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.

翻译：[译摘要] 优化建模支撑着物流、制造、能源和公共服务等领域的现实决策，但当前大语言模型仍难以从自然语言需求中可靠地解决此类问题。本文提出Agora-Opt——一个面向优化建模的模块化智能体框架，它结合去中心化辩论与读写记忆库。Agora-Opt允许多个智能体团队独立产生端到端解决方案，并通过基于结果验证的辩论协议协调分歧，同时记忆库存储求解器验证过的工件及历史分歧解决记录，以支持无需重新训练的持续改进。该设计在主干模型和方法层面均具灵活性：既减少对基座模型的锁定依赖，又可跨不同LLM家族迁移，并能以最小耦合度集成到现有流程中。在公开基准测试中，Agora-Opt在所有对比方法中取得最佳整体性能，超越强零样本LLM、以训练为中心的方法及先前的智能体基线。进一步分析表明，该方法在不同主干模型选择与组件变体下均具有稳健增益，并证明去中心化辩论相比集中式选择具有结构性优势——智能体可通过交互优化候选方案，甚至在所有初始候选方案均有缺陷时恢复正确公式。这些结果表明，可靠优化建模受益于协作性交叉验证与可重用经验的结合，同时也将Agora-Opt定位为可信赖优化建模助手的实用可扩展基础。我们的代码与数据开源于https://github.com/CHIANGEL/Agora-Opt。