Learning to solving vehicle routing problems via local–global feature fusion transformer - Li, Wei; Dai, Bing Tian; Yan, Xueming; Zou, Junying; Liang, Zhijie; Li, Jingwen (Complex & intelligent systems, 2025)
Applying Combinatorial optimization problems such as the Vehicle Routing Problems (VRPs) have attracted increasing interest with the emergence of learning-based methods. However, existing neural approaches often struggle to generalize across diverse problem sizes and node distributions, limiting their applicability in real-world scenarios. To overcome these challenges, we propose Local-Global Feature Fusion Transformer (FusionFormer), a novel deep reinforcement learning framework that enhances both solution quality and generalization capability for solving VRPs. Specifically, we introduce a Distance-Assisted Multi-Head Attention (DA-MHA) mechanism that incorporates explicit spatial distance information into the attention computation, thereby preserving spatial consistency and facilitating more robust global representation learning. In addition, we design a Proximity-Guided Attention (PGA) mechanism that dynamically fuses local and global contexts based on node proximity, enabling the model to focus on more relevant decision-making information while reducing sensitivity to distributional shifts. Extensive experiments on both real-world and synthetic benchmarks demonstrate that our FusionFormer consistently outperforms existing neural routing solvers (including those specifically designed for generalization enhancement) and achieves performance competitive with the highly-optimized benchmark LKH3 solver, particularly on unseen problem sizes and node distributions.