大模型正从直接优化转向工具增强，提升求解效率与可审计性。
Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers
- 通过自然语言转形式化指令，调用外部求解器实现精准优化
- 在多个基准上超越传统方法，解决复杂组合优化问题
- 适合需要可解释、可复现的自动化决策场景
大型语言模型（LLMs）正越来越多地应用于复杂的数学优化任务，即使实际使用者并未察觉。现实世界中的许多问题本质上都是寻找更优或最优解的过程。当前的LLM作为优化器主要有三种范式：直接优化、工具增强优化和工具生成优化。直接优化通过迭代提示和启发式生成探索解空间；工具增强优化将自然语言问题转化为形式化规范，并协调外部求解器执行；工具生成优化则进一步利用大模型发现可复用的算法或启发式策略，实现零边际成本部署。本文基于文献中的基准测试描述了当前性能边界。我们指出当前架构存在关键推理鸿沟，并主张未来直接优化潜力与工具增强优化可审计性之间需权衡。即便未来更强大的模型，也可能选择工具生成以提升重复性问题的运行效率。
原文摘要 · Abstract (English)
Large Language Models (LLMs) are increasingly involved in complex mathematical optimization, even if the pragmatic user who triggers them is unaware of it. After all, many real-world problems reduce to the search for better or the best solutions. The field of LLM-as-optimizer has three paradigms: direct optimization, tool-augmented optimization, and tool-creating optimization. Direct optimization uses iterative prompting and heuristic generation to navigate solution spaces. Tool-augmented optimization translates natural language problems into formal specifications and orchestrates external solvers. Tool-creating optimization goes further, using LLMs to discover reusable algorithms or heuristics that can be deployed at zero marginal LLM cost. We describe current performance frontiers based on the benchmarks from the literature. We identify the critical reasoning gap in current architectures and argue for trade-offs between the future potential of direct optimization and the auditability of tool-augmented optimization. Even future, more powerful models might opt for tool-making to improve operational efficiency for repetitive families of problems.
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