Nagata, Y., Bräysy, O., Dullaert, W.: A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows. Comput. Oper. Res. 37(4), 724–737 (2010)CrossRefMATHGoogle Scholar
  25. 25.
    Prescott-Gagnon, E., Desaulniers, G., Rousseau, L.-M.: A branch-and-price-based large neighborhood search algorithm for the vehicle routing problem with time windows. Netw. 54(4), 190–204 (2009)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Ren, Y., Dessouky, M., Ordóñez, F.: The multi-shift vehicle routing problem with overtime. Comput. Oper. Res. 37(11), 1987–1998 (2010)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research 35, 254–265 (1987)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Vokřínek, J., Komenda, A., Pěchouček, M.: Abstract architecture for task-oriented multi-agent problem solving. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 41(1), 31–40 (2011)CrossRefGoogle Scholar
  29. 29.
    Wang, F., Tao, Y., Shi, N.: A survey on vehicle routing problem with loading constraints. In: Proceedings of the 2009 International Joint Conference on Computational Sciences and Optimization, CSO 2009, vol. 2, pp. 602–606. IEEE Computer Society, Washington, DC (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Petr Kalina
    • 1
  • Jiří Vokřínek
    • 2
  • Vladimír Mařík
    • 3
  1. 1.Intelligent Systems GroupCzech Technical University in PragueCzech Republic
  2. 2.Agent Technology CenterCzech Technical University in PragueCzech Republic
  3. 3.Department of CyberneticsCzech Technical University in PragueCzech Republic

Personalised recommendations