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

arXiv: https://arxiv.org/abs/2604.20183 · HTML: https://mlsanity.com/paper/2604.20183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agent memory systems, one of 16 directions in LLM agents and tool use.
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Placed in

- LLM agents and tool use / [Agent memory systems](https://mlsanity.com/agents/agent-memory-systems/)

## Builds on (most cited first, 18 of 18)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [PhysReason: A Comprehensive Benchmark towards Physics-Based Reasoning](https://mlsanity.com/paper/2502.12054/) (2025)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [MM-Agent: LLM as Agents for Real-world Mathematical Modeling Problem](https://mlsanity.com/paper/2505.14148/) (2025)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
- [ORMind: A Cognitive-Inspired End-to-End Reasoning Framework for Operations Research](https://mlsanity.com/paper/2506.01326/) (2025)
- [CoFFT: Chain of Foresight-Focus Thought for Visual Language Models](https://mlsanity.com/paper/2509.22010/) (2025)
- [AutoOpt: A Dataset and a Unified Framework for Automating Optimization Problem Solving](https://mlsanity.com/paper/2510.21436/) (2025)

## Abstract (arXiv)

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.