A Monte Carlo tree search for traveling salesman problem with drone

The use of drones and trucks working collaboratively has gained drastically attentions in recent years. We develop a new Monte Carlo Tree Search algorithm (MCTS) to solve the Traveling Salesman Problem with Drone (TSP-D) arising in the management of parcel last-mile-delivery systems. The approach seeks to find optimal decisions by taking random samples in decision space and building a search tree based on the results. We address several major issues in adapting the tree search concept to solve the TSP-D in this paper. The solution approach, aimed to minimize the total completion time, is tested on various problem instances derived from the well-known TSPLIB benchmark. Experimental results show a very promising performance of the proposed search method where it outperforms the compared heuristic method, providing new best solutions for 23 instances and an average 12% improvement in terms of solution quality.