Deep Policy Dynamic Programming for Vehicle Routing Problems

Wouter Kool, Herke van Hoof, Joaquim Gromicho, Max Welling

Keywords: vehicle routing, travelling salesman problem, dynamic programming, neural, network, policy, time windows, constraints

TL;DR: A Dynamic Programming framework with state space restricted using a neural network policy, applied to Vehicle Routing Problems

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 \emph{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.

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Community Implementations: [ 5 code implementations](https://www.catalyzex.com/paper/arxiv:2102.11756/code)