Abstract
This paper proposes an abstraction of emerging vehicle routing problems, the Vehicle Routing Problem with Black Box Feasibility. In this problem the routes of a basic VRP need to satisfy an unknown set of constraints. A black box function to test the feasibility of a route is provided. This function is considered of non-linear complexity (in the length of the route). Practical examples of such problems are combinations of VRP with Loading problems or VRP with Scheduling problems. The difficulty in addressing the VRP with Black Box Feasibility lies in the unknown problem structure and the costly feasibility check. We propose a column generation-based approach to locally optimize this problem. Columns are heuristically generated by so-called Collector ants, executing a construction heuristic while guided by pheromones. To find an integer solution we solve an integer Set Partitioning Problem defined on the set of columns generated by the ants. We test the proposed approach on two applications from the literature, the Three-Dimensional Loading Capacitated Vehicle Routing Problem and the Multi-Pile Vehicle Routing Problem, showing the applicability of our approach and its good behavior compared to dedicated approaches.
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 subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Beasley, J., Christofides, N.: Vehicle routing with a sparse feasibility graph. Eur. J. Oper. Res. 98 (1997)
Bortfeldt, A.: A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. Tech. rep., FernUniversität in Hagen (2010)
Clarke, G., Wright, J.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12 (1964)
Doerner, K., Fuellerer, G., Hartl, R., Gronalt, M., Iori, M.: Metaheuristics for the vehicle routing problem with loading constraints. Networks 49 (2007)
Fuellerer, G., Doerner, K.F., Hartl, R., Iori, M.: Metaheuristics for vehicle routing problems with three-dimensional loading constraints. Eur. J. Oper. Res. 201 (2010)
Gendreau, M., Iori, M., Laporte, G., Martello, S.: A tabu search algorithm for a routing and container loading problem. Transport. Sci. 40 (2006)
Iori, M., Martello, S.: Routing problems with loading constraints. TOP 18 (2010)
Jones, D., Schonlau, M., Welch, W.: Efficient global optimization of expensive black-box functions. J. Global Opt. 13 (1998)
Laguna, M., Molina, J., Pérez, F., Caballero, R., G-Hernández-Díaz, A.: The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach. J. Oper. Res. Soc. 61 (2010)
Prescott-Gagnon, E., Desaulniers, G., Drexl, M., Rousseau, L.M.: European driver rules in vehicle routing with time windows. Transport. Sci. 44 (2010)
Reimann, M., Doerner, K., Hartl, R.: D-ants: Savings based ants divide and conquer the vehicle routing problem. Comput. Oper. Res. 31 (2004)
Reimann, M., Stummer, M., Doerner, K.: A savings based ant system for the vehicle routing problem. In: Proceedings of the Genetic and Evolutionary Computation Conference (2002)
Strodl, J., Doerner, K.F., Tricoire, F., Hartl, R.F.: On Index Structures in Hybrid Metaheuristics for Routing Problems with Hard Feasibility Checks: An Application to the 2-Dimensional Loading Vehicle Routing Problem. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds.) HM 2010. LNCS, vol. 6373, pp. 160–173. Springer, Heidelberg (2010)
Tarantilis, C., Zachariadis, E., Kiranoudis, C.: A hybrid metaheuristic algorithm for the integrated vehicle routing and three-dimensional container-loading problem. IEEE Trans. Intell. Transp. Syst. 10 (2009)
Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. SIAM Monographs on Discrete Mathematics and Applications (2002)
Tricoire, F., Doerner, K.F., Hartl, R.F., Iori, M.: Heuristic and exact algorithms for the multi-pile vehicle routing problem. OR Spectrum (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Massen, F., Deville, Y., Van Hentenryck, P. (2012). Pheromone-Based Heuristic Column Generation for Vehicle Routing Problems with Black Box Feasibility. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds) Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol 7298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29828-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-29828-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29827-1
Online ISBN: 978-3-642-29828-8
eBook Packages: Computer ScienceComputer Science (R0)