Variable neighborhood search for the stochastic and dynamic vehicle routing problem
In this paper, the authors consider the vehicle routing problem (VRP) with stochastic demand and/or dynamic requests. The classical VRP consists of determining a set of routes starting and ending at a depot that provide service to a set of customers. Stochastic demands are only revealed when the vehicle arrives at the customer location; dynamic requests mean that new orders from previously unknown customers can be received and scheduled over time. The variable neighborhood search algorithm (VNS) proposed in this study can be extended by sampling for stochastic scenarios and adapted for the dynamic setting. We use standard sets of benchmark instances to evaluate our algorithms. When applying sampling based VNS, on average we were able to improve results obtained by a classical VNS by 4.39 %. Individual instances could be improved by up to 8.12 %. In addition, the proposed VNS framework matches 32 out of 40 best known solutions and provides one new best solution. In the dynamic case, VNS improves on existing results and provides new best solutions for 7 out of 21 instances. Finally, this study offers results for stochastic and dynamic scenarios. Our experiments show that the sampling based dynamic VNS provides better results when the demand deviation is small, and reduces the excess route duration by 45–90 %.
KeywordsVariable neighborhood search Vehicle routing problem Dynamic requests Stochastic demands
- Christofides, N., Mingozzi, A., & Toth, P. (1979). The vehicle routing problem, chap. 11. London: Wiley.Google Scholar
- Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco: W. H. Freeman.Google Scholar
- Geekbench benchmark. (2010). http://www.primatelabs.ca/.
- Gutjahr, W. J., Katzensteiner, S., & Reiter, P. (2007). A VNS algorithm for noisy problems and its application to project portfolio analysis. In SAGA 2007, lecture notes in computer science, vol. 4665, (pp. 93–104). Berlin: Springer.Google Scholar
- Khouadjia, M. R., Sarasola, B., Alba, E., Jourdan, L., & Talbi, E. G. (2011). Multi-environmental cooperative parallel metaheuristics for solving dynamic optimization problems. In IPDPS Workshops, (pp. 395–403). IEEE.Google Scholar
- Kilby, P., Prosser, P., & Shaw, P. (1998). Dynamic VRPs: A study of scenarios. Tech. rep.: University of Strathclyde, UK.Google Scholar
- Kritzinger, S., Tricoire, F., Doerner, K. F., Hartl, R. F., & Stützle, T. (2012). A unified framework for routing problems with fixed fleet size. Technical Report, submitted.Google Scholar
- Mendoza, J. E., Rousseau, L. M., & Villegas, J. G. A hybrid metaheuristic for the vehicle routing problem with stochastic demand and duration constraints. Under review.Google Scholar
- Psaraftis, H. N. (1988). Dynamic vehicle routing problems (vol. 16). North Holland.Google Scholar
- Sarasola, B., Khouadjia, M. R., Alba, E., Jourdan, L., & Talbi, E. G. (2011). Flexible variable neighborhood search in dynamic vehicle routing. In EvoApplications (1), lecture notes in computer science, vol. 6624, (pp. 344–353). Berlin: Springer.Google Scholar
- Ulmer, M. W., Brinkmann, J., & Mattfeld, D. C. (2013). Anticipatory planning for courier, express and parcel services. To appear in Proceedings of Logistik Management.Google Scholar