Publication Type
Journal Article
Version
publishedVersion
Publication Date
7-2025
Abstract
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.
Keywords
Cross-size and cross-distribution generalization, Deep reinforcement learning, Learning to optimize, Vehicle routing problems
Discipline
Numerical Analysis and Scientific Computing | Software Engineering
Research Areas
Data Science and Engineering
Publication
Complex & Intelligent Systems
Volume
11
Issue
9
First Page
1
Last Page
16
ISSN
2199-4536
Identifier
10.1007/s40747-025-02018-0
Publisher
Springer
Citation
LI, Wei; DAI, Bing Tian; YAN, Xueming; ZOU, Junying; LIANG, Zhijie; and LI, Jingwen.
Learning to solving vehicle routing problems via local-global feature fusion transformer. (2025). Complex & Intelligent Systems. 11, (9), 1-16.
Available at: https://ink.library.smu.edu.sg/sis_research/11357
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1007/s40747-025-02018-0