Learning to Search, Searching to Learn: A Closed-Loop Framework for Large-Scale Vehicle Routing Problems
Yongji Fu, Yong Wang, Jun Deng, et al.
NeurIPS 2026 (submission), Under review, 2025
Large-scale Vehicle Routing Problems (VRPs) face two long-standing difficulties. On the one hand, many scalable methods rely on partitioning, local candidate restriction, or staged decision making to control computation, which weakens their modeling of global structure. On the other hand, although many methods introduce search at test time to improve the final solution, search is still typically used only as a one-shot post-processing step after model prediction. The model makes a prediction, search repairs it, and little sustained feedback is formed between the two. Improved structural states are rarely fed back to the model for subsequent inference, and high-quality search solutions are seldom turned into later training supervision.
To address this issue, we propose LSL (Learning to Search, Searching to Learn), a closed-loop learning-search framework for large-scale VRPs. LSL first predicts search-friendly structural priors on a sparse candidate graph, and search then iteratively refines the current solution under the guidance of these priors. In turn, search does not leave the system after one round of refinement. At inference time, the structural states returned by search are fed back to the model for the next round of prediction, while at training time, multiple high-quality search solutions are reorganized into row-wise soft targets for model update. In this way, learning tells search where to explore, and search tells the model which structures are worth learning. Experiments show that LSL achieves strong scalability, efficiency, and solution quality across multiple large-scale VRP benchmarks.
@article{fu2025learning,
title={Learning to Search, Searching to Learn: A Closed-Loop Framework for Large-Scale Vehicle Routing Problems},
author={Fu, Yongji and Wang, Yong and Deng, Jun and others},
journal={Submitted to NeurIPS 2026},
year={2025}
}