Abstract
Vehicle Routing Problem (VRP) is a popular combinatorial optimization problem which consists in finding an optimal set of routes for a fleet of vehicles in order to serve a specified collection of clients. Capacitated VRP (CVRP) is a version of VRP in which every vehicle has a capacity parameter assigned.
The UCT (Upper Confidence bounds applied to Trees) is a heuristic simulation-based algorithm used for learning an optimal policy in games. The algorithm is an extension of the Monte Carlo Tree Search (MCTS) method, however, unlike MCTS which makes use of uniformly distributed simulations in a game tree (in order to find the most promising move), the UCT aims at maintaining an optimal balance between exploration and exploitation, which results in more frequent visits to and deeper expansion of the most promising branches of a game tree.
The paper is the first attempt to apply the UCT algorithm to solving CVRP. The critical issue here is suitable mapping of the CVRP onto a game tree structure, which is not straightforward in this problem domain. Furthermore, in order to keep the tree size within reasonable limits the appropriate way of child nodes selection must be considered. Another pertinent issue is interpretation of game-related terms “win” and “loss” in the CVRP context.
Experimental results of several mappings of CVRP to game tree-like structure are presented for a collection of popular benchmark sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Breedam, A.V.: An analysis of the behavior of heuristics for the vehicle routing problem for a selection of problems with vehicle-related, customer-related, and time-related constraints. Ph.D. thesis, University of Antwerp, Belgium (1994)
Chaslot, G., Winands, M.H.M., Szita, I., van den Herik, H.J.: Cross-Entropy for Monte-Carlo Tree Search. ICGA Journal (3), 145–156 (2008)
Clarke, G., Wright, J.: Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12(4), 568–581 (1964)
Dantzig, G.B., Ramser, J.: The truck dispatching problem. Management Science 6(1), 80–91 (1959)
Dorigo, M.: Optimization, Learning and Natural Algorithms. Ph.D. thesis, Politecnico di Milano (1992)
Eilon, S., Watson-Gandy, C., Christofides, N.: Distribution Management: Mathematical Modelling and Practical Analysis, 1st edn., Griffin (January 1976)
Fisher, M., Jaikumar, R.: A Decomposition Algorithm for Large-scale Vehicle Routing. Paper / Department of Decision Sciences, Wharton School, University of Pennsylvania, Philadelphia, Pa. Dep. of Decision Sciences, Wharton School, Univ. of Pennsylvania (1978)
Gelly, S., Silver, D.: Monte-carlo tree search and rapid action value estimation in computer go. Artificial Intelligence 175(11), 1856–1875 (2011)
Genesereth, M.R., Love, N., Pell, B.: General game playing: Overview of the aaai competition. AI Magazine 26(2), 62–72 (2005)
Gillett, B., Miller, L.: A heuristic algorithm for the vehicle dispatch problem. Operations Research 22(2), 340–349 (1974)
Lenstra, J.K., Rinnooy Kan, A.R.K.: Complexity of vehicle routing and scheduling problems. Networks 11, 221–227 (1981)
Khouadjia, M.R., Alba, E., Jourdan, L., Talbi, E.-G.: Multi-Swarm Optimization for Dynamic Combinatorial Problems: A Case Study on Dynamic Vehicle Routing Problem. In: Dorigo, M., et al. (eds.) ANTS 2010. LNCS, vol. 6234, pp. 227–238. Springer, Heidelberg (2010)
Kocsis, L., Szepesvári, C.: Bandit based Monte-Carlo planning. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 282–293. Springer, Heidelberg (2006)
Mańdziuk, J.: Knowledge-Free and Learning-Based Methods in Intelligenet Game Playing. SCI, vol. 276. Springer, Heidelberg (2010)
Mańdziuk, J.: Towards cognitively-plausible game playing systems. IEEE Computational Intelligence Magazine 6(2), 38–51 (2011)
Christofides, N., Mingozz, A., Exact, P.T.: algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Mathematical Programming 20(1), 255–282 (1981)
Networking, N.: Emerging Optmization (2013), http://neo.lcc.uma.es/vrp/vrp-instances/capacitated-vrp-instances/
Okulewicz, M., Mańdziuk, J.: Application of Particle Swarm Optimization Algorithm to Dynamic Vehicle Routing Problem. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS(LNAI), vol. 7895, pp. 547–558. Springer, Heidelberg (2013)
Okulewicz, M., Mańdziuk, J.: Application of Particle Swarm Optimization Algorithm to Dynamic Vehicle Routing Problem. In: Proceedings of the 2nd IEEE Symposium on Computational Intelligence for Human-Like Intelligence, pp. 86–93. IEEE Press (2014)
Świechowski, M., Mańdziuk, J.: Self-adaptation of playing strategies in general game playing. IEEE Transactions on Computational Intelligence and AI in Games 6(4), 367–381 (2014)
Xie, F., Liur, Z.: Backpropagation modification in monte-carlo game tree search. In: IITA 2009 Proceedings of the 2009 Third International Symposium on Intelligent Information Technology Application, vol. 2, pp. 125–128 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Mańdziuk, J., Nejman, C. (2015). UCT-Based Approach to Capacitated Vehicle Routing Problem. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9120. Springer, Cham. https://doi.org/10.1007/978-3-319-19369-4_60
Download citation
DOI: https://doi.org/10.1007/978-3-319-19369-4_60
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19368-7
Online ISBN: 978-3-319-19369-4
eBook Packages: Computer ScienceComputer Science (R0)