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Ant colony optimization for real-world vehicle routing problems

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Abstract

Ant colony optimization (ACO) is a metaheuristic for combinatorial optimization problems. In this paper we report on its successful application to the vehicle routing problem (VRP). First, we introduce the VRP and some of its variants, such as the VRP with time windows, the time dependent VRP, the VRP with pickup and delivery, and the dynamic VRP. These variants have been formulated in order to bring the VRP closer to the kind of situations encountered in the real-world.

Then, we introduce the basic principles of ant colony optimization, and we briefly present its application to the solution of the VRP and of its variants.

Last, we discuss the applications of ACO to a number of real-world problems: a VRP with time windows for a major supermarket chain in Switzerland; a VRP with pickup and delivery for a leading distribution company in Italy; a time dependent VRP for freight distribution in the city of Padua, Italy, where the travel times depend on the time of the day; and an on-line VRP in the city of Lugano, Switzerland, where customers’ orders arrive during the delivery process.

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References

  • Aksoy, Y., & Derbez, A. (2003). Software survey: supply chain management. OR/MS Today, 30(3), 1–13.

    Google Scholar 

  • Albritton, M. D., & McMullen, P. R. (2007). Optimal product design using a colony of virtual ants. European Journal of Operational Research, 176(1), 498–520.

    Article  MATH  Google Scholar 

  • Bianchi, L., Birattari, M., Chiarandini, M., Manfrin, M., Mastrolilli, M., Paquete, L., Rossi-Doria, O., & Schiavinotto, T. (2004). Metaheuristics for the vehicle routing problem with stochastic demands. X. Yao, et al. (Eds.), Lecture notes in computer science : Vol. 3242. Parallel problem solving from nature—PPSN VIII (pp. 450–460). Berlin: Springer.

    Google Scholar 

  • Blum, C. (2005). Beam-ACO—Hybridizing ant colony optimization with beam search: an application to open shop scheduling. Computers and Operations Research, 32(6), 1565–1591.

    Article  Google Scholar 

  • Blum, C., & Dorigo, M. (2004). The hyper-cube framework for ant colony optimization. IEEE Transactions on Systems, Man and Cybernetics—Part B: Cybernetics, 34(2), 1161–1172.

    Article  Google Scholar 

  • Blum, C., & Roli, A. (2003). Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Computing Surveys, 35(3), 268–308.

    Article  Google Scholar 

  • Bräysy, O. (2003). A reactive variable neighborhood search for the vehicle routing problem with time windows. INFORMS Journal on Computing, 15(4), 347–368.

    Article  MathSciNet  Google Scholar 

  • Bullnheimer, B., Hartl, R. F., & Strauss, C. (1999). A new rank-based version of the ant system: a computational study. Central European Journal of Operations Research, 7(1), 25–38.

    MATH  MathSciNet  Google Scholar 

  • Desaulniers, G., Desrosiers, J., Erdmann, A., Solomon, M. M., & Soumis, F. (2000). VRP with pickup and delivery. In P. Toth & D. Vigo (Eds.), The vehicle routing problem (pp. 225–242). Philadelphia: SIAM.

    Google Scholar 

  • Donati, A. V., Montemanni, R., Casagrande, N., Rizzoli, A. E., & Gambardella, L. M. (2007, in press). Time dependent vehicle routing problem with a multi ant colony system. European Journal of Operational Research.

  • Dorigo, M. (1992). Optimization, learning and natural algorithms. PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy.

  • Dorigo, M., & Gambardella, L. M. (1997). Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1(1), 53–66.

    Article  Google Scholar 

  • Dorigo, M., & Stützle, T. (2004). Ant colony optimization. Cambridge: MIT Press.

    MATH  Google Scholar 

  • Dorigo, M., Maniezzo, V., & Colorni, A. (1996). Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man and Cybernetics—Part B: Cybernetics, 26(1), 29–41.

    Article  Google Scholar 

  • Dorigo, M., Di Caro, G., & Gambardella, L. M. (1999). Ant algorithms for discrete optimization. Artificial Life, 5, 137–172.

    Article  Google Scholar 

  • Gambardella, L. M., Rizzoli, A. E., & Zaffalon, M. (1998). Simulation and planning of an intermodal container terminal. Simulation, 71(2), 107–116.

    Article  Google Scholar 

  • Gambardella, L. M., Taillard, É., & Agazzi, G. (1999). MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows. In D. Corne, M. Dorigo & F. Glover (Eds.), New ideas in optimization (pp. 63–76). London: McGraw–Hill.

    Google Scholar 

  • Gendreau, M., & Potvin, J.-Y. (1998). Dynamic vehicle routing and dispatching. In T. G. Crainic & G. Laporte (Eds.), Fleet management and logistic (pp. 115–226). Berlin: Springer.

    Google Scholar 

  • Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management Science, 40(10), 1276–1290.

    MATH  Google Scholar 

  • Gendreau, M., Laporte, G., & Séguin, R. (1996). Stochastic vehicle routing. European Journal of Operational Research, 88(1), 3–12.

    Article  MATH  Google Scholar 

  • Glover, F., & Laguna, M. (1997). Tabu search. Boston: Kluwer Academic.

    MATH  Google Scholar 

  • Guntsch, M., & Middendorf, M. (2001). Pheromone modification strategies for ant algorithms applied to dynamic TSP. In E. J. W. Boers et al. (Eds.), Lecture notes in computer science : Vol. 2037. Applications of evolutionary computing: EvoWorkshops 2001: EvoCOP, EvoFlight, EvoIASP, EvoLearn, and EvoSTIM (pp. 213–222), Como, Italy, 18–20 April 2001. Berlin: Springer.

    Google Scholar 

  • Hartl, R. F., Hasle, G., & Janssens, G. K. (2006). Special issue on rich vehicle routing problems: editorial. Central European Journal of Operations Research, 14(2), 103–104.

    Article  MATH  Google Scholar 

  • Ichoua, S., Gendreau, M., & Potvin, J.-Y. (2003). Vehicle dispatching with time-dependent travel times. European Journal of Operational Research, 144(2), 379–396.

    Article  MATH  Google Scholar 

  • Kallehauge, B., Larsen, J., & Madsen, O. B. G. (2006). Lagrangian duality applied to the vehicle routing problem with time windows. Computers and Operations Research, 33(5), 1464–1487.

    Article  MATH  MathSciNet  Google Scholar 

  • Kilby, P., Prosser, P., & Shaw, P. (1999). Guided local search for the vehicle routing problem. In S. Voss, S. Martello, I. H. Osman & C. Roucairol (Eds.), Meta-heuristics: advances and trends in local search paradigms for optimization (pp. 473–486). Boston: Kluwer Academic.

    Google Scholar 

  • Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.

    Article  MathSciNet  Google Scholar 

  • Kytöjoki, J., Nuortio, T., Bräysy, O., & Gendreau, M. (2007). An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Computers and Operations Research, 34(9), 2743–2757.

    Article  MATH  Google Scholar 

  • Labbé, M., Laporte, G., & Mercure, H. (1991). Capacitated vehicle routing on trees. Operations Research, 39(4), 616–622.

    MATH  Google Scholar 

  • Laporte, G., & Louveaux, F. V. (1998). Solving stochastic routing problems with the integer L-shaped method. In T. G. Crainic & G. Laporte (Eds.), Fleet management and logistics (pp. 159–167). Boston: Kluwer Academic.

    Google Scholar 

  • Li, Y., & Chan Hilton, A. B. (2007). Optimal groundwater monitoring design using an ant colony optimization paradigm. Environmental Modelling and Software, 22(1), 110–116.

    Article  Google Scholar 

  • Li, F., Golden, B., & Wasil, E. (2005). Very large-scale vehicle routing: new test problems, algorithms, and results. Computers and Operations Research, 32(5), 1165–1179.

    MATH  Google Scholar 

  • Lourenço, H. R., Martin, O., & Stützle, T. (2003). Iterated local search. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 321–353). Boston: Kluwer Academic.

    Google Scholar 

  • Maniezzo, V., & Carbonaro, A. (2000). ANTS heuristic for the frequency assignment problem. Future Generation Computer Systems, 16(8), 927–935.

    Article  Google Scholar 

  • Mester, D., & Bräysy, O. (2005). Active guided evolution strategies for the large scale vehicle routing problem with time windows. Computers & Operations Research, 32(6), 1593–1614.

    Article  Google Scholar 

  • Montemanni, R., Gambardella, L. M., Rizzoli, A. E., & Donati, A. V. (2005). Ant colony system for a dynamic vehicle routing problem. Journal of Combinatorial Optimization, 10, 327–343.

    Article  MATH  MathSciNet  Google Scholar 

  • Osman, I. H. (1993). Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of Operations Research, 41, 421–451.

    Article  MATH  Google Scholar 

  • Potvin, J.-Y., Xu, Y., & Benyahia, I. (2006). Vehicle routing and scheduling with dynamic travel times. Computers and Operations Research, 33(4), 1129–1137.

    Article  MATH  Google Scholar 

  • Psaraftis, H. (1995). Dynamic vehicle routing: status and prospects. Annals of Operations Research, 61, 143–164.

    Article  MATH  Google Scholar 

  • Psaraftis, H. (1988). Dynamic vehicle routing problems. In B. L. Golden & A. A. Assad (Eds.), Vehicle routing: methods and studies (pp. 223–248). Amsterdam: North-Holland.

    Google Scholar 

  • Reimann, M., Doerner, K., & Hartl, R. F. (2002). A savings based ant system for the vehicle routing problem. In W. B. Langdon et al. (Eds.), Proceedings of the genetic and evolutionary computation conference (GECCO-2002) (pp. 1317–1325). San Francisco: Kaufmann.

    Google Scholar 

  • Reimann, M., Doerner, K., & Hartl, R. F. (2003). Analyzing a unified ant system for the VRP and some of its variants. In G. Raidl et al. (Eds.), Lecture notes in computer science : Vol. 2611. Applications of evolutionary computing: EvoWorkshops 2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and EvoSTIM (pp. 300–310), Essex, UK, 14–16 April 2003. Berlin: Springer.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Resende, M. G. C., & Ribeiro, C. C. (2003). Greedy randomized adaptive search procedures. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 219–249). Boston: Kluwer Academic.

    Chapter  Google Scholar 

  • Savelsbergh, M. W. P. (1985). Local search in routing problems with time windows. Annals of Operations Research, 4, 285–305.

    Article  MathSciNet  Google Scholar 

  • Stützle, T., & Hoos, H. H. (2000). MAX-MIN ant-system. Future Generation Computer Systems, 16(8), 889–914.

    Article  Google Scholar 

  • Taillard, È. D., Badeau, E. P., Gendreau, M., Guertin, F., & Potvin, J.-Y. (1997). A tabu search heuristic for the vehicle routing problem with soft time windows. Transportation Science, 31(2), 170–186.

    Article  MATH  Google Scholar 

  • Toth, P., & Vigo, D. (2001a). Branch-and-bound algorithms for the capacitated VRP. In P. Toth & D. Vigo (Eds.), The vehicle routing problem (pp. 29–51). Philadelphia: SIAM.

    Google Scholar 

  • Toth, P., & Vigo, D. (2001b). An overview of vehicle routing problems. In P. Toth & D. Vigo (Eds.), The vehicle routing problem (pp. 1–26). Philadelphia: SIAM.

    Google Scholar 

  • Toth, P., & Vigo, D. (2003). The granular tabu search and its application to the vehicle routing problem. INFORMS Journal on Computing, 15(4), 333–346.

    Article  MathSciNet  Google Scholar 

  • Van Breedam, A. (1996). An analysis of the effect of local improvement operators in genetic algorithms and simulated annealing for the vehicle routing problem. RUCA Working Paper 96/14, University of Antwerp, Belgium, 1996.

  • Zecchin, A. C., Maier, H. R., Simpson, A. R., Leonard, M., & Nixon, J. B. (2007). Ant colony optimization applied to water distribution system design: comparative study of five algorithms. Journal of Water Resources Planning and Management, 133(1), 87–92.

    Article  Google Scholar 

  • Zeimpekis, V., Tarantilis, C. D., Giaglis, G. M., & Minis, I. (2007). Dynamic fleet management—concepts, systems, algorithms & case studies. Berlin: Springer.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Galleria 2, 6928, Manno, Switzerland

    A. E. Rizzoli, R. Montemanni & L. M. Gambardella

  2. AntOptima, via Fusoni 4, 6900, Lugano, Switzerland

    E. Lucibello

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  1. A. E. Rizzoli
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  2. R. Montemanni
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  3. E. Lucibello
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  4. L. M. Gambardella
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Correspondence to A. E. Rizzoli.

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Rizzoli, A.E., Montemanni, R., Lucibello, E. et al. Ant colony optimization for real-world vehicle routing problems. Swarm Intell 1, 135–151 (2007). https://doi.org/10.1007/s11721-007-0005-x

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