Solving Real-World Vehicle Routing Problems with Evolutionary Algorithms

  • Thomas Weise
  • Alexander Podlich
  • Christian Gorldt

Abstract

In this chapter, we present the freight transportation planning component of the in.west project. This system uses an Evolutionary Algorithm with intelligent search operations in order to achieve a high utilization of resources and a minimization of the distance travelled by freight carriers in real-world scenarios. We test our planner rigorously with real-world data and obtain substantial improvements when compared to the original freight plans. Additionally, different settings for the Evolutionary Algorithm are studied with further experiments and their utility is verified with statistical tests.

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References

  1. 1.
    Alba, E., Dorronsoro, B.: Solving the vehicle routing problem by using cellular genetic algorithms. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 11–20. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Alba, E., Dorronsoro, B.: Computing nine new best-so-far solutions for capacitated vrp with a cellular genetic algorithm. Information Processing Letters 98, 225–230 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Amberg, A., Domschke, W., Voß, S.: Multiple center capacitated arc routing problems: A tabu search algorithm using capacitated trees. European Journal of Operational Research (EJOR) 124(2), 360–376 (2000)MATHCrossRefGoogle Scholar
  4. 4.
    Augerat, P., Belenguer, J.M., Benavent, E., Corberán, A., Naddef, D., Rinaldi, G.: Computational results with a branch and cut code for the capacitated vehicle routing problem. Research Report 949-M, Universite Joseph Fourier, Grenoble, France (1995)Google Scholar
  5. 5.
    Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)MATHGoogle Scholar
  6. 6.
    Badeau, P., Gendreau, M., Guertin, F., Potvin, J.-Y., Taillard, É.D.: A parallel tabu search heuristic for the vehicle routing problem with time windows. Transportation Research Part C: Emerging Technologies 5(2), 109–122 (1997)CrossRefGoogle Scholar
  7. 7.
    van Betteray, K.: Gesetzliche und handelsspezifische anforderungen an die rückverfolgung. In: Vorträge des 7. VDEB-Infotags 2004, VDEB Verband IT-Mittelstand e.V, EU Verordnung 178/2002 (2004)Google Scholar
  8. 8.
    Box, G.E.P., Hunter, J.S., Hunter, W.G.: Statistics for Experimenters: Design, Innovation, and Discovery. John Wiley & Sons, Chichester (2005)MATHGoogle Scholar
  9. 9.
    Bräysy, O.: Genetic algorithms for the vehicle routing problem with time windows. Arpakannus – Newsletter of the Finnish Artificial Intelligence Society (FAIS) 1, 33–38 (2001); Special issue on Bioinformatics and Genetic AlgorithmsGoogle Scholar
  10. 10.
    Bräysy, O., Gendreau, M.: Tabu search heuristics for the vehicle routing problem with time windows. TOP: An Official Journal of the Spanish Society of Statistics and Operations Research 10(2), 211–237 (2002)MATHGoogle Scholar
  11. 11.
    Breedam, A.V.: An analysis of the behavior of heuristics for the vehicle routing problem for a selection of problems with vehicle-related, customer-related, and time-related constraints. Ph.D. thesis, University of Antwerp, RUCA, Belgium (1994)Google Scholar
  12. 12.
    Bullnheimer, B., Hartl, R.F., Strauss, C.: An improved ant system algorithm for the vehicle routing problem. Annals of Operations Research 89, 319–328 (1999)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Bundesministerium für Verkehr, Bau- und Stadtentwicklung: Verkehr in Zahlen 2006/2007. Deutscher Verkehrs-Verlag GmbH, Hamburg (2006)Google Scholar
  14. 14.
    Bundesministerium für Wirtschaft und Technologie: Mobilität und Verkehrstechnologien das 3. Verkehrsforschungsprogramm der Bundesregierung. BMWi, Öffentlichkeitsarbeit, Berlin, Germany (2008)Google Scholar
  15. 15.
    CEN/TC 119: Swap bodies – non-stackable swap bodies of class C – dimensions and general requirements. EN 284, CEN-CEN ELEC, Brussels, Belgium (2006)Google Scholar
  16. 16.
    Ceollo Coello, C.A.: A short tutorial on evolutionary multiobjective optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 21–40. Springer, Heidelberg (2001)Google Scholar
  17. 17.
    Ceollo Coello, C.A., Lamont, G.B., van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. In: Genetic and Evolutionary Computation, 2nd edn. (1st edn: 2002 ), vol. 5. Kluwer Academic Publishers, Springer (2007) doi:10.1007/978-0-387-36797-2Google Scholar
  18. 18.
    Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.) Combinatorial Optimization, ch. 11, pp. 315–338. John Wiley & Sons, Chichester (1979)Google Scholar
  19. 19.
    Confessore, G., Galiano, G., Stecca, G.: An evolutionary algorithm for vehicle routing problem with real life constraints. In: Mitsuishi, M., Ueda, K., Kimura, F. (eds.) Manufacturing Systems and Technologies for the New Frontier – The 41st CIRP Conference on Manufacturing Systems, pp. 225–228. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Czech, Z.J., Czarnas, P.: Parallel simulated annealing for the vehicle routing problem with time windows. In: 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing (PDP 2002), pp. 376–383. IEEE Computer Society, Los Alamitos (2002)CrossRefGoogle Scholar
  21. 21.
    Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Management Science 6(1), 80–91 (1959)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Deb, K., Goldberg, D.E.: An investigation of niche and species formation in genetic function optimization. In: Schaffer, J.D. (ed.) Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 42–50. Morgan Kaufmann Publishers Inc., San Francisco (1989)Google Scholar
  23. 23.
    Díaz, B.D.: Known best results (2007), http://neo.lcc.uma.es/radi-aeb/WebVRP/results/BestResults.htm (accessed 2007-12-28)
  24. 24.
    Doerner, K., Gronalt, M., Hartl, R.F., Reimann, M., Strauss, C., Stummer, M.: Savings ants 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, Heidelberg (2002)CrossRefGoogle Scholar
  25. 25.
    Domschke, W.: Logistik, Rundreisen und Touren, fourth edn. Oldenbourgs Lehr- und Handbücher der Wirtschafts- u. Sozialwissenschaften. Oldenbourg Verlag (1997)Google Scholar
  26. 26.
    Glover, F.: Future paths for integer programming and links to artificial intelligence. Computers & Operations Research 13(5), 533–549 (1986)MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Longman Publishing Co., Inc., Boston (1989)MATHGoogle Scholar
  28. 28.
    Golden, B., Wasil, E., Kelly, J., Chao, I.-M.: The impact of metaheuristics on solving the vehicle routing problem: Algorithms, problem sets, and computational results. In: Crainic, T.G., Laporte, G. (eds.) Teodor Gabriel Crainic and Gilbert Laporte, ch. 2. Center for Research on Transportation 25th Anniversary Series, 1971–1996, pp. 33–56. Kluwer/Springer, Boston/USA (1998)Google Scholar
  29. 29.
    Gorges-Schleuter, M.: Explicit parallelism of genetic algorithms through population structures. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 150–159. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  30. 30.
    Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. The University of Michigan Press, Ann Arbor (1975); Reprinted by MIT Press, NetLibrary, Inc. (April 1992)Google Scholar
  31. 31.
    Jih, W., Hsu, J.Y.: Dynamic vehicle routing using hybrid genetic algorithms. In: IEEE International Conference on Robotics and Automation, pp. 453–458 (1999) doi: 10.1109/ROBOT.1999.770019Google Scholar
  32. 32.
    Luke, S., Panait, L., Balan, G., Paus, S., Skolicki, Z., Bassett, J., Hubley, R., Chircop, A.: Ecj: A java-based evolutionary computation research system (2006); Version 18, http://cs.gmu.edu/~eclab/projects/ecj/ (accessed 2007-07-10)
  33. 33.
    Machado, P., Tavares, J., Pereira, F.B., Costa, E.J.F.: Vehicle routing problem: Doing it the evolutionary way. In: Langdon, W.B., Cantú-Paz, E., Mathias, K.E., Roy, R., Davis, D., Poli, R., Balakrishnan, K., Honavar, V., Rudolph, G., Wegener, J., Bull, L., Potter, M.A., Schultz, A.C., Miller, J.F., Burke, E.K., Jonoska, N. (eds.) GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, p. 690. Morgan Kaufmann Publishers Inc., San Francisco (2002)Google Scholar
  34. 34.
    Martin, W.N., Lienig, J., Cohoon, J.P.: Island (migration) models: Evolutionary algorithms based on punctuated equilibria. In: Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.) Handbook of Evolutionary Computation, Computational Intelligence Library, ch. 6.3. Oxford University Press, Oxford (1997)Google Scholar
  35. 35.
    Ombuki-Berman, B.M., Hanshar, F.: Using genetic algorithms for multi-depot vehicle routing. In: Bio-inspired Algorithms for the Vehicle Routing Problem, pp. 77–99. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  36. 36.
    Pankratz, G., Krypczyk, V.: Benchmark data sets for dynamic vehicle routing problems (2007), http://www.fernuni-hagen.de/WINF/inhfrm/benchmark_data.htm (accessed 2008-10-27)
  37. 37.
    Pereira, F.B., Tavares, J. (eds.): Bio-inspired Algorithms for the Vehicle Routing Problem. SCI, vol. 161. Springer, Heidelberg (2009)Google Scholar
  38. 38.
    Pétrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation, CEC 1996, pp. 798–803. IEEE Computer Society Press, Piscataway (1996)CrossRefGoogle Scholar
  39. 39.
    Podlich, A.: Intelligente planung und optimierung des güterverkehrs auf straße und schiene mit evolutionären algorithmen. Master’s thesis, University of Kassel, FB-16, Distributed Systems Group, Wilhelmshöher Allee 73, 34121 Kassel, Germany (2009)Google Scholar
  40. 40.
    Podlich, A., Weise, T., Menze, M., Gorldt, C.: Intelligente wechselbrückensteuerung für die logistik von morgen. In: Wagner, M., Hogrefe, D., Geihs, K., David, K. (eds.) First Workshop on Global Sensor Networks, GSN 2009 (2009); Electronic Communications of the EASST (ECASST), vol. 17, part Global Sensor Networks (GSN 2009), The European Association of Software Science and Technology (2009) ISSN 1863-2122Google Scholar
  41. 41.
    Potvin, J.-Y.: A review of bio-inspired algorithms for vehicle routing. In: Bio-inspired Algorithms for the Vehicle Routing Problem, pp. 1–34. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  42. 42.
    Radcliffe, N.J.: The algebra of genetic algorithms. Annals of Mathematics and Artificial Intelligence 10(4), 339–384 (1994)MATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Ralphs, T.: Vehicle routing data sets (2003), http://www.coin-or.org/SYMPHONY/branchandcut/VRP/data/ (accessed 2009-04-08)
  44. 44.
    Ralphs, T.K., Kopman, L., Pulleyblank, W.R., Trotter, L.E.: On the capacitated vehicle routing problem. Mathematical Programming 94(2–3), 343–359 (2003)MATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    von Randow, M.: Güterverkehr und logistik als tragende säule der wirtschaft zukunftssicher gestalten. In: Baumgarten, H. (ed.) Das Beste Der Logistik: Innovationen, Strategien, Umsetzungen. Bundesvereinigung Logistik (BVL), pp. 49–53. Springer, Heidelberg (2008)Google Scholar
  46. 46.
    Sareni, B., Krähenbühl, L.: Fitness sharing and niching methods revisited. IEEE Transactions on Evolutionary Computation 2(3), 97–106 (1998)CrossRefGoogle Scholar
  47. 47.
    Siegel, S., Castellan Jr., N.J.: Nonparametric Statistics for The Behavioral Sciences. Humanities/Social Sciences/Languages. McGraw-Hill, New York (1988)Google Scholar
  48. 48.
    Sigurjónsson, K.: Taboo search based metaheuristic for solving multiple depot vrppd with intermediary depots. Master’s thesis, Informatics and Mathematical Modelling, IMM, Technical University of Denmark, DTU (2008), http://orbit.dtu.dk/getResource?recordId=224453&objectId=1&versionId=1 (accessed 2009-04-09)
  49. 49.
    Steierwald, G., Künne, H.D., Vogt, W.: Stadtverkehrsplanung: Grundlagen, Methoden, Ziele, 2., neu bearbeitete und erweiterte auflage edn. Springer, Berlin (2005)Google Scholar
  50. 50.
    Taillard, É.D.: Parallel iterative search methods for vehicle routing problems. Networks 23(8), 661–673 (1993)MATHCrossRefGoogle Scholar
  51. 51.
    Thangiah, S.R.: Vehicle routing with time windows using genetic algorithms. In: Practical Handbook of Genetic Algorithms: New Frontiers, pp. 253–277. CRC, Boca Raton (1995)Google Scholar
  52. 52.
    Weise, T.: Global Optimization Algorithms – Theory and Application, 2nd edn (2009), http://www.it-weise.de/ (accessed 2009-07-14)
  53. 53.
    Weise, T., Geihs, K.: DGPF – An Adaptable Framework for Distributed Multi-Objective Search Algorithms Applied to the Genetic Programming of Sensor Networks. In: Filipič, B., Šilc, J. (eds.) Proceedings of the Second International Conference on Bioinspired Optimization Methods and their Applications (BIOMA 2006), pp. 157–166. Jožef Stefan Institute (2006)Google Scholar
  54. 54.
    Weise, T., Podlich, A., Reinhard, K., Gorldt, C., Geihs, K.: Evolutionary freight transportation planning. In: Giacobini, M., et al. (eds.) EvoWorkshops 2009. LNCS, vol. 5484, pp. 768–777. Springer, Heidelberg (2009)Google Scholar
  55. 55.
    Weise, T., Zapf, M., Chiong, R., Nebro, A.J.: Why is optimization difficult? In: Chiong, R. (ed.) Nature-Inspired Algorithms for Optimisation, ch. 1. SCI, vol. 193, pp. 1–50. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  56. 56.
    Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics Bulletin 1(6), 80–83 (1945)CrossRefGoogle Scholar
  57. 57.
    Yates, F.: The Design and Analysis of Factorial Experiments. Imperial Bureau of Soil Science, Commonwealth Agricultural Bureaux (1937); Tech. Comm. No. 35Google Scholar
  58. 58.
    Zhu, K.Q.: A diversity-controlling adaptive genetic algorithm for the vehicle routing problem with time windows. In: 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 176–183. IEEE Computer Society Press, Los Alamitos (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Thomas Weise
    • 1
  • Alexander Podlich
    • 2
  • Christian Gorldt
    • 3
  1. 1.Distributed Systems GroupUniversity of KasselKasselGermany
  2. 2.Micromata GmbH KasselKasselGermany
  3. 3.BIBABremer Institut für Produktion und Logistik GmbHBremenGermany

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