Dual-Cluster Memory Agent: Resolving Multi-Paradigm Ambiguity in Optimization Problem Solving

TL;DR

The paper introduces DCM-Agent, a novel approach that leverages structured memory and dynamic inference to resolve ambiguity in optimization problems, significantly improving performance across benchmarks.

Contribution

It presents a training-free memory-augmented framework that enhances optimization problem solving by structuring historical solutions and enabling adaptive reasoning.

Findings

Achieves 11%-21% performance improvement on seven benchmarks.

Memory constructed by larger models can guide smaller models effectively.

Introduces a dual-cluster memory construction and dynamic inference mechanism.

Abstract

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.