用AI自动把非线性问题转成可解的线性形式，提升求解效率。
LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems
- 分步式智能体识别非线性模式并选最优线性化方法
- 在40个测试案例中平均成功率73%，比基线高8.3倍
- 适合希望用自然语言建模复杂优化问题的研究者
将非线性优化问题转化为求解器可用的线性形式在实际应用中至关重要，但传统方法依赖人工且需领域知识。我们提出LinearizeLLM，一个基于智能体的大型语言模型框架，可生成求解器就绪的线性重写。智能体首先检测非线性模式（如双线性项），再采用模式感知的重写技术，选择最合适的线性化策略。我们在40个实例上进行评估：27个来自ComplexOR，通过注入可精确线性化的算子构建；13个为自动生成的深层嵌套非线性实例。LinearizeLLM在非线性深度范围内实现73%的平均端到端成功率，比单次提示的LLM基线高8.3倍，比Pyomo高4.3倍。结果表明，一组针对特定模式设计的智能体可实现线性化自动化，支持以自然语言进行非线性优化建模。
原文摘要 · Abstract (English)
Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an agent-based LLM framework that produces solver-ready linear reformulations of nonlinear optimization problems. Agents first detect the nonlinearity pattern (e.g., bilinear products) and apply nonlinearity pattern-aware reformulation techniques, selecting the most suitable linearization technique. We benchmark on 40 instances: 27 derived from ComplexOR by injecting exactly-linearizable operators, and 13 automatically generated instances with deeply nested nonlinearities. LinearizeLLM achieves 73\% mean end-to-end overall success (OSR) across nonlinearity depths (8.3x higher than a one-shot LLM baseline; 4.3x higher than Pyomo). The results suggest that a set of pattern-specialized agents can automate linearization, supporting natural-language-based modeling of nonlinear optimization.
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