Zi Ling

Yitian Chen, Cheng Cheng, Yinan Sun et al.

Large Language Models (LLMs) have demonstrated impressive progress in optimization modeling, fostering a rapid expansion of new methodologies and evaluation benchmarks. However, the boundaries of their capabilities in automated formulation and problem solving remain poorly understood, particularly when extending to complex, real-world tasks. To bridge this gap, we propose OPT-ENGINE, an extensible benchmark framework designed to evaluate LLMs on optimization modeling with controllable and scalable difficulty levels. OPT-ENGINE spans 10 canonical tasks across operations research, with five Linear Programming and five Mixed-Integer Programming. Utilizing OPT-ENGINE, we conduct an extensive study of LLMs' reasoning capabilities, addressing two critical questions: 1.) Do LLMs' performance remain robust when generalizing to out-of-distribution optimization tasks that scale in complexity beyond current benchmark levels? and 2.) At what stage, from problem interpretation to solution generation, do current LLMs encounter the most significant bottlenecks? Our empirical results yield two key insights: first, tool-integrated reasoning with external solvers exhibits significantly higher robustness as task complexity escalates, while pure-text reasoning reaches a ceiling; second, the automated formulation of constraints constitutes the primary performance bottleneck. These findings provide actionable guidance for developing next-generation LLMs for advanced optimization. Our code is publicly available at \textcolor{blue}{https://github.com/Cardinal-Operations/OPTEngine}.

Jianghao Lin, Zi Ling, Chenyu Zhou et al.

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.