Two-Stage Learned Decomposition for Scalable Routing on Multigraphs

TL;DR

This paper introduces a scalable two-stage neural routing method for multigraph vehicle routing problems, combining a novel policy factorization with hierarchical reinforcement learning to improve efficiency and solution quality.

Contribution

The paper proposes Node-Edge Policy Factorization (NEPF), a new scalable approach for VRPs on multigraphs, with a pre-encoding scheme and non-autoregressive architecture.

Findings

NEPF matches or outperforms state-of-the-art solutions.

NEPF is significantly faster in training and inference.

Effective across six VRP variants.

Abstract

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g., distance vs time). Few methods are designed for such formulations and those that do exist face major scalability issues. We mitigate these scalability issues via a Node-Edge Policy Factorization (NEPF) approach, which splits the routing policy into a node permutation stage and an edge selection stage. To enable the decomposition, we introduce a pre-encoding edge aggregation scheme and a non-autoregressive architecture for the edge stage, as well as a hierarchical reinforcement learning method to train the stages jointly. Our experiments across six VRP variants demonstrate that NEPF matches or outperforms the state-of-the-art in terms of solution quality, while being significantly faster in training and inference.