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An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem

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Abstract

This paper deals with the Heterogeneous Fleet Vehicle Routing Problem (HFVRP). The HFVRP is \(\mathcal{NP}\)-hard since it is a generalization of the classical Vehicle Routing Problem (VRP), in which clients are served by a heterogeneous fleet of vehicles with distinct capacities and costs. The objective is to design a set of routes in such a way that the sum of the costs is minimized. The proposed algorithm is based on the Iterated Local Search (ILS) metaheuristic which uses a Variable Neighborhood Descent procedure, with a random neighborhood ordering (RVND), in the local search phase. To the best of our knowledge, this is the first ILS approach for the HFVRP. The developed heuristic was tested on well-known benchmark instances involving 20, 50, 75 and 100 customers. These test-problems also include dependent and/or fixed costs according to the vehicle type. The results obtained are quite competitive when compared to other algorithms found in the literature.

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References

  • Baldacci, R., Mingozzi, A.: A unified exact method for solving different classes of vehicle routing problems. Math. Program. 120, 347–380 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Baldacci, R., Battarra, M., Vigo, D.: Routing a heterogeneous fleet of vehicles. In: The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 11–35. Springer, Berlin (2008)

    Google Scholar 

  • Bianchi, L., Birattari, M., Chiarandini, M., Manfrin, M., Mastrolilli, M., Paquete, L., Rossi-Doria, O., Schiavinotto, T.: Hybrid metaheuristics for the vehicle routing problem with stochastic demands. J. Math. Model. Algorithms 5(1), 91–110 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Brandão, J.: A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. Eur. J. Oper. Res. 195, 716–728 (2009)

    Article  MATH  Google Scholar 

  • Chen, P., Huang, H.K., Dong, X.Y.: Iterated variable neighborhood descent algorithm for the capacitated vehicle routing problem. Expert Syst. Appl. 37(2), 1620–1627 (2010)

    Article  Google Scholar 

  • Cheung, R., Hang, D.: Multi-attribute label matching algorithms for vehicle routing problems with time windows and backhauls. IIE Trans. 35, 191–205 (2003)

    Article  Google Scholar 

  • Choi, E., Tcha, D.W.: A column generation approach to the heterogeneous fleet vehicle routing problem. Comput. Oper. Res. 34, 2080–2095 (2007)

    Article  MATH  Google Scholar 

  • Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12, 568–581 (1964)

    Article  Google Scholar 

  • Cordeau, J.F., Gendreau, M., Laporte, G., Potvin, J.Y., Semet, F.: A guide to vehicle routing problem. J. Oper. Res. Soc. 53, 512–522 (2002)

    Article  MATH  Google Scholar 

  • Dongarra, J.J.: Performance of various computers using standard linear equations software. Tech. Rep. CS-89-85. Computer Science Department, University of Tennessee (2010)

  • Gendreau, M., Laporte, G., Musaraganyi, C., Taillard, E.D.: A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Comput. Oper. Res. 26, 1153–1173 (1999)

    Article  MATH  Google Scholar 

  • Glover, F.: Future paths in integer programming and links to Artificial Intelligence. Comput. Oper. Res. 13(5), 533–549 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Glover, F., Laguna, M., Marti, R.: Scatter search and path relinking: advances and appl. In: Handbook of Metaheuristics, pp. 1–36. Kluwer Academic, Dordrecht (2003)

    Google Scholar 

  • Golden, B.L., Assad, A.A., Levy, L., Gheysens, F.G.: The feet size and mix vehicle routing problem. Comput. Oper. Res. 11, 49–66 (1984)

    Article  MATH  Google Scholar 

  • Hoff, A., Andersson, H., Christiansen, M., Hasle, G., Løkketangen, A.: Industrial aspects and literature survey: Fleet composition and routing. Comput. Oper. Res. 37, 1515–1536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  • Ibaraki, T., Imahori, S., Nonobe, K., Sobue, K., Uno, T., Yagiura, M.: An iterated local search algorithm for the vehicle routing problem with convex time penalty functions. Discrete Appl. Math. 156(11), 2050–2069 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Imran, A., Salhi, S., Wassan, N.A.: A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem. Eur. J. Oper. Res. 197, 509–518 (2009)

    Article  MATH  Google Scholar 

  • Lee, Y., Kim, J., Kang, K., Kim, K.: A heuristic for vehicle fleet mix problem using tabu search and set partitioning. J. Oper. Res. Soc.. 59, 833–841 (2008)

    Article  MATH  Google Scholar 

  • Li, F., Golden, B., Wasil, E.: A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem. Comput. Oper. Res. 34, 2734–2742 (2007)

    Article  MATH  Google Scholar 

  • Lima, C.M.R.R., Goldbarg, M.C., Goldbarg, E.F.G.: A memetic algorithm for the heterogeneous fleet vehicle routing problem. Electron. Notes Discrete Math. 18, 171–176 (2004)

    Article  MathSciNet  Google Scholar 

  • Liu, S., Huang, W., Ma, H.: An effective genetic algorithm for the fleet size and mix vehicle routing problems. Transp. Res., Part B, Methodol. 45, 434–445 (2009)

    Article  Google Scholar 

  • Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Handbook of Metaheuristics, pp. 321–353. Kluwer Academic, Dordrecht (2003)

    Google Scholar 

  • Mladenovic, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Moscato, P., Cotta, C.: A gentle introduction to memetic algorithm. In: Handbook of Metaheuristics, pp. 105–144. Kluwer Academic, Dordrecht (2003)

    Google Scholar 

  • Ochi, L., Vianna, D., Drummond, L.M.A., Victor, A.: An evolutionary hybrid metaheuristic for solving the vehicle routing problem with heterogeneous fleet. Lect. Notes Comput. Sci. 1391, 187–195 (1998a)

    Article  Google Scholar 

  • Ochi, L., Vianna, D., Drummond, L.M.A., Victor, A.: A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet. Future Gener. Comput. Syst. 14, 285–292 (1998b)

    Article  Google Scholar 

  • Or, I.: Traveling salesman-type combinational problems and their relation to the logistics of blood banking. PhD thesis, Northwestern University, USA (1976)

  • Osman, I.H.: Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann. Oper. Res. 41(1–4), 421–451 (1993)

    Article  MATH  Google Scholar 

  • Pessoa, A., Uchoa, E., de Aragão, M.P.: Robust branch-and-cut-and-price algorithms for vehicle routing problems. In: The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 297–325. Springer, Berlin (2008)

    Chapter  Google Scholar 

  • Pessoa, A., Uchoa, E., de Aragão, M.P.: A robust branch-cut-and-price algorithm for the heterogeneous fleet vehicle routing problem. Network 54(4), 167–177 (2009)

    Article  MATH  Google Scholar 

  • Prins, C.: Efficient heuristics for the heterogeneous fleet multitrip vrp with application to a large-scale real case. J. Math. Model. Algorithms 1, 135–150 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Prins, C.: A GRASP × evolutionary local search hybrid for the Vehicle Routing Problem. In: Bio-inspired Algorithms for the Vehicle Routing Problem, Studies in Computational Intelligence, vol. 161, pp. 35–53. Springer, Berlin (2009a)

    Chapter  Google Scholar 

  • Prins, C.: Two memetic algorithms for heterogeneous fleet vehicle routing problems. Eng. Appl. Artif. Intell. 22(6), 916–928 (2009b)

    Article  Google Scholar 

  • Renaud, J., Boctor, F.: A sweep-based algorithm for the fleet size and mix vehicle routing problem. Eur. J. Oper. Res. 140, 618–628 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Subramanian, A., Drummond, L., Bentes, C., Ochi, L., Farias, R.: A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res. 37(11), 1899–1911 (2010)

    Article  MATH  Google Scholar 

  • Taillard, E.D.: A heuristic column generation method for heterogeneous fleet. RAIRO. Rech. Opér. 33, 1–14 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Taillard, E., Badeau, P., Gendreau, M., Guertin, F., Jy, P.: A tabu search heuristic for the vehicle routing problem with soft time windows. Transp. Sci. 31, 170–186 (1997)

    Article  MATH  Google Scholar 

  • Tarantilis, C.D., Kiranoudis, C.T.: A meta-heuristic algorithm for the efficient distribution of perishable foods. J. Food Eng. 50, 1–9 (2001)

    Article  Google Scholar 

  • Tarantilis, C.D., Kiranoudis, C.T.: A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector. Eur. J. Oper. Res. 179, 806–822 (2007)

    Article  MATH  Google Scholar 

  • Tarantilis, C.D., Kiranoudis, C.T., Vassiliadis, V.S.: A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. J. Oper. Res. Soc. 54, 65–71 (2003)

    Article  MATH  Google Scholar 

  • Tarantilis, C.D., Kiranoudis, C.T., Vassiliadis, V.S.: A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Eur. J. Oper. Res. 152, 148–158 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Yaman, H.: Formulations and valid inequalities for the heterogeneous vehicle routing problem. Math. Program. 106, 365–390 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Instituto do Noroeste Fluminense de Educação Superior, Universidade Federal Fluminense, Rua João Jazbik s/n, Santo Antônio de Pádua, RJ, 28470-000, Brazil

    Puca Huachi Vaz Penna

  2. Departamento de Engenharia de Produção, Centro de Tecnologia, Universidade Federal da Paraíba, Campus I—Bloco G, Cidade Universitária, João Pessoa, PB, 58051-970, Brazil

    Anand Subramanian

  3. Instituto de Computação, Universidade Federal Fluminense, Rua Passo da Pátria 156, Bloco E, 3° andar, São Domingos, Niterói, RJ, 24210-240, Brazil

    Puca Huachi Vaz Penna, Anand Subramanian & Luiz Satoru Ochi

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  1. Puca Huachi Vaz Penna
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  2. Anand Subramanian
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  3. Luiz Satoru Ochi
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Correspondence to Puca Huachi Vaz Penna.

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Penna, P.H.V., Subramanian, A. & Ochi, L.S. An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem. J Heuristics 19, 201–232 (2013). https://doi.org/10.1007/s10732-011-9186-y

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  • DOI: https://doi.org/10.1007/s10732-011-9186-y

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