# Grammar-Aware Literate Generative Mathematical Programming with Compiler-in-the-Loop

arXiv: https://arxiv.org/abs/2601.17670 · HTML: https://mlsanity.com/paper/2601.17670/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Scaling Large Language Model-based Multi-Agent Collaboration](https://mlsanity.com/paper/2406.07155/) (2024)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (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)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [Grammar Prompting for Domain-Specific Language Generation with Large Language Models](https://mlsanity.com/paper/2305.19234/) (2023)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://mlsanity.com/paper/2502.14760/) (2025)

## Built on by (most cited first, 1 of 1)

- [Agentic AI-Assisted Modeling for Production Scheduling: Assessment in Constraint Programming](https://mlsanity.com/paper/2610.10184/) (2026)

## Abstract (arXiv)

Mathematical programming is widely employed across various sectors - such as logistics, energy, and workforce planning - to model and solve industrial optimisation problems, but its use requires substantial domain expertise. Large language models offer a promising way to translate natural-language problem descriptions into optimisation models, yet existing approaches are costly and generally produce models written in general-purpose computer code (e.g. Python), which can be difficult to inspect, validate, and reuse. In this work, we introduce SyntAGM, a system that generates optimisation models in a readable algebraic modelling language through an iterative generate-compile-assess-revise loop. SyntAGM leverages PyOPL, an OPL-like modelling language compiler designed to provide actionable feedback for iterative model repair. To obtain a valid PyOPL model that matches the problem description, SyntAGM mobilises compiler feedback and an LLM-based alignment judge. In addition, it combines in-context exposure to the target language grammar, and few-shot retrieval of modelling exemplars. Across multiple benchmarks, SyntAGM achieves a more favourable cost-quality trade-off compared to established prompting baselines.