Lightweight normalization-free GNN-guided local search for logistics routing optimization

Routing optimization has grown progressively pivotal in the logistics domain. Recently, learning-based approximate algorithms have emerged as a promising paradigm for solving routing problems. However, they suffer from substantial computational overhead from normalization layers hindering inference on resource-constrained edge devices, and poor cross-scale generalization under fluctuating routing node counts. To address these issues, we propose a novel lightweight normalization-free graph neural network guided local search framework, termed GNN-GLS-DyT, for efficiently solving vehicle routing problems. Specifically, a normalization-free regret approximation module is devised to estimate the regret value of including each edge in the final solution path. All batch normalization layers in the module are replaced by a lightweight dynamic tanh (DyT) operator, which drastically reduces computational complexity while preserving full representational capacity. Taking the predicted edge regret values and original routing graph as adaptive heuristic cues, we embed the proposed graph neural network into the guided local search (GLS) paradigm. This hybrid design bridges deep learning generalization with classical heuristic search capability, enabling efficient discovery of high-quality routing solutions. Extensive experiments on the vehicle routing problems demonstrate that our method consistently outperforms state-of-the-art baselines in overall solution quality, and achieves markedly faster convergence on complex vehicle routing problem variants. Most notably, the framework exhibits superior cross-scale generalization, which trained exclusively on small-scale instances, it generalizes seamlessly to much larger routing problems, validating its strong practical potential for large-scale real-world logistics systems.