A zone-based training approach for last-mile routing using Graph Neural Networks and Pointer Networks

2026-01-08

arXiv.org

AI Summary

This work addresses the challenge of optimizing last-mile delivery routes in highly asymmetric road networks—such as those with one-way streets or severe congestion—where conventional heuristics struggle to perform effectively. To tackle this, the authors propose a geography-aware training strategy that partitions the service area into balanced subregions using a Discrete Global Grid System (DGGS). Within each subregion, an encoder-decoder model composed of a Graph Neural Network (GNN) and a Pointer Network is independently trained to generate optimal stop sequences. By tailoring the model to local spatial characteristics, this approach significantly enhances route prediction performance in high-stop-density scenarios. Experiments on the 2021 Amazon Los Angeles dataset demonstrate that the partitioning strategy yields shorter average predicted route lengths compared to global training, with performance gains becoming more pronounced as the number of stops increases.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Rapid e-commerce growth has pushed last-mile delivery networks to their limits, where small routing gains translate into lower costs, faster service, and fewer emissions. Classical heuristics struggle to adapt when travel times are highly asymmetric (e.g., one-way streets, congestion). A deep learning-based approach to the last-mile routing problem is presented to generate geographical zones composed of stop sequences to minimize last-mile delivery times. The presented approach is an encoder-decoder architecture. Each route is represented as a complete directed graph whose nodes are stops and whose edge weights are asymmetric travel times. A Graph Neural Network encoder produces node embeddings that captures the spatial relationships between stops. A Pointer Network decoder then takes the embeddings and the route's start node to sequentially select the next stops, assigning a probability to each unvisited node as the next destination. Cells of a Discrete Global Grid System which contain route stops in the training data are obtained and clustered to generate geographical zones of similar size in which the process of training and inference are divided. Subsequently, a different instance of the model is trained per zone only considering the stops of the training routes which are included in that zone. This approach is evaluated using the Los Angeles routes from the 2021 Amazon Last Mile Routing Challenge. Results from general and zone-based training are compared, showing a reduction in the average predicted route length in the zone-based training compared to the general training. The performance improvement of the zone-based approach becomes more pronounced as the number of stops per route increases.

Problem

• last-mile routing
• asymmetric travel times
• delivery optimization
• route planning
• e-commerce logistics

Innovation

• Zone-based training
• Graph Neural Networks
• Pointer Networks
• Last-mile routing
• Discrete Global Grid System