Abstract
The capacitated vehicle routing problem (CVRP) is a well-known NP-hard combinatorial optimization problem with numerous real-world applications in logistics. In this work, we present a literature review with recent successful parallel implementations of variable neighborhood search regarding different variants of vehicle routing problems. We conduct an experimental study for the CVRP using well-known benchmark instances, and we present and investigate three parallelization strategies that coordinate the communication of the multiple processors. We experimentally evaluate a non-cooperative and two novel cooperation models, the managed cooperative and the parameterized cooperative strategies. Our results constitute a first proof-of-concept for the benefits of this new self-adaptive parameterized cooperative approach, especially in computationally hard instances.
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References
Antoniadis, N., Sifaleras, A.: A hybrid CPU–GPU parallelization scheme of variable neighborhood search for inventory optimization problems. Electron. Not. Discrete Math. 58, 47–54 (2017)
Augerat, P., Belenguer, J., Benavent, E., Corberán, A., Naddef, D., Rinaldi, G.: Computational Results with a Branch and Cut Code for the Capacitated Vehicle Routing Problem. Tech. Rep. 495, Institute for Systems Analysis and Computer Science (IASI), Rome (1995)
Baldacci, R., Toth, P., Vigo, D.: Exact algorithms for routing problems under vehicle capacity constraints. Ann. Oper. Res. 175(1), 213–245 (2010)
Christofides, N., Eilon, S.: An algorithm for the vehicle-dispatching problem. J. Oper. Res. Soc. 20(3), 309–318 (1969)
Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.) Combinatorial Optimization, vol. 1, Chap. 11, pp. 315–338. Wiley, Chichester (1979)
Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12(4), 568–581 (1964)
Coelho, I.M., Ochi, L.S., Munhoz, P.L.A., Souza, M.J.F., Farias, R., Bentes, C.: The single vehicle routing problem with deliveries and selective pickups in a CPU–GPU heterogeneous environment. In: 14th IEEE International Conference on High Performance Computing and Communication & 9th IEEE International Conference on Embedded Software and Systems (HPCC-ICESS), pp. 1606–1611. IEEE (2012)
Cordeau, J.F., Laporte, G., Savelsbergh, M.W., Vigo, D.: Vehicle routing. In: Barnhart, C., Laporte, G. (eds.) Transportation, Handbooks in Operations Research and Management Science, vol. 14, Chap. 6, pp. 367–428. Elsevier, Amsterdam (2007)
Crainic, T.G.: Parallel solution methods for vehicle routing problems. In: Golden, B., Raghavan, S., Wasil, E. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 171–198. Springer, Boston (2008)
Crainic, T.G., Gendreau, M., Hansen, P., Mladenović, N.: Cooperative parallel variable neighborhood search for the p-median. J. Heurist. 10(3), 293–314 (2004)
Crainic, T.G., Hail, N.: Parallel metaheuristics applications. In: Alba, E. (ed.) Parallel Metaheuristics, Chap. 19, pp. 447–494. Wiley, New York (2005)
Crainic, T.G., Toulouse, M., Gendreau, M.: Toward a taxonomy of parallel tabu search heuristics. INFORMS J. Comput. 9(1), 61–72 (1997)
Damerau, F.J.: A technique for computer detection and correction of spelling errors. Commun. ACM 7(3), 171–176 (1964)
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)
Davidović, T., Crainic, T.G.: MPI parallelization of variable neighborhood search. Electron. Not. Discrete Math. 39, 241–248 (2012)
Davidović, T., Crainic, T.G.: Parallel local search to schedule communicating tasks on identical processors. Parallel Comput. 48, 1–14 (2015)
Golden, B.L., Wasil, E.A., Kelly, J.P., Chao, I.M.: The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results. In: Crainic, T.G., Laporte, G. (eds.) Fleet Management and Logistics, pp. 33–56. Springer, Boston (1998)
Groër, C., Golden, B., Wasil, E.: A parallel algorithm for the vehicle routing problem. INFORMS J. Comput. 23(2), 315–330 (2011)
Hansen, P., Mladenović, N., Brimberg, J., Pérez, J.A.M.: Variable neighborhood search. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, pp. 57–97. Springer, Cham (2019)
Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423–454 (2017)
Karakostas, P., Sifaleras, A., Georgiadis, M.C.: A general variable neighborhood search-based solution approach for the location-inventory-routing problem with distribution outsourcing. Comput. Chem. Eng. 126, 263–279 (2019)
Laporte, G., Nobert, Y.: Exact algorithms for the vehicle routing problem. In: Martello, S., Laporte, G., Minoux, M., Ribeiro, C. (eds.) Surveys in Combinatorial Optimization. North-Holland Mathematics Studies, vol. 132, pp. 147–184. North-Holland, UK (1987)
Le Bouthillier, A., Crainic, T.G.: A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Comput. Oper. Res. 32(7), 1685–1708 (2005)
Li, F., Golden, B., Wasil, E.: Very large-scale vehicle routing: new test problems, algorithms, and results. Comput. Oper. Res. 32(5), 1165–1179 (2005)
Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)
Munera, D., Diaz, D., Abreu, S.: Solving the quadratic assignment problem with cooperative parallel extremal optimization. In: Chicano, F., Hu, B., García-Sánchez, P. (eds.) Evolutionary Computation in Combinatorial Optimization, pp. 251–266. Springer, Berlin (2016)
Pérez, J.A.M., Hansen, P., Mladenović, N.: Parallel variable neighborhood search. In: Alba, E. (ed.) Parallel Metaheuristics, Chap. 11, pp. 247–266. Wiley, New York (2005)
Polacek, M., Benkner, S., Doerner, K.F., Hartl, R.F.: A cooperative and adaptive variable neighborhood search for the multi depot vehicle routing problem with time windows. Bus. Res. 1(2), 207–218 (2008)
Polat, O.: A parallel variable neighborhood search for the vehicle routing problem with divisible deliveries and pickups. Comput. Oper. Res. 85, 71–86 (2017)
Ribeiro, C.C., Maniezzo, V., Stützle, T., Blum, C., Juan, A.A., Ramalhinho, H., Mladenović, N., Sifaleras, A., Sörensen, K., Souza, M.J.: Preface to the special issue on matheuristics and metaheuristics. Int. Trans. Oper. Res. 27(1), 5–8 (2020)
Schulz, C., Hasle, G., Brodtkorb, A.R., Hagen, T.R.: GPU computing in discrete optimization. Part II: survey focused on routing problems. EURO J. Transp. Logist. 2(1–2), 159–186 (2013)
Skouri, K., Sifaleras, A., Konstantaras, I.: Open problems in green supply chain modeling and optimization with carbon emission targets. In: Pardalos, P.M., Migdalas, A. (eds.) Open Problems in Optimization and Data Analysis. Springer Optimization and Its Applications, pp. 83–90. Springer, Berlin (2018)
Taillard, É.: Parallel iterative search methods for vehicle routing problems. Networks 23(8), 661–673 (1993)
Toro, O., Eliana, M., Escobar, Z., Antonio, H., Granada, E.: Literature review on the vehicle routing problem in the green transportation context. Revista Luna Azul 42, 362–387 (2016)
Toth, P., Vigo, D.: The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia (2002)
Uchoa, E., Pecin, D., Pessoa, A., Poggi, M., Vidal, T., Subramanian, A.: New benchmark instances for the capacitated vehicle routing problem. Eur. J. Oper. Res. 257(3), 845–858 (2017)
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Kalatzantonakis, P., Sifaleras, A. & Samaras, N. Cooperative versus non-cooperative parallel variable neighborhood search strategies: a case study on the capacitated vehicle routing problem. J Glob Optim 78, 327–348 (2020). https://doi.org/10.1007/s10898-019-00866-y
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DOI: https://doi.org/10.1007/s10898-019-00866-y