用历史解法构建双簇记忆，让大模型帮小模型更准解优化题。
Dual-Cluster Memory Agent: Resolving Multi-Paradigm Ambiguity in Optimization Problem Solving
- 将过往解法分入建模与编码两类，提炼出方法、清单和陷阱三类通用知识
- 在7个基准上平均提升11%-21%，能动态纠错并切换推理路径
- 大模型的记忆可指导小模型，体现良好可扩展性，适合资源有限场景
大型语言模型在求解优化问题时常因结构歧义而受阻，同一问题可能对应多个相互冲突的建模范式。为此，我们提出无训练的双簇记忆代理（DCM-Agent），通过历史解决方案增强性能。核心是双簇记忆构建：将历史解法分配至建模与编码簇，并分别提炼出方法、检查清单和陷阱三类结构化知识，形成可泛化的指导信息。此外，该代理引入记忆增强型推理机制，实现解题路径的动态导航、错误检测与修复，以及基于结构化知识的自适应路径切换。在七个优化基准上的实验表明，DCM-Agent实现了11%至21%的平均性能提升。值得注意的是，分析揭示了‘知识继承’现象：由大模型构建的记忆可引导小模型达到更优表现，凸显该框架的可扩展性与高效性。
原文摘要 · Abstract (English)
Large Language Models (LLMs) often struggle with structural ambiguity in optimization problems, where a single problem admits multiple related but conflicting modeling paradigms, hindering effective solution generation. To address this, we propose Dual-Cluster Memory Agent (DCM-Agent) to enhance performance by leveraging historical solutions in a training-free manner. Central to this is Dual-Cluster Memory Construction. This agent assigns historical solutions to modeling and coding clusters, then distills each cluster's content into three structured types: Approach, Checklist, and Pitfall. This process derives generalizable guidance knowledge. Furthermore, this agent introduces Memory-augmented Inference to dynamically navigate solution paths, detect and repair errors, and adaptively switch reasoning paths with structured knowledge. The experiments across seven optimization benchmarks demonstrate that DCM-Agent achieves an average performance improvement of 11%- 21%. Notably, our analysis reveals a ``knowledge inheritance'' phenomenon: memory constructed by larger models can guide smaller models toward superior performance, highlighting the framework's scalability and efficiency.
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