# PEARL: Solver-in-the-Loop Interactive Optimization Modeling from Natural Language

arXiv: https://arxiv.org/abs/2607.18256 · HTML: https://mlsanity.com/paper/2607.18256/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 27 of 27)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Small Language Models are the Future of Agentic AI](https://mlsanity.com/paper/2506.02153/) (2025)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [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)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [AgentRL: Scaling Agentic Reinforcement Learning with a Multi-Turn, Multi-Task Framework](https://mlsanity.com/paper/2510.04206/) (2025)
- [rStar2-Agent: Agentic Reasoning Technical Report](https://mlsanity.com/paper/2508.20722/) (2025)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Octopus v2: On-device language model for super agent](https://mlsanity.com/paper/2404.01744/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://mlsanity.com/paper/2509.22558/) (2025)
- [MM-Agent: LLM as Agents for Real-world Mathematical Modeling Problem](https://mlsanity.com/paper/2505.14148/) (2025)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://mlsanity.com/paper/2407.07924/) (2024)
- [OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.09092/) (2025)
- [Synthesis of Mathematical programs from Natural Language Specifications](https://mlsanity.com/paper/2304.03287/) (2023)
- [CALM Before the STORM: Unlocking Native Reasoning for Optimization Modeling](https://mlsanity.com/paper/2510.04204/) (2025)

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

- [Right Answers, Costly Models: The Efficiency Gap in LLM-based Optimization Modeling](https://mlsanity.com/paper/2609.38884/) (2026)

## Abstract (arXiv)

Optimization modeling is the process of translating real-world decision problems, often described in natural language, into formal mathematical formulations and executable solver code. While recent advances in large language models have shown promise in automating this process, most existing approaches remain one-shot: a model produces a formulation once, without executing it, conditioning on solver feedback, or iteratively revising errors. This stands in sharp contrast to real-world optimization modeling, which is inherently interactive and proceeds through repeated solve-debug-revise cycles. We introduce PEARL, a system for interactive optimization modeling that uses Python execution and mathematical programming solvers inside this loop. Rather than relying on a fixed repair workflow, PEARL learns when to test partial models, how to revise from solver diagnostics, and when to stop. It operates in a multi-turn tool-integrated setting where intermediate execution results, feasibility signals, and solution checks are used to improve both formulations and solver code before finalization. Across diverse optimization benchmarks, PEARL substantially improves verified solve rates over strong one-shot and tool-augmented baselines; notably, our PEARL-Qwen3-4B model outperforms the much larger DeepSeek-V3.2-685B in both macro- and micro-averaged accuracy on optimization modeling tasks.