Solving Single Vehicle Pickup and Delivery Problems with Time Windows and Capacity Constraints using Nested Monte-Carlo Search

Transporting goods by courier and express services increases the service quality through short transit times and satisfies individual demands of customers. Determining the optimal route for a vehicle to satisfy transport requests while minimizing the total cost refers to the Single Vehicle Pickup and Delivery Problem. Beside time and distance objectives, in real world operations it is mandatory to consider further constraints such as time windows and the capacity of the vehicle. This paper presents a novel approach to solve Single Vehicle Pickup and Delivery Problems with time windows and capacity constraints by applying Nested Monte-Carlo Search (NMCS). NMCS is a randomized exploration technique which has successfully solved complex combinatorial search problems. To evaluate the approach, we apply benchmarks instances with up to 400 cities which have to be visited. The effects of varying the number of iterations and the search level are investigated. The results reveal, that the algorithm computes state-of-the-art solutions and is competitive with other approaches.