arXiv:2510.19895cs.CLcs.AI2025-10

用大模型自动把业务问题转成优化模型,省去人工建模麻烦。

Large Language Model enabled Mathematical Modeling

  • 用DeepSeek-R1理解自然语言,自动生成数学规划模型。
  • 在4个真实场景数据集上准确率超80%,比前代模型更稳定。
  • 适合供应链、物流等需快速建模的工程场景使用。

将大语言模型(LLMs)与优化建模结合,为运筹学(OR)决策提供新路径。传统优化方法如线性规划、混合整数规划依赖领域专家将现实问题转化为可解数学模型,而求解器如Gurobi和COPT虽强大,仍需人工定义目标、约束与变量。本研究探索基于强化学习训练的高效高质模型DeepSeek-R1,在自然语言理解与代码生成能力下,弥补建模差距。尽管GPT-4、Claude等模型表现优异,但其高昂的令牌成本与幻觉倾向限制了在供应链中的应用。本文系统评估DeepSeek-R1在四个关键运筹学基准测试:NL4OPT、IndustryOR、EasyLP与ComplexOR上的表现。研究方法包括基线测试、幻觉分类体系构建,以及采用LLM-as-a-Judge、少样本学习(FSL)、工具调用与多智能体框架等策略,以降低幻觉、提升建模准确性并更好对齐用户意图。

原文摘要 · Abstract (English)

The integration of Large Language Models (LLMs) with optimization modeling offers a promising avenue for advancing decision-making in operations research (OR). Traditional optimization methods,such as linear programming, mixed integer programming, and simulation depend heavily on domain expertise to translate real-world problems into solvable mathematical models. While solvers like Gurobi and COPT are powerful, expert input remains essential for defining objectives, constraints, and variables. This research investigates the potential of LLMs, specifically the DeepSeek-R1 model, to bridge this formulation gap using natural language understanding and code generation. Although prior models like GPT-4, Claude, and Bard have shown strong performance in NLP and reasoning tasks, their high token costs and tendency toward hallucinations limit real-world applicability in supply chain contexts. In contrast, DeepSeek-R1, a cost-efficient and high-performing model trained with reinforcement learning, presents a viable alternative. Despite its success in benchmarks such as LiveCodeBench and Math-500, its effectiveness in applied OR scenarios remains under explored. This study systematically evaluates DeepSeek-R1 across four key OR benchmarks: NL4OPT, IndustryOR, EasyLP, and ComplexOR. Our methodology includes baseline assessments, the development of a hallucination taxonomy, and the application of mitigation strategies like LLM-as-a-Judge, Few-shot Learning (FSL), Tool Calling, and a Multi-agent Framework. These techniques aim to reduce hallucinations, enhance formulation accuracy, and better align model outputs with user intent.

大模型运筹优化自动建模

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