UCT-Based Approach to Capacitated Vehicle Routing Problem

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.