Abstract: The Vehicle Routing Problem (VRP) is a fundamental optimization problem in the field of logistics and distribution. The construction and dynamic modification of VRP models heavily rely on expert knowledge from professional modelers, while a significant semantic gap exists between business-oriented requirements and formal mathematical models. To address this issue, this paper proposes a Chain-of-Experts (CoE)-based dynamic VRP model modification method. Without relying on gradient updates, the proposed method establishes a collaborative workflow of large language model (LLM)-based experts to perform requirement interpretation and task decomposition, thereby enabling the mapping from business semantics to mathematical model formulations. Furthermore, a multi-level LLM collaboration mechanism and a dynamic knowledge-enhanced reasoning strategy are introduced, in which the knowledge base is rewritten online according to model validation feedback, allowing continuous refinement of modification strategies. Experimental results demonstrate that, compared with standard prompting, Chain-of-Thought (CoT) prompting, and standard prompting based on GPT-4o, the proposed method improves accuracy by 48, 40, and 39 percentage points, respectively, achieving an overall accuracy of 84% with an average response time of 54.45 seconds. These results verify that the proposed method effectively enhances the capability of LLMs in dynamic VRP model modification tasks and is more suitable for large-scale problem instances.

Key words:  Large Language Model (LLM), context learning, text embedding, Vehicle Routing Problem (VRP), dynamic model modification

摘要： 车辆路径问题（VRP）是物流配送领域的关键优化问题，VRP模型的建立和修改高度依赖专业建模人员，且业务语言与数学模型间存在语义断层问题。因此，提出一种基于专家链的车辆路径问题模型动态修改方法。该方法在不依赖梯度更新的前提下，构建基于大语言模型（LLM）的专家链（CoE）协作工作流，实现需求解析和任务分解，完成业务语义到数学模型的映射；引入多层级LLM协作机制和动态知识增强推理方法，根据验证结果反馈进行动态知识库在线重写，实现策略持续改进。实验结果表明，相较于标准提示词方法、思维链（CoT）技术以及基于GPT-4o的标准提示词方法，该方法在准确率上分别提高了48、40和39个百分点，达到了84%的准确率和54.45 s的平均响应时间。实验结果验证了所提方法能够有效地提升LLM在VRP模型动态修改任务中的处理能力并且更适用于大规模问题实例。

关键词: 大语言模型, 上下文学习, 文本嵌入, 车辆路径问题, 模型动态修改