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

2026-04-22

AI Summary

This work addresses the modeling ambiguities and solving difficulties that large language models (LLMs) often encounter when tackling optimization problems due to structural inconsistencies across multiple paradigms. To resolve this, the authors propose the Dual-Cluster Memory Agent (DCM-Agent), a training-free framework that constructs two types of memory clusters—“modeling paradigms” and “encoding implementations”—from historical solutions. These clusters are distilled into structured knowledge comprising methods, checklists, and pitfalls, enabling dynamic reasoning path selection and error correction. The approach introduces a novel dual-cluster memory mechanism and a memory-augmented reasoning framework that facilitates cross-model knowledge inheritance, allowing smaller models to effectively leverage memories generated by larger ones. Evaluated on seven optimization benchmarks, DCM-Agent achieves average performance gains of 11%–21%, demonstrating its effectiveness, scalability, and capacity for cross-model knowledge transfer.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• structural ambiguity
• optimization problems
• modeling paradigms
• large language models
• multi-paradigm ambiguity

Innovation

• Dual-Cluster Memory
• Memory-augmented Inference
• Optimization Problem Solving
• Structural Ambiguity
• Knowledge Inheritance