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Particle Evolutionary Swarm Multi-Objective Optimization for Vehicle Routing Problem with Time Windows

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Swarm Intelligence for Multi-objective Problems in Data Mining

Abstract

The Vehicle Routing Problem with Time Windows (VRPTW), is an extension to the standard vehicle routing problem. VRPTW includes an additional constraint that restricts every customer to be served within a given time window. An approach for the VRPTW with the next three objectives is presented: 1)total distance (or time), 2)total waiting time, 3)number of vehicles. A data mining strategy, namely space partitioning, is adopted in this work. Optimal routes are extracted as features hidden in variable size regions where depots and customers are located. This chapter proposes the sector model for partitioning the space into regions. A new hybrid Particle Swarm Optimization algorithm (PSO), and combinatorial operators ad-hoc with space partitioning are described. A set of well-known benchmark functions in VRPTW are used to compare the effectiveness of the proposed method. The results show the importance of examining characteristics of a set of non-dominated solutions, that fairly consider the three dimensions, when a user should select only one solution according to problem conditions.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Salvelsberg, M.: Local search in routing problems with time windows. Annals of Operations Research 4, 285–305 (1985)

    Article  MathSciNet  Google Scholar 

  3. Solomon, M.: Algorithms for the vehicle routing problem with time windows. Transportation Science 29(2), 156–166 (1995)

    Article  Google Scholar 

  4. Cordeau, J., Desaulniers, G., Desrosiers, J., Solomon, M., Soumis, F.: The VRP with time windows. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. SIAM, Monographs on Discrete Mathematics and Applications, Philadelphia USA, pp. 157–193 (2002)

    Google Scholar 

  5. Kolen, A., Rinnooy, K., Trienekens, H.: Vehicle routing with time windows. Operations Research 35, 256–273 (1987)

    Article  Google Scholar 

  6. Bard, J., Kontoravdis, G., Yu, G.: A branch-and-cut procedure for the vehicle routing problem with time windows. Transportation Science 36, 250–269 (2002)

    Article  MATH  Google Scholar 

  7. Laporte, G.: The vehicle routing problem: an overview of exact and approximate algorithms. European Journal of Operational Research 59, 345–358 (1992)

    Article  MATH  Google Scholar 

  8. Laporte, G., Semet, F.: Classical heuristics for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. SIAM, Monographs on Discrete Mathematics and Applications, Philadelphia USA, pp. 109–128 (2002)

    Google Scholar 

  9. Solomon, M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research 35, 254–265 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Russell, R.: An effective heuristic for the M-tour traveling salesman problem with some side conditions. Operations Research 25, 517–524 (1977)

    Article  MATH  Google Scholar 

  11. Baker, E., Schaffer, J.: Computational experience with branch exchange heuristics for vehicle routing problems with time window constraints. American Journal of Mathematical and Management Sciences 6, 261–300 (1986)

    MATH  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. Gendreau, M., Laporte, G., Potvin, J.: Metaheuristics for the VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. SIAM, Monographs on Discrete Mathematics and Applications, Philadelphia USA, pp. 129–154 (2002)

    Google Scholar 

  14. Kontoravdis, G., Bard, J.: A GRASP for the vehicle routing problem with time windows. ORSA Journal on Computing 7, 10–23 (1995)

    MATH  Google Scholar 

  15. Potvin, J., Kervahut, T., Garcia, B., Rousseau, J.: The vehicle routing problem with time windows - Part I: tabu search. INFORMS Journal on Computing 8, 158–164 (1996)

    Article  MATH  Google Scholar 

  16. Cordeau, J., Laporte, G., Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society 52, 928–936 (2001)

    Article  MATH  Google Scholar 

  17. Bent, R., Van Hentenryck, P.: A two-stage hybrid local search for the vehicle routing problem with time windows. Technical Report CS-01-06, Computer Science Department, Brown University (2001)

    Google Scholar 

  18. Gambardella, L., Taillard, E., Agazzi, G.: MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 63–76. McGraw-Hill, New York (1999)

    Google Scholar 

  19. Blanton, J., Wainwright, R.: Multiple vehicle routing with time and capacity constraints using genetic algorithms. In: Forrest, S. (ed.) Proceedings of the 5th International Conference on Genetic Algorithms, pp. 452–459. Morgan Kaufmann, San Francisco (1993)

    Google Scholar 

  20. Thangiah, S.: Vehicle routing with time windows using genetic algorithms. In: Chambers, L. (ed.) Application Handbook of Genetic Algorithms: New Frontiers, vol. II, pp. 253–277. CRC Press, Boca Raton (1995)

    Google Scholar 

  21. Osman, I.: Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problems. Annals of Operations Research 41, 421–452 (1993)

    Article  MATH  Google Scholar 

  22. Bräysy, O.: A new algorithm for the vehicle routing problem with time windows based on the hybridization of a genetic algorithm and route construction heuristics. In: Proceedings of the University of Vaasa, Research papers, Vaasa, Finland (1999)

    Google Scholar 

  23. Homberger, J., Gehring, H.: Two evolutionary metaheuristics for the vehicle routing problem with time windows. INFOR 37, 297–318 (1999)

    Google Scholar 

  24. Or, I.: Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking. Ph.D. Thesis, Northwestern University, Evanston, USA (1976)

    Google Scholar 

  25. Potvin, J., Rousseau, J.: An exchange heuristic for routeing problems with time windows. Journal of the Operational Research Society 46, 1433–1446 (1995)

    Article  MATH  Google Scholar 

  26. Ghosh, A., Dehuri, S.: Evolutionary algorithms for multi-criterion optimization: a survey. International Journal of Computing & Information Sciences 2(1), 38–57 (2004)

    Google Scholar 

  27. Pareto, V.: Cours d’Economie Politique, vol. I - II (1896)

    Google Scholar 

  28. Coello, C.: A short tutorial on evolutionary multiobjective optimization. In: Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization, pp. 21–40 (1993)

    Google Scholar 

  29. Tan, K., Chew, Y., Lee, L.: A hybrid multiobjective evolutionary algorithm for solving vehicle routing problem with time windows. Computational Optimization and Applications 34(1), 115–151 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  30. Ombuki, B., Ross, B., Hanshar, F.: Multi-objective genetic algorithms for vehicle routing problem with time windows. Applied Intelligence 24(1), 17–30 (2006)

    Article  Google Scholar 

  31. Chitty, D.M., Hernandez, M.L.: A hybrid ant colony optimisation technique for dynamic vehicle routing. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 48–59. Springer, Heidelberg (2004)

    Google Scholar 

  32. Murata, T., Itai, R.: Multi-objective vehicle routing problems using two-fold EMO algorithms to enhance solution similarity on non-dominated solutions. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 885–896. Springer, Heidelberg (2005)

    Google Scholar 

  33. Sa’adah, S., Ross, P., Paechter, B.: Improving vehicle routing using a customer waiting time colony. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 188–198. Springer, Heidelberg (2004)

    Google Scholar 

  34. Moura, A.: A multi-objective genetic algorithm for the vehicle routing with time windows and loading problem. In: Bortfeldt, A., Homberger, J., Kopfer, H., Pankratz, G., Strangmeier, R. (eds.) Intelligent Decision Support, Current Challenges and Approaches, pp. 187–201. Gabler-Verlag, Wiesbaden (2008)

    Google Scholar 

  35. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference On Neural Networks, pp. 1942–1948 (1995)

    Google Scholar 

  36. Eberhart, R., Dobbins, R., Simpson, P.: Computational Intelligence PC Tools. Academic Press Professional (1996)

    Google Scholar 

  37. Van den Bergh, F.: An Analysis of Particle Swarm Optimizers. University of Pretoria, South Africa (2002)

    Google Scholar 

  38. Muñoz, A., Hernández, A., Villa, E.: Robust PSO-based constrained optimization by perturbing the particle’s memory. In: Chan, F., Tiwari, M. (eds.) Swarm Intelligence, Focus on Ant and Particle Swarm Optimization, pp. 57–76. I-Tech Education and Publishing, Vienna (2007)

    Google Scholar 

  39. Kennedy, J., Eberhart, R.: The Particle Swarm: Social Adaptation in Information-Processing Systems. McGraw-Hill, London (1999)

    Google Scholar 

  40. Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Appplied Mechanics and Engineering 186(2-4), 311–338 (2000)

    Article  MATH  Google Scholar 

  41. Ester, M., Kriegel, H., Sander, J.: Algorithms and applications for spatial data mining. In: Miller, H., Han, J. (eds.) Geographic Data Mining and Knowledge Discovery, pp. 160–187. Taylor & Francis, London (2001)

    Google Scholar 

  42. Price, K., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Berlin (2005)

    MATH  Google Scholar 

  43. Dehuri, S., Ghosh, A., Mall, R.: Genetic algorithms for multi-criterion classification and clustering in data mining. International Journal of Computing & Information Sciences 4(3), 143–154 (2006)

    Google Scholar 

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Muñoz-Zavala, A., Hernández-Aguirre, A., Villa-Diharce, E. (2009). Particle Evolutionary Swarm Multi-Objective Optimization for Vehicle Routing Problem with Time Windows. In: Coello, C.A.C., Dehuri, S., Ghosh, S. (eds) Swarm Intelligence for Multi-objective Problems in Data Mining. Studies in Computational Intelligence, vol 242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03625-5_10

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  • DOI: https://doi.org/10.1007/978-3-642-03625-5_10

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