Deep Policy Dynamic Programming for Vehicle Routing Problems

TL;DR

This paper introduces Deep Policy Dynamic Programming (DPDP), a hybrid approach that combines neural network-guided heuristics with classical dynamic programming to efficiently solve vehicle routing problems with near-optimal solutions.

Contribution

The paper proposes DPDP, a novel method that integrates deep learning with dynamic programming, improving scalability and solution quality for routing problems.

Findings

DPDP outperforms traditional DP on large instances.

Neural policy enhances DP efficiency and accuracy.

Competitive with state-of-the-art heuristics like LKH.

Abstract

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.