Learning to solving vehicle routing problems via local–global feature fusion transformer

• Published in: Complex & intelligent systems Vol. 11; no. 9; pp. 392 - 16
• Main Authors: Li, Wei, Dai, Bing Tian, Yan, Xueming, Zou, Junying, Liang, Zhijie, Li, Jingwen
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.09.2025; Springer Nature B.V; Springer
• Subjects: Architecture; Benchmarks; Combinatorial analysis; Complexity; Computational Intelligence; Cross-size and cross-distribution generalization; Data Structures and Information Theory; Decision making; Deep learning; Deep reinforcement learning; Design; Engineering; Heuristic; Learning to optimize; Neural networks; Nodes; Optimization; Original Article; Paradigms; Proximity; Solvers; Traveling salesman problem; Vehicle routing; Vehicle routing problems; Cross-size and cross-distribution generalization; Deep reinforcement learning; Learning to optimize; Vehicle routing problems
• ISSN: 2199-4536; 2198-6053
• DOI: 10.1007/s40747-025-02018-0

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.