Abstract
This work presents a new hybrid method based on the route-first-cluster-second approach using Greedy Randomized Adaptive Search Procedure (GRASP), Differential Evolution (DE), Evolutionary Local Search (ELS) and set-partitioning problem (SPP) to solve well-known instances of Capacitated Vehicle Routing Problem (CVRP). The CVRP consists of minimizing the cost of a fleet of vehicles serving a set of customers from a single depot, in which every vehicle has the same capacity. The DE heuristic is used to build an initial feasible solution and ELS is applied until a local minimum is found during the local search phase of the GRASP. Finally, the SPP model provides a new optimal solution with regard to the built solutions in the GRASP. We perform computational experiments for benchmarks available in the literature and the results show that our method was effective to solve CVRP instances with a satisfactory performance. Moreover, a statistical test shows that there is not significant difference between the best known solutions of benchmark instances and the solutions of the proposed method.
We want to express our thanks to the National Council for Scientific and Technological Development – CNPq (processes 302261/2019-2 and 307797/2019-8) and FAPES (process 75528452/2016) for financial support.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Afsar, H.M., Prins, C., Santos, A.C.: Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size. Int. Trans. Oper. Res. 21(1), 153–175 (2014)
Agarwal, Y., Mathur, K., Salkin, H.M.: A set-partitioning-based exact algorithm for the vehicle routing problem. Networks 19(7), 731–749 (1989)
Alba, E., Nakib, A., Siarry, P.: Metaheuristics for Dynamic Optimization. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-30665-5
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, vol. 34. IMAG (1995)
Beasley, J.E.: Route first-cluster second methods for vehicle routing. Omega 11(4), 403–408 (1983)
Christofides, N., Eilon, S.: An algorithm for the vehicle-dispatching problem. J. Oper. Res. Soc. 20(3), 309–318 (1969)
Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8(2), 67–71 (1989)
Gendreau, M., Laporte, G., Vigo, D.: Heuristics for the traveling salesman problem with pickup and delivery. Comput. Oper. Res. 26(7), 699–714 (1999)
Goldberg, A., Radzik, T.: A heuristic improvement of the bellman-ford algorithm. Stanford Univ CA Dept. of Computer Science, Technical report (1993)
Irnich, S., Funke, B., Grünert, T.: Sequential search and its application to vehicle-routing problems. Comput. Oper. Res. 33(8), 2405–2429 (2006)
Prins, C.: A grasp\(\times \) evolutionary local search hybrid for the vehicle routing problem. In: Bio-inspired algorithms for the vehicle routing problem, pp. 35–53. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-85152-3_2
Snyder, L.V., Daskin, M.S.: A random-key genetic algorithm for the generalized traveling salesman problem. Eur. J. Oper. Res. 174(1), 38–53 (2006)
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Toth, P., Vigo, D.: Vehicle Routing: Problems, Methods, and Applications. SIAM (2014)
Ulusoy, G., et al.: The fleet size and mix problem for capacitated arc routing. Eur. J. Oper. Res. 22(3), 329–337 (1985)
Ursani, Z., Essam, D., Cornforth, D., Stocker, R.: Localized genetic algorithm for vehicle routing problem with time windows. Appl. Soft Comput. 11(8), 5375–5390 (2011)
Wang, C.H., Lu, J.Z.: A hybrid genetic algorithm that optimizes capacitated vehicle routing problems. Exp. Syst. Appl. 36(2), 2921–2936 (2009)
Wolf, S., Merz, P.: Evolutionary local search for the super-peer selection problem and the p-hub median problem. In: Bartz-Beielstein, T., et al. (eds.) HM 2007. LNCS, vol. 4771, pp. 1–15. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75514-2_1
Zachariadis, E.E., Kiranoudis, C.T.: A strategy for reducing the computational complexity of local search-based methods for the vehicle routing problem. Comput. Oper. Res. 37(12), 2089–2105 (2010)
Zhu, W., Qin, H., Lim, A., Wang, L.: A two-stage tabu search algorithm with enhanced packing heuristics for the 3l-cvrp and m3l-cvrp. Comput. Oper. Res. 39(9), 2178–2195 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Machado, A.M., Boeres, M.C.S., Rosa, R.d.A., Mauri, G.R. (2020). A New Hybridization of Evolutionary Algorithms, GRASP and Set-Partitioning Formulation for the Capacitated Vehicle Routing Problem. In: Cerri, R., Prati, R.C. (eds) Intelligent Systems. BRACIS 2020. Lecture Notes in Computer Science(), vol 12319. Springer, Cham. https://doi.org/10.1007/978-3-030-61377-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-61377-8_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-61376-1
Online ISBN: 978-3-030-61377-8
eBook Packages: Computer ScienceComputer Science (R0)