Abstract
In this paper, we address the elementary shortest path problem with 2-dimensional loading constraints. The aim is to find the path with the smallest cost on a graph where the nodes represent clients whose items may have different heights and widths. Beyond its practical relevance, this problem appears as a subproblem in vehicle routing problems with loading constraints where feasible routes have to be generated dynamically. To the best of our knowledge, there are no results reported in the literature related to this problem. Here, we explore a variable neighborhood search approach for this problem. The method relies on constructive heuristics to generate feasible paths, while improved incumbents are sought in different neighborhoods of a given solution through a variable neighborhood search procedure. The resulting variants of the algorithm were tested extensively on benchmark instances from the literature. The results are reported and discussed at the end of the paper.
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References
Feillet, D., Dejax, P., Gendreau, M., Gueguen, C.: An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems. Networks 44(3), 216–229 (2004)
Gendreau, M., Iori, M., Laporte, G., Martello, S.: A Tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints. Networks 51(1), 4–18 (2008)
Hansen, P., Mladenovic, N., Pérez, J.: Variable neighborhood search: methods and applications. Annals of Operations Research 175, 367–407 (2010)
Iori, M., Martello, S.: Routing problems with loading constraints. Top 18(1), 4–27 (2010)
Iori, M., Salazar-Gonzalez, J.J., Vigo, D.: An exact approach for the vehicle routing problem with two-dimensional loading constraints. Transportation Science 41(2), 253–264 (2007)
Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)
Pinto, T., Alves, C., de Carvalho, J.V.: Column generation based heuristic for a vehicle routing problem with 2-dimensional loading constraints: a prototype. In: XI Congresso Galego de Estatística e Investigación de Operacións, Spain (2013)
Righini, G., Salani, M.: Symmetry helps: bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints. Discrete Optimization 3(3), 255–273 (2006)
Righini, G., Salani, M.: New dynamic programming algorithms for the resource constrained elementary shortest path problem. Networks 51(3), 155–170 (2008)
Zachariadis, E.E., Tarantilis, C.D., Kiranoudis, C.T.: A guided tabu search for the vehicle routing problem with two-dimensional loading constraints. European Journal of Operational Research 195(3), 729–743 (2009)
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Pinto, T., Alves, C., de Carvalho, J.V. (2015). Variable Neighborhood Search for the Elementary Shortest Path Problem with Loading Constraints. In: Gervasi, O., et al. Computational Science and Its Applications -- ICCSA 2015. ICCSA 2015. Lecture Notes in Computer Science(), vol 9156. Springer, Cham. https://doi.org/10.1007/978-3-319-21407-8_34
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DOI: https://doi.org/10.1007/978-3-319-21407-8_34
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