Routing problems are a class of combinatorial problems with many practical
applications. Recently, end-to-end deep learning methods have been proposed to
learn approximate solution heuristics for such problems. In contrast, classical
dynamic programming (DP) algorithms guarantee optimal solutions, but scale
badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP),
which aims to combine the strengths of learned neural heuristics with those of
DP algorithms. DPDP prioritizes and restricts the DP state space using a policy
derived from a deep neural network, which is trained to predict edges from
example solutions. We evaluate our framework on the travelling salesman problem
(TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and
show that the neural policy improves the performance of (restricted) DP
algorithms, making them competitive to strong alternatives such as LKH, while
also outperforming most other 'neural approaches' for solving TSPs, VRPs and
TSPTWs with 100 nodes.

Deep Policy Dynamic Programming 优先和限制来自深度神经网络的策略，以结合学习嵌入式启发式和动态规划 (DP) 算法的优点，以优化旅行商问题 (TSP)、车辆路径问题 (VRP) 和带时间窗口的 TSP (TSPTW) 的性能，同时胜过大多数其他解决 TSPs、VRPs 和 TSPTWs 的 ' 神经方法 '。