DGL: Dynamic Global-Local Information Aggregation for Scalable VRP Generalization with Self-Improvement Learning

The Vehicle Routing Problem (VRP) is a critical combinatorial optimization problem with wide-reaching real-world applications, particularly in logistics, transportation. While neural network-based VRP solvers have shown impressive results on test instances similar to training data, their performance often degrades when faced with varying scales and unseen distributions, limiting their practical applicability. To overcome these limitations, we introduce DGL (Dynamic Global-Local Information Aggregation), a novel model that combines global and local information to effectively solve VRPs. DGL dynamically adjusts local node selections within a localized range, capturing local invariance across problems of different scales and distributions, thereby enhancing generalization. At the same time, DGL integrates global context into the decision-making process, providing richer information for more informed decisions. Additionally, we propose a replacement-based self-improvement learning framework that leverages data augmentation and random replacement techniques, further enhancing DGL's robustness. Extensive experiments on synthetic datasets, benchmark datasets, and real-world country map instances demonstrate that DGL achieves state-of-the-art performance, particularly in generalizing to large-scale VRPs and real-world scenarios. These results showcase DGL's effectiveness in solving complex, realistic optimization challenges and highlight its potential for practical applications.