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    <abstract>Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently shown promise in automated MIP modeling from natural language, they prioritize semantic correctness but overlook formulation strength, severely bottlenecking the efficiency of downstream solvers. We propose FormuEvo, an LLM-guided evolutionary framework for automated discovery of solver-efficient MIP formulations. FormuEvo frames MIP formulation design as evolutionary optimization over the symbolic space of MIP formulations, represented as executable modeling programs, by iteratively generating, evaluating, and selecting stronger candidates via LLM-driven crossover, mutation, and repair operations. To move beyond blind exploration, FormuEvo introduces a solver-informed diagnosis mechanism that exploits fine-grained solver statistics as verbal gradients for targeted refinement. Additionally, a structured memory abstracts prior experience into reusable modeling strategies, avoiding redundant exploration while enabling zero-shot transfer to unseen problems and bootstrapping smaller LLMs. Experiments across diverse linear and non-linear problems demonstrate that FormuEvo discovers formulations that significantly outperform both expert-designed formulations and existing LLM-based approaches, accelerating solvers by up to 5.5\times, with distilled knowledge transferring effectively across problems and model scales.</abstract>
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%0 Conference Proceedings
%T FormuEvo: LLM-Guided Evolution for Discovering Solver-Efficient Mixed-Integer Programming Formulations
%A Yuan, Haofeng
%A Peng, Jianing
%A Bi, Jieyi
%A Zhang, Ni
%A Song, Shiji
%A Cao, Zhiguang
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F yuan-etal-2026-formuevo
%X Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently shown promise in automated MIP modeling from natural language, they prioritize semantic correctness but overlook formulation strength, severely bottlenecking the efficiency of downstream solvers. We propose FormuEvo, an LLM-guided evolutionary framework for automated discovery of solver-efficient MIP formulations. FormuEvo frames MIP formulation design as evolutionary optimization over the symbolic space of MIP formulations, represented as executable modeling programs, by iteratively generating, evaluating, and selecting stronger candidates via LLM-driven crossover, mutation, and repair operations. To move beyond blind exploration, FormuEvo introduces a solver-informed diagnosis mechanism that exploits fine-grained solver statistics as verbal gradients for targeted refinement. Additionally, a structured memory abstracts prior experience into reusable modeling strategies, avoiding redundant exploration while enabling zero-shot transfer to unseen problems and bootstrapping smaller LLMs. Experiments across diverse linear and non-linear problems demonstrate that FormuEvo discovers formulations that significantly outperform both expert-designed formulations and existing LLM-based approaches, accelerating solvers by up to 5.5\times, with distilled knowledge transferring effectively across problems and model scales.
%U https://aclanthology.org/2026.emnlp-main.221/
%P 5109-5135

Markdown (Informal)

[FormuEvo: LLM-Guided Evolution for Discovering Solver-Efficient Mixed-Integer Programming Formulations](https://aclanthology.org/2026.emnlp-main.221/) (Yuan et al., EMNLP 2026)

• FormuEvo: LLM-Guided Evolution for Discovering Solver-Efficient Mixed-Integer Programming Formulations (Yuan et al., EMNLP 2026)

ACL

• Haofeng Yuan, Jianing Peng, Jieyi Bi, Ni Zhang, Shiji Song, and Zhiguang Cao. 2026. FormuEvo: LLM-Guided Evolution for Discovering Solver-Efficient Mixed-Integer Programming Formulations. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 5109–5135, Budapest, Hungary. Association for Computational Linguistics.