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

Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains challenging for current large language models (LLMs). In this paper, we propose \emph{Agora-Opt}, a modular agentic framework for optimization modeling that combines decentralized debate with a read-write memory bank. Agora-Opt allows multiple agent teams to independently produce end-to-end solutions and reconcile them through an outcome-grounded debate protocol, while memory stores solver-verified artifacts and past disagreement resolutions to support training-free improvement over time. This design is flexible across both backbones and methods: it reduces base-model lock-in, transfers across different LLM families, and can be layered onto existing pipelines with minimal coupling. Across public benchmarks, Agora-Opt achieves the strongest overall performance among all compared methods, outperforming strong zero-shot LLMs, training-centric approaches, and prior agentic baselines. Further analyses show robust gains across backbone choices and component variants, and demonstrate that decentralized debate offers a structural advantage over centralized selection by enabling agents to refine candidate solutions through interaction and even recover correct formulations when all initial candidates are flawed. These results suggest that reliable optimization modeling benefits from combining collaborative cross-checking with reusable experience, and position Agora-Opt as a practical and extensible foundation for trustworthy optimization modeling assistance. Our code and data are available at https://github.com/CHIANGEL/Agora-Opt.

Large language model (LLM) agents operate in dynamic environments where knowledge continuously evolves. Existing memory systems typically treat external memory as a monotonically growing repository, inevitably leading to retrieval degradation and increasing computational costs over time. We argue that the core challenge is not retrieval alone, but managing the knowledge lifecycle: deciding what to externalize, update, or ultimately internalize. Inspired by Complementary Learning Systems (CLS) theory in neuroscience, we propose Dual-Layer Agentic Memory, a framework that shifts memory management to the write phase through cost-aware epistemic routing and periodic parametric consolidation. Incoming information is categorized as non-write, write-new, or write-update, and routed through a small-to-large model cascade that minimizes routing overhead while filtering redundant memories. A subsequent write-back phase selectively consolidates high-value external memories into model parameters via supervised fine-tuning. Experiments demonstrate the dual efficiency of our approach: a 1.7B/8B cascade prunes up to 68% of redundant external memory while escalating fewer than 50% of inputs, yet retains over 98% of the downstream QA Exact Match (EM) achieved by an exhaustive retention baseline. We further show that periodic consolidation successfully internalizes external knowledge, allowing the router to adaptively suppress redundant writes as the model's epistemic boundaries evolve. Overall, our framework presents a unified paradigm for agent memory: selective externalization followed by selective internalization. Code and dataset will be released upon acceptance.

Leveraging Large Language Models (LLMs) to automatically formulate and solve optimization problems from natural language has emerged as an efficient paradigm for automated optimization. However, existing methods still exhibit limited generalization: they are sensitive to superficial narrative variations, reuse experience mainly at the case level, and struggle to adapt to shifted or emerging problem types. We propose OptSkills, an archetype-centric skill learning and reasoning agent system for optimization modeling and solving. To improve robust generalization, our system clusters problems by their underlying archetypes rather than surface narratives. To improve in-distribution generalization, it explores diverse modeling paradigms and solver configurations within each cluster, then distills successful trajectories into reusable workflow-level skills. To improve out-of-distribution generalization, it refines existing skills or expands the skill library using newly obtained trajectories. Our system achieves a state-of-the-art micro-averaged accuracy of 68.27% on datasets encompassing diverse problem types and scenarios. In addition, on MIPLIB-NL, a highly challenging large-scale and high-dimensional benchmark, it achieves 26.91% accuracy, outperforming DeepSeek-V3.2-Thinking by 4.53%. After skill learning on Nano-CO, it reaches 72.79% on the OOD NLCO benchmark. Code and skills are available at https://github.com/fujiwaranoM0kou/OptSkills.