# Execution-Verified Reinforcement Learning for Optimization Modeling

arXiv: https://arxiv.org/abs/2604.00442 · HTML: https://mlsanity.com/paper/2604.00442/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 22 of 22)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [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)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [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)
- [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)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.09092/) (2025)
- [Cardinal Optimizer (COPT) User Guide](https://mlsanity.com/paper/2208.14314/) (2022)

## Built on by (most cited first, 2 of 2)

- [Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limits](https://mlsanity.com/paper/2607.16646/) (2026)
- [Learning to Optimize through Solver-Grounded Self-Play](https://mlsanity.com/paper/2609.34205/) (2026)

## Abstract (arXiv)

Automating optimization modeling with LLMs is a promising path toward scalable decision intelligence, but existing approaches either rely on agentic pipelines built on closed-source LLMs with high inference latency, or fine-tune smaller LLMs using costly process supervision that often overfits to a single solver API. Inspired by reinforcement learning with verifiable rewards, we propose Execution-Verified Optimization Modeling (EVOM), an execution-verified learning framework that treats a mathematical programming solver as a deterministic, interactive verifier. Given a natural-language problem and a target solver, EVOM generates solver-specific code, executes it in a sandboxed harness, and converts execution outcomes into scalar rewards, optimized with GRPO and DAPO in a closed-loop generate-execute-feedback-update process. This outcome-only formulation removes the need for process-level supervision, and enables cross-solver generalization by switching the verification environment rather than reconstructing solver-specific datasets. Experiments on NL4OPT, MAMO, IndustryOR, and OptiBench across Gurobi, OR-Tools, and COPT show that EVOM matches or outperforms process-supervised SFT, supports zero-shot solver transfer, and achieves effective low-cost solver adaptation by continuing training under the target solver backend.