  We present an end-to-end framework for solving the Vehicle Routing Problem
(VRP) using reinforcement learning. In this approach, we train a single model
that finds near-optimal solutions for problem instances sampled from a given
distribution, only by observing the reward signals and following feasibility
rules. Our model represents a parameterized stochastic policy, and by applying
a policy gradient algorithm to optimize its parameters, the trained model
produces the solution as a sequence of consecutive actions in real time,
without the need to re-train for every new problem instance. On capacitated
VRP, our approach outperforms classical heuristics and Google's OR-Tools on
medium-sized instances in solution quality with comparable computation time
(after training). We demonstrate how our approach can handle problems with
split delivery and explore the effect of such deliveries on the solution
quality. Our proposed framework can be applied to other variants of the VRP
such as the stochastic VRP, and has the potential to be applied more generally
to combinatorial optimization problems.
