Journal of Heuristics

, Volume 16, Issue 6, pp 795–834 | Cite as

DVRP: a hard dynamic combinatorial optimisation problem tackled by an evolutionary hyper-heuristic

Article

Abstract

In this paper we propose and evaluate an evolutionary-based hyper-heuristic approach, called EH-DVRP, for solving hard instances of the dynamic vehicle routing problem. A hyper-heuristic is a high-level algorithm, which generates or chooses a set of low-level heuristics in a common framework, to solve the problem at hand. In our collaborative framework, we have included three different types of low-level heuristics: constructive, perturbative, and noise heuristics. Basically, the hyper-heuristic manages and evolves a sophisticated sequence of combinations of these low-level heuristics, which are sequentially applied in order to construct and improve partial solutions, i.e., partial routes. In presenting some design considerations, we have taken into account the allowance of a proper cooperation and communication among low-level heuristics, and as a result, find the most promising sequence to tackle partial states of the (dynamic) problem. Our approach has been evaluated using the Kilby’s benchmarks, which comprise a large number of instances with different topologies and degrees of dynamism, and we have compared it with some well-known methods proposed in the literature. The experimental results have shown that, due to the dynamic nature of the hyper-heuristic, our proposed approach is able to adapt to dynamic scenarios more naturally than low-level heuristics. Furthermore, the hyper-heuristic can obtain high-quality solutions when compared with other (meta) heuristic-based methods. Therefore, the findings of this contribution justify the employment of hyper-heuristic techniques in such changing environments, and we believe that further contributions could be successfully proposed in related dynamic problems.

Keywords

Hyper-heuristics Dynamic vehicle routing problem Evolutionary algorithms Heuristic search 

References

  1. Altinkemer, K., Gavish, B.: Parallel savings based heuristic for the delivery problem. Oper. Res. 39(3), 456–469 (1991) MATHCrossRefMathSciNetGoogle Scholar
  2. Alvarenga, G., de Abreu Silva, R., Mateus, G.: A hybrid approach for the dynamic vehicle routing problem with time windows. In: 5th International Conference on Hybrid Intelligent Systems, HIS ’05, pp. 61–67. IEEE Comput. Soc., Alamitos (2005) CrossRefGoogle Scholar
  3. Babin, G., Deneault, S., Laporte, G.: Improvements to the or-opt heuristic for the symmetric travelling salesman problem. J. Oper. Res. Soc. 58(3), 402–407 (2007) MATHCrossRefGoogle Scholar
  4. Bader-El-Den, M., Poli, R.: Generating SAT local-search heuristics using a GP hyper-heuristic framework. In: 8th International Conference on Artificial Evolution, Evolution Artificielle, EA 2007. Lecture Notes in Computer Science, vol. 4926, pp. 37–49. Springer, Berlin (2008) Google Scholar
  5. Balinsky, M., Quandt, R.: On an integer program for a delivery problem. Oper. Res. 12(2), 300–304 (1964) CrossRefGoogle Scholar
  6. Beasley, J.: Route first—cluster second methods for vehicle routing. Omega 11(4), 403–408 (1983) CrossRefGoogle Scholar
  7. Berger, J., Barkaoui, M.: A new hybrid genetic algorithm for the capacitated vehicle routing problem. J. Oper. Res. Soc. 54(12), 1254–1262 (2003) MATHCrossRefGoogle Scholar
  8. Bertsimas, D., van Ryzin, G.: A stochastic and dynamic vehicle routing problem in the euclidean plane. Oper. Res. 39(4), 601–615 (1991) MATHCrossRefGoogle Scholar
  9. Bertsimas, D., van Ryzin, G.: Stochastic and dynamic vehicle routing in the euclidean plane with multiple capacitated vehicles. Oper. Res. 41(1), 60–76 (1993) MATHCrossRefMathSciNetGoogle Scholar
  10. Bianchi, L.: Notes on dynamic vehicle routing—the state of the art. Technical Report IDSIA-05-01, IDSIA, Lugano, Switzerland (2000) Google Scholar
  11. Bosman, P., La-Poutré, H.: Computationally intelligent online dynamic vehicle routing by explicit load prediction in an evolutionary algorithm. In: 9th International Conference on Parallel Problem Solving from Nature, PPSN IX. Lecture Notes in Computer Science, vol. 4193, pp. 312–321. Springer, Berlin (2006) CrossRefGoogle Scholar
  12. Bramel, J., Simchi-Levi, D.: A location based heuristic for general routing problems. Oper. Res. 43(4), 649–660 (1995) MATHCrossRefMathSciNetGoogle Scholar
  13. Bullnheimer, B., Hartl, R., Strauss, C.: An improved ant system algorithm for the vehicle routing problem. Ann. Oper. Res. 89, 319–328 (1999) MATHCrossRefMathSciNetGoogle Scholar
  14. Burke, E., Kendall, G., Newall, J., Hart, E., Ross, P., Schulenburg, S.: Hyper-heuristics: An emerging direction in modern search technology. In: Handbook of Metaheuristics, vol. 57, pp. 457–474 (2003) Google Scholar
  15. Burke, E., Hyde, M., Kendall, G., Woodward, J.: Automatic heuristic generation with genetic programming: evolving a jack-of-all-trades or a master of one. In: Genetic and Evolutionary Computation Conference, GECCO ’07, pp. 1559–1565. ACM, New York (2007) CrossRefGoogle Scholar
  16. Burke, E., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Qu, R.: A survey and classification of hyper-heuristics. J. Heuristics (2010, to appear). Special Issue on Hyper-heuristics in Search and Optimisation Google Scholar
  17. Burke, E., Landa-Silva, J., Soubeiga, E.: Multi-objective hyper-heuristic approaches for space allocation and timetabling. In: Meta-heuristics: Progress as Real Problem Solvers, vol. 32, pp. 129–158 (2005) Google Scholar
  18. Caramia, M., Italiano, G., Oriolo, G., Pacifici, A., Perugia, A.: Routing a fleet of vehicles for dynamic combined pick-up and deliveries services. In: Proceedings of the Symposium on Operation Research, pp. 3–8. Springer, Berlin (2002) Google Scholar
  19. Christofides, N., Beasley, J.: The period routing problem. Networks 14(2), 237–256 (1984) MATHCrossRefGoogle Scholar
  20. Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. Comb. Optim., pp. 315–338 (1979) Google Scholar
  21. Clarke, G., Wright, J.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12(4), 568–581 (1964) CrossRefGoogle Scholar
  22. Cordeau, J., Laporte, G., Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows. J. Oper. Res. Soc. 52(8), 928–936 (2001) MATHCrossRefGoogle Scholar
  23. Cordeau, J., Gendreau, M., Hertz, A., Laporte, G., Sormany, J.: New heuristics for the vehicle routing problem. In: Logistics Systems: Design and Optimization, pp. 279–297 (2005) Google Scholar
  24. Desrochers, M., Verhoog, T.: A matching based savings algorithm for the vehicle routing problem. Technical Report Les Cahiers du GERARD G-89-04, École des Hautes Études Commerciales de Montréal, Montréal, Canada (1989) Google Scholar
  25. Elwell, R., Polikar, R.: Incremental learning of variable rate concept drift. In: 8th International Workshop on Multiple Classifier Systems, MCS ’09. Lecture Notes in Computer Science, vol. 5519, pp. 142–151. Springer, Berlin (2009) CrossRefGoogle Scholar
  26. Ergun, O., Orlin, J., Steele-Feldman, A.: Creating very large scale neighborhoods out of smaller ones by compounding moves. J. Heuristics 12, 115–140 (2006) MATHCrossRefGoogle Scholar
  27. Ersoy, E., Özcan, E., Uyar, A.: Memetic algorithms and hyperhill-climbers. In: Proceedings of the 3rd Multidisciplinary International Conference on Scheduling: Theory and Applications, MISTA ’07, Paris, France, pp. 159–166 (2007) Google Scholar
  28. Fisher, M.: Optimal solution of vehicle routing problems using minimum k-trees. Oper. Res. 42(4), 626–642 (1994) MATHCrossRefMathSciNetGoogle Scholar
  29. Fisher, M., Jaikumar, R., van Wassenhove, L.: A generalized assignment heuristic for vehicle routing. Networks 11, 109–124 (1981) CrossRefMathSciNetGoogle Scholar
  30. Fonseca, E., Fuchshuber, R., Santos, L., Plastino, A., Martins, S.: Hybrid dm-grasp metaheuristic: Evaluating mining frequency. In: 10th International Conference on Parallel Problem Solving From Nature (PPSN X)—Workshop on Hyper-heuristics, Dortmund, Germany (2008) Google Scholar
  31. Gambardella, L., Taillard, E., Agazzi, G.: Macs-vrptw: A multiple ant colony system for vehicle routing problems with time windows. In: New Ideas in Optimization, pp. 63–76 (1999) Google Scholar
  32. Garrido, P., Riff, M.C.: An evolutionary hyperheuristic to solve strip-packing problems. In: 8th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2007. Lecture Notes in Computer Science, vol. 4881, pp. 406–415. Springer, Berlin (2007) CrossRefGoogle Scholar
  33. Gendreau, M., Guertin, F., Potvin, J.Y., Taillard, E.: Parallel tabu search for real-time vehicle routing and dispatching. Transp. Sci. 33(4), 381–390 (1999) MATHCrossRefGoogle Scholar
  34. Gendreau, M., Guertin, F., Potvin, J., Séguin, R.: Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries. Transp. Res., Part C Emerg. Technol. 14(3), 157–174 (2006) CrossRefGoogle Scholar
  35. Gendreau, M., Potvin, J.Y., Bräysy, O., Hasle, G., Løkketangen, A.: Metaheuristics for the vehicle routing problem and its extensions: A categorized bibliography. In: The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces Series, vol. 43, pp. 143–169. Springer, Berlin (2008) CrossRefGoogle Scholar
  36. Ghiani, G., Guerriero, F., Laporte, G., Musmanno, R.: Real-time vehicle routing: solution concepts, algorithms and parallel computing strategies. Eur. J. Oper. Res. 151(1), 1–11 (2003) MATHCrossRefGoogle Scholar
  37. Gillett, B., Miller, L.: A heuristic algorithm for the vehicle-dispatch problem. Oper. Res. 22(2), 340–349 (1974) MATHCrossRefGoogle Scholar
  38. Goel, A., Gruhn, V.: Solving a dynamic real-life vehicle routing problem. In: Operations Research Proceedings 2005, pp. 367–372. Springer, Berlin (2006) CrossRefGoogle Scholar
  39. Han, L., Kendall, G.: An investigation of a tabu assisted hyper-heuristic genetic algorithm. In: Congress on Evolutionary Computation, CEC 2003, vol. 3, pp. 2230–2237. IEEE Press, New York (2003) Google Scholar
  40. Hanshar, F.T., Ombuki-Berman, B.M.: Dynamic vehicle routing using genetic algorithms. Appl. Intell. 27(1), 89–99 (2007) MATHCrossRefGoogle Scholar
  41. Housroum, H., Hsu, T., Dupas, R., Goncalves, G.: A hybrid ga approach for solving the dynamic vehicle routing problem with time windows. In: 2nd International Conference on Information and Communication Technologies: from Theory to Applications, ICTTA ’06, vol. 1, pp. 787–792. IEEE Press, New York (2006) Google Scholar
  42. Ichoua, S., Gendreau, M., Potvin, J.: Diversion issues in real-time vehicle dispatching. Transp. Sci. 34(4), 426–438 (2000) MATHCrossRefGoogle Scholar
  43. Jakobovic, D., Jelenkovic, L., Budin, L.: Genetic programming heuristics for multiple machine scheduling. In: 10th European Conference on Genetic Programming, EuroGP 2007. Lecture Notes in Computer Science, vol. 4445, pp. 321–330. Springer, Berlin (2007) Google Scholar
  44. Kilby, P., Prosser, P., Shaw, P.: Dynamic vrps: A study of scenarios. Technical Report APES-06-1998, University of Strathclyde, Glasgow, Scotland (1998) Google Scholar
  45. Kindervater, G., Savelsbergh, M.: Vehicle routing: handling edge exchanges. In: Local Search in Combinatorial Optimization, pp. 337–360 (1997) Google Scholar
  46. Krasnogor, N., Gustafson, S.: A study on the use of “self-generation” in memetic algorithms. Nat. Comput. 3(1), 53–76 (2004) MATHCrossRefMathSciNetGoogle Scholar
  47. Krasnogor, N., Smith, J.: Emergence of profitable search strategies based on a simple inheritance mechanism. In: Proceedings of the 2001 Genetic and Evolutionary Computation Conference, GECCO ’01, pp. 432–439. Morgan Kaufmann, San Francisco (2001) Google Scholar
  48. Krumke, S., Rambau, J., Torres, L.: Real-time dispatching of guided and unguided automobile service units with soft time windows. In: 10th Annual European Symposium on Algorithms, ESA ’02. Lecture Notes in Computer Science, vol. 2461, pp. 637–648. Springer, Berlin (2002) Google Scholar
  49. Kumar, R., Joshi, A., Banka, K., Rockett, P.: Evolution of hyperheuristics for the biobjective 0/1 knapsack problem by multiobjective genetic programming. In: Conference on Genetic and Evolutionary Computation, GECCO ’08, pp. 1227–1234. ACM, New York (2008) CrossRefGoogle Scholar
  50. Laporte, G., Semet, F.: Classical heuristics for the capacitated vrp. In: The Vehicle Routing Problem, pp. 109–128 (2001) Google Scholar
  51. Laporte, G., Gendreau, M., Potvin, J., Semet, F.: Classical and modern heuristics for the vehicle routing problem. Int. Trans. Oper. Res. 7, 285–300 (2000) CrossRefMathSciNetGoogle Scholar
  52. Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973) MATHCrossRefMathSciNetGoogle Scholar
  53. Lysgaard, J., Letchford, A., Eglese, R.: A new branch-and-cut algorithm for the capacitated vehicle routing problems. Math. Program. 100(2), 423–445 (2004) MATHCrossRefMathSciNetGoogle Scholar
  54. Marín-Blázquez, J.G., Schulenburg, S.: Multi-step environment learning classifier systems applied to hyper-heuristics. In: Conference on Genetic and Evolutionary Computation, GECCO ’06, pp. 1521–1528. ACM, New York (2006) CrossRefGoogle Scholar
  55. Mester, D., Bräysy, O.: Active guided evolution strategies for large-scale vehicle routing problems with time windows. Comput. Oper. Res. 32(6), 1593–1614 (2005) CrossRefGoogle Scholar
  56. Mole, R., Jameson, S.: A sequential route-building algorithm employing a generalised savings criterion. Oper. Res. Q. 27(2), 503–511 (1976) CrossRefGoogle Scholar
  57. Montemanni, R., Gambardella, L., Rizzoli, A., Donati, A.: A new algorithm for a dynamic vehicle routing problem based on ant colony system. In: Proceedings of 2nd International Workshop on Freight Transportation and Logistics, ODYSSEUS 2003, Palermo, Italy (2003) Google Scholar
  58. Montemanni, R., Gambardella, L., Rizzoli, A., Donati, A.: Ant colony system for a dynamic vehicle routing problem. J. Comb. Optim. 10(4), 327–343 (2005) MATHCrossRefMathSciNetGoogle Scholar
  59. Or, I.: Traveling salesman-type combinatorial optimization problems and their relation to the logistics of regional blood banking. PhD thesis, Northwestern University, Evanston, Illinois, USA (1976) Google Scholar
  60. Özcan, E.: An empirical investigation on memes, self-generation and nurse rostering. In: Proceedings of the 6th International Conference on the Practice and Theory of Automated Timetabling, PATAT ’06, Brno, Czech Republic, pp. 246–263 (2006) Google Scholar
  61. Özcan, E., Alkan, A.: A memetic algorithm for solving a timetabling problem: An incremental strategy. In: Proceedings of the 3rd Multidisciplinary International Conference on Scheduling: Theory and Applications, MISTA ’07, pp. 394–401. Paris, France (2007) Google Scholar
  62. Özcan, E., Kalender, M., Burke, E.: A greedy gradient-simulated annealing hyperheuristic. In: 10th International Conference on Parallel Problem Solving From Nature (PPSN X)—Workshop on Hyper-heuristics, Dortmund, Germany (2008) Google Scholar
  63. Pankratz, G.: Dynamic vehicle routing by means of a genetic algorithm. Int. J. Phys. Distrib. Logist. Manag. 35(5), 362–383 (2005) CrossRefGoogle Scholar
  64. Papastavrou, J.: A stochastic and dynamic routing policy using branching processes with state dependent immigration. Eur. J. Oper. Res. 95(1), 167–177 (1996) MATHCrossRefGoogle Scholar
  65. Pillay, N.: An analysis of representations for hyper-heuristics for the uncapacitated examination timetabling problem in a genetic programming system. In: Annual Research Conference of the South African Institute of Computer Scientists and Information Technologists on IT Research in Developing Countries, SAICSIT ’08, pp. 188–192. ACM, New York (2008) CrossRefGoogle Scholar
  66. Poli, R., Woodward, J., Burke, E.: A histogram-matching approach to the evolution of bin-packing strategies. In: IEEE Congress on Evolutionary Computation, CEC 2007, pp. 3500–3507. IEEE Press, New York (2007) CrossRefGoogle Scholar
  67. Polikar, R., Upda, L., Upda, S.S., Honavar, V.: Learn++: an incremental learning algorithm for supervised neural networks. IEEE Trans. Syst. Man Cybern., Part C 31(4), 497–508 (2001) CrossRefGoogle Scholar
  68. Potvin, J., Xu, Y., Benyahia, I.: Vehicle routing and scheduling with dynamic travel times. Comput. Oper. Res. 33(4), 1129–1137 (2006) MATHCrossRefGoogle Scholar
  69. Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31(12), 1985–2002 (2004) CrossRefMathSciNetGoogle Scholar
  70. Rego, C.: A subpath ejection chain method for the vehicle routing problem. Manag. Sci. 44(10), 1447–1459 (1996) CrossRefGoogle Scholar
  71. Reimann, M., Doerner, K., Hartl, R.: D-ants: savings based ants divide and conquer the vehicle routing problem. Comput. Oper. Res. 31(4), 563–591 (2004) MATHCrossRefGoogle Scholar
  72. Rochat, Y., Taillard, E.: Probabilistic diversification and intensification in local search for vehicle routing. J. Heuristics 1(1), 147–167 (1995) MATHCrossRefGoogle Scholar
  73. Ross, P., Marín-Blázquez, J.G., Schulenburg, S., Hart, E.: Learning a procedure that can solve hard bin-packing problems: A new ga-based approach to hyperheuristics. In: Genetic and Evolutionary Computation Conference, GECCO ’03. Lecture Notes in Computer Science, vol. 2724, pp. 1295–1306. Springer, Berlin (2003) Google Scholar
  74. Ross, P., Marin-Blazquez, J., Hart, E.: Hyper-heuristics applied to class and exam timetabling problems. In: Congress on Evolutionary Computation, CEC 2004, Edinburgh, UK, vol. 2, pp. 1691–1698 (2004) Google Scholar
  75. Savelsbergh, M., Sol, M.: Drive: dynamic routing of independent vehicles. Oper. Res. 46(4), 474–490 (1998) MATHCrossRefGoogle Scholar
  76. Scholz, M., Klinkenberg, R.: Boosting classifiers for drifting concepts. Intell. Data Anal. 11(1), 3–28 (2007) Google Scholar
  77. Song, J., Hu, J., Tian, Y., Xu, Y.: Re-optimization in dynamic vehicle routing problem based on wasp-like agent strategy. In: 8th International IEEE Conference on Intelligent Transportation Systems, ITSC ’05, pp. 231–236. IEEE Press, New York (2005) Google Scholar
  78. Soubeiga, E.: Development and application of hyperheuristics to personnel scheduling. PhD thesis, University of Nottingham, UK (2003) Google Scholar
  79. Swihart, M., Papastavrou, J.: A stochastic and dynamic model for the single-vehicle pick-up and delivery problem. Eur. J. Oper. Res. 114(3), 447–464 (1999) MATHCrossRefGoogle Scholar
  80. Taillard, E.: Parallel iterative search methods for vehicle routing problem. Networks 23, 661–673 (1993) MATHCrossRefGoogle Scholar
  81. Tay, J.C., Ho, N.B.: Evolving dispatching rules for solving multi-objective flexible job-shop problems. Comput. Ind. Eng. 54(3), 453–473 (2008) CrossRefGoogle Scholar
  82. Terashima-Marín, H., Farías-Zárate, C., Ross, P., Valenzuela-Rendón, M.: A ga-based method to produce generalized hyper-heuristics for the 2d-regular cutting stock problem. In: Conference on Genetic and Evolutionary Computation, GECCO ’06, pp. 591–598. ACM, New York (2006) CrossRefGoogle Scholar
  83. Terashima-Marin, H., Farías-Zárate, C., Ross, P., Valenzuela-Rendon, M.: Comparing two models to generate hyper-heuristics for the 2d-regular bin-packing problem. In: Conference on Genetic and Evolutionary Computation, GECCO ’07, pp. 2182–2189. ACM, New York (2007) CrossRefGoogle Scholar
  84. Terashima-Marín, H., Ortiz-Bayliss, J., Ross, P., Valenzuela-Rendón, M.: Hyper-heuristics for the dynamic variable ordering in constraint satisfaction problems. In: Conference on Genetic and Evolutionary Computation, GECCO ’08, pp. 571–578. ACM, New York (2008) CrossRefGoogle Scholar
  85. Thompson, P., Psaraftis, H.: Cyclic transfer algorithms for multivehicle routing and scheduling problems. Oper. Res. 41(5), 935–946 (1993) MATHCrossRefMathSciNetGoogle Scholar
  86. Tighe, A., Smith, F., Lyons, G.: Priority based solver for a real-time dynamic vehicle routing. In: IEEE International Conference on Systems, Man & Cybernetics, SMC ’04, vol. 7, pp. 6237–6242. IEEE Press, New York (2004) Google Scholar
  87. Toth, P., Vigo, D.: The granular tabu search and its application to the vehicle-routing problem. INFORMS J. Comput. 15(4), 333–346 (2003) CrossRefMathSciNetGoogle Scholar
  88. Tuzun, D., Magent, M., Burke, L.: Selection of vehicle routing heuristic using neural networks. Int. Trans. Oper. Res. 4(3), 211–221 (2006) CrossRefGoogle Scholar
  89. van Breedam, A.: 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 constrains. PhD thesis, University of Antwerp, Belgium (1994) Google Scholar
  90. Wark, P., Holt, J.: A repeated matching heuristic for the vehicle routing problem. J. Oper. Res. Soc. 45(10), 1156–1167 (1994) MATHGoogle Scholar
  91. Zhu, K.Q., Ong, K.: A reactive method for real time dynamic vehicle routing problem. In: 12th IEEE International Conference on Tools with Artificial Intelligence, ICTAI ’00, pp. 176–180. IEEE Comput. Soc., Los Alamitos (2000) Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversidad Técnica Federico Santa MaríaValparaísoChile

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