让大模型像优化专家一样精准构建数学规划模型。
OptiMind: Teaching LLMs to Think Like Optimization Experts
- 用类级错误分析指导训练与推理，预防常见建模错误。
- 在多个基准上准确率提升20.7%，且在多轮反馈下持续有效。
- 适合需要高精度建模的科研与工业用户，如运筹优化场景。
数学规划——将运营和决策问题精确表达为数学语言——是跨领域基础任务，但长期依赖运筹学专业知识，难以自动化。尽管大模型在复杂推理方面取得进展，现有方法因训练数据稀缺且噪声大，准确性受限，未充分融合领域知识。本文提出OptiMind框架，系统性整合优化专家经验，针对混合整数线性规划（MILP）这一关键数学规划家族，通过半自动的类级错误分析，指导训练与推理过程，显式规避各类优化中的常见错误。微调后的语言模型在多个优化基准上实现20.7%的准确率提升，并在自一致性、多轮反馈等测试时缩放方法下保持一致增益，推动了大模型辅助优化建模向鲁棒化迈进。
原文摘要 · Abstract (English)
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise. Recent advances in large language models for complex reasoning have spurred interest in automating this task, translating natural language into executable optimization models. Current approaches, however, achieve limited accuracy, hindered by scarce and noisy training data without leveraging domain knowledge. In this work, we systematically integrate optimization expertise to improve formulation accuracy for mixed-integer linear programming, a key family of mathematical programs. Our OptiMind framework leverages semi-automated, class-based error analysis to guide both training and inference, explicitly preventing common mistakes within each optimization class. Our resulting fine-tuned LLM significantly improves formulation accuracy by 20.7% across multiple optimization benchmarks, with consistent gains under test-time scaling methods such as self-consistency and multi-turn feedback, enabling further progress toward robust LLM-assisted optimization formulation.
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