用大模型在测试时动态调整，让小规模训练的算法能解百万节点路径问题。
Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning
- 用大模型学习小规模与大规模数据间的映射关系
- 100节点训练模型在10万节点问题上性能超越现有方法
- 仅需推理阶段调整，无需重新训练模型
神经组合优化（NCO）作为解决车辆路径问题（VRPs）的学习范式，可减少对人工工程的依赖。尽管现有方法在小规模实例（如100个节点）上表现良好，但在大规模场景中性能显著下降，这是由于训练与测试数据分布差异所致。为此，我们提出一种基于大语言模型（LLMs）的新框架，学习训练与测试分布之间的投影，并在推理阶段应用以提升模型可扩展性。该方法无需与神经网络联合训练，仅在测试时执行。大量实验表明，该方法使一个在100节点实例上训练的骨干模型，在来自不同分布的超大规模旅行商问题（TSP）和容量约束车辆路径问题（CVRP）（最多10万节点）上达到更优性能。
原文摘要 · Abstract (English)
Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on small-scale instances (e.g., 100 nodes), have demonstrated considerable success on problems of similar scale, their performance significantly degrades when applied to large-scale scenarios. This degradation arises from the distributional shift between training and testing data, rendering policies learned on small instances ineffective for larger problems. To overcome this limitation, we introduce a novel learning framework driven by Large Language Models (LLMs). This framework learns a projection between the training and testing distributions, which is then deployed to enhance the scalability of the NCO model. Notably, unlike prevailing techniques that necessitate joint training with the neural network, our approach operates exclusively during the inference phase, obviating the need for model retraining. Extensive experiments demonstrate that our method enables a backbone model (trained on 100-node instances) to achieve superior performance on large-scale Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) of up to 100K nodes from diverse distributions.
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