A deep learning Attention model to solve the Vehicle Routing Problem and the Pick-up and Delivery Problem with Time Windows

SNCF, the French public train company, is experimenting to develop new types of transportation services by tackling vehicle routing problems. While many deep learning models have been used to tackle efficiently vehicle routing problems, it is difficult to take into account time related constraints. In this paper, we solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and the Capacitated Pickup and Delivery Problem with Time Windows (CPDPTW) with a constructive iterative Deep Learning algorithm. We use an Attention Encoder-Decoder structure and design a novel insertion heuristic for the feasibility check of the CPDPTW. Our models yields results that are better than best known learning solutions on the CVRPTW. We show the feasibility of deep learning techniques for solving the CPDPTW but witness the limitations of our iterative approach in terms of computational complexity.