Optimization plays a vital role in scientific research and practical applications, but formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise. We introduce \textbf{OptimAI}, a framework for solving \underline{Optim}ization problems described in natural language by leveraging LLM-powered \underline{AI} agents, achieving superior performance over current state-of-the-art methods. Our framework is built upon four key roles: (1) a \emph{formulator} that translates natural language problem descriptions into precise mathematical formulations; (2) a \emph{planner} that constructs a high-level solution strategy prior to execution; and (3) a \emph{coder} and a \emph{code critic} capable of interacting with the environment and reflecting on outcomes to refine future actions. Ablation studies confirm that all roles are essential; removing the planner or code critic results in $5.8\times$ and $3.1\times$ drops in productivity, respectively. Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional $3.3\times$ productivity gain. Our design emphasizes multi-agent collaboration, allowing us to conveniently explore the synergistic effect of combining diverse models within a unified system. Our approach attains 88.1\% accuracy on the NLP4LP dataset and 71.2\% on the Optibench (non-linear w/o table) subset, reducing error rates by 58\% and 50\% respectively over prior best results.

本研究解决了将自然语言描述的优化问题转化为数学形式所需的专业知识缺乏的问题。提出的OptimAI框架通过四个关键角色（形式化者、规划者、编码者和代码评论者）协同工作，显著提高了解决问题的效率与准确性。研究表明，该方法在多个数据集上取得了优异的表现，具有较大潜在影响。

OptimAI：基于大型语言模型的人工智能代理进行自然语言优化