# SemOPT: Fixing Semantic Errors in LLM-based Optimization Modeling via Reward-Guided Search

arXiv: https://arxiv.org/abs/2609.37361 · HTML: https://mlsanity.com/paper/2609.37361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

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

- [How Abilities in Large Language Models are Affected by Supervised Fine-tuning Data Composition](https://mlsanity.com/paper/2310.05492/) (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)
- [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)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [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)
- [Dynamic Parallel Tree Search for Efficient LLM Reasoning](https://mlsanity.com/paper/2502.16235/) (2025)
- [SuperCorrect: Advancing Small LLM Reasoning with Thought Template Distillation and Self-Correction](https://mlsanity.com/paper/2410.09008/) (2024)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [SolverLLM: Leveraging Test-Time Scaling for Optimization Problem via LLM-Guided Search](https://mlsanity.com/paper/2510.16916/) (2025)
- [MITS: Enhanced Tree Search Reasoning for LLMs via Pointwise Mutual Information](https://mlsanity.com/paper/2510.03632/) (2025)
- [SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling](https://mlsanity.com/paper/2510.05115/) (2025)
- [Enhancing Source Code Security with LLMs: Demystifying The Challenges and Generating Reliable Repairs](https://mlsanity.com/paper/2409.00571/) (2024)
- [OptiVerse: A Comprehensive Benchmark towards Optimization Problem Solving](https://mlsanity.com/paper/2604.21510/) (2026)
- [A Semantic-based Optimization Approach for Repairing LLMs: Case Study on Code Generation](https://mlsanity.com/paper/2503.12899/) (2025)
- [SemGuard: Real-Time Semantic Evaluator for Correcting LLM-Generated Code](https://mlsanity.com/paper/2509.24507/) (2025)

## Abstract (arXiv)

Operations research supports decision-making in domains such as energy, economics, and healthcare. Solving operations research problems typically begins with optimization modeling, which translates a natural-language problem description into executable solver code. LLMs offer a promising way to automate this process, but they remain prone to errors. In practice, these errors can be divided into two categories: syntactic errors refer to solver code that fails to run successfully or is judged infeasible by the solver; semantic errors refer to solver code that successfully returns an objective value but violates the intent of the original problem. Since semantic errors do not trigger runtime failures, they are difficult to detect and rectify. To address this problem, we introduce SemOPT, a semantic-guided framework for correcting LLM-based optimization models. SemOPT combines a semantic reward model that distinguishes faithful math models from plausible but incorrect ones with an adaptive correction system that applies hierarchical reward-guided search over the modeling space. Experiments on seven optimization modeling benchmarks show that SemOPT establishes a new state of the art and achieves an average 7.6% accuracy improvement over the strongest baseline on complex datasets.