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---
license: mit
language:
- en
metrics:
- accuracy
base_model:
- Qwen/Qwen2.5-7B-Instruct
tags:
- code
- math
---
<h2 align="center"> Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling</h2>
<p align="center">
<!-- Yitian Chen<sup>*</sup>, Jingfan Xia<sup>*</sup>, Siyu Shao<sup></sup>, Dongdong Ge<sup>†</sup>, Yinyu Ye
<br>
<div align='center'>
<sup>*</sup>Equal Contribution, <sup>†</sup>Corresponding Authors
</div>
<p align="center">
<b>Cardinal Operations, China</b><br>
<b>Shanghai University of Finance and Economics</b><br>
<b>The University of Hong Kong</b><br>
<b>Antai School of Economics and Management, Shanghai Jiao Tong University</b><br>
<b>Department of Management Science and Engineering, Stanford University</b>
</p> -->
<p align="center" style="white-space: nowrap;">
<a href="https://arxiv.org/abs/2505.11792" style="display: inline-block;"><img src='https://img.shields.io/badge/Paper-SIRL-red'></a>
<a href="[https://huggingface.co/chenyitian-shanshu/SIRL](https://huggingface.co/chenyitian-shanshu/SIRL)" style="display: inline-block;"><img src='https://img.shields.io/badge/Model-%F0%9F%A4%97%20HuggingFace-yellow'></a>
<a href="[https://modelscope.cn/models/oneday88/SIRL-7B](https://modelscope.cn/models/oneday88/SIRL-7B)" style="display: inline-block;"><img src="https://img.shields.io/static/v1?label=Model&message=ModeScope&color=green"></a>
<a href="[https://github.com/Cardinal-Operations/SIRL](https://github.com/Cardinal-Operations/SIRL)" style="display: inline-block;"><img src='https://img.shields.io/badge/Github-SIRL-blue'></a>
</p>
</p>
## Updates
- **2025.09.19** - [Our paper](https://neurips.cc/virtual/2025/poster/119660) has been accepted for a poster presentation at NeurIPS 2025! 🔥
- **2025.09.28** - [SIRL-Qwen2.5-32B-COPT](https://huggingface.co/chenyitian-shanshu/SIRL-COPT32B), which leverages the COPT optimization solver, is publicly available on Hugging Face and ModelScope. This model integrates the COPT solver and achieves performance comparable to [SIRL-Qwen2.5-32B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL-Gurobi32B) across all optimization benchmarks.
- **2025.09.09** - [SIRL-Qwen2.5-32B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL-Gurobi32B), which leverages the Gurobi optimization solver, is publicly available on Hugging Face and ModelScope. This model integrates the Gurobi solver and achieves state-of-the-art performance, surpassing OpenAI-o3 and Deepseek-v3, and is comparable to Deepseek-R1 across various optimization benchmarks.
- **2025.09.02** - We performed a quick correction on the NL4OPT, IndustryOR, MAMO-ComplexLP, and MAMO-EasyLP dataset. We encourage other researchers to use these revised versions for their future work on LLMs for optimization modeling. A detailed description of the correction process can be found here [Benchmark Data Descriptions](https://github.com/Cardinal-Operations/SIRL/tree/main/test_data/). Users can also access the cleaned dataset on the Hugging Face Hub at: https://huggingface.co/datasets/chenyitian-shanshu/ORLMBenchmark.
- **2025.07.28** - [SIRL-Qwen2.5-7B-COPT](https://huggingface.co/chenyitian-shanshu/SIRL/tree/main/Copt) ,which leverages the COPT optimization solver, is publicly available on Hugging Face and ModelScope.
- **2025.05.20** - [SIRL-Qwen2.5-7B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL/tree/main) ,which leverages the Gurobi optimization solver, is publicly available on Hugging Face and ModelScope.
- **2025.05.17** - SIRL paper published on arXiv: [Solver-Informed Reinforcement Learning for Optimization Modeling](https://arxiv.org/abs/2505.11792).
## Overview & Examples
We introduce **SIRL (Solver-Informed Reinforcement Learning)**, a novel reasoning paradigm that integrates solver feedback with reinforcement learning to train large language models (LLMs) for optimization modeling. This approach represents the first application of Reinforcement Learning with Verifiable Reward (RLVR) in the domain of optimization modeling, enabling LLMs to generate accurate mathematical formulations and code generations from natural language descriptions. SIRL leverages solver outputs to iteratively refine model performance.
Our SIRL-Qwen2.5-32B model surpasses the performance of DeepSeek-V3 and OpenAI-O3 on optimization modeling benchmarks,demonstrating the effectiveness of our approach.
Currently, we offer LLM model checkpoints that seamlessly integrate with both Gurobi and COPT optimization solver.
COPT (Cardinal Optimizer) is a mathematical optimization solver for large-scale optimization problems developed by Cardinal Operations, and it includes high-performance solvers for LP, MIP, NLP and so on.
To explore its full functionalities or to request a trial, please visit the official website: www.shanshu.ai/copt.
## Model Release
The checkpoints of [SIRL-Qwen2.5-7B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL-Gurobi), [SIRL-Qwen2.5-7B-COPT](https://huggingface.co/chenyitian-shanshu/SIRL-COPT), [SIRL-Qwen2.5-32B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL-Gurobi32B) and [SIRL-Qwen2.5-32B-COPT](https://huggingface.co/chenyitian-shanshu/SIRL-COPT32B) are avaiable on Hugging Face and Model Scope.
Looking ahead, we aim to develop our next-generation LLM models to tackle a broader range of general optimization and mathematical tasks.
| Solver Type | Hugging Face | ModelScope |
|---------------------|---------------- | ---|
| Gurobi-7B | [SIRL-Qwen2.5-7B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL-Gurobi) | [SIRL-Qwen2.5-7B-Gurobi](https://modelscope.cn/models/oneday88/SIRL-7B) |
| Gurobi-32B | [SIRL-Qwen2.5-32B-Gurobi](https://huggingface.co/chenyitian-shanshu/SIRL-Gurobi32B) | [SIRL-Qwen2.5-32B-Gurobi](https://modelscope.cn/models/oneday88/sirl-qwen2-5-32b-gurobi) |
| COPT-7B | [SIRL-Qwen2.5-7B-COPT](https://huggingface.co/chenyitian-shanshu/SIRL-COPT) | [SIRL-Qwen2.5-7B-COPT](https://modelscope.cn/models/oneday88/sirl-qwen2-5-7b-copt) |
| COPT-32B | [SIRL-Qwen2.5-32B-COPT](https://huggingface.co/chenyitian-shanshu/SIRL-COPT32B) | [SIRL-Qwen2.5-32B-COPT](https://modelscope.cn/models/oneday88/sirl-qwen2-5-32b-copt) |
## Performance
We evaluated the performance of the proposed SIRL framework on four benchmarks: NL4OPT, MAMO, IndustryOR and OptMATH.
Performance is assessed based on the pass@1 accuracy(acc). Following the rigorous evaluation protocol proposed by OptMATH, a solution is considered valid if the relative error is less than 1e-6.
The performance metrics for [SIRL](https://huggingface.co/chenyitian-shanshu/SIRL) are as follows. The highest results are highlighted in bold.
| Types | Models | NL4OPT | MAMO Easy fixed | MAMO Complex fixed | IndustryOR | OptMATH_166 | OptiBench | Macro AVG |
|---------------|-------------------|--------|-----------|--------------|------------|---------|-----------|-----------|
| Baseline | GPT-4 | 89.0%* | 87.3%* | 49.3%* | 33.0%* | 16.6%* | 68.6%* | 57.4%* |
| | Deepseek-V3 | 95.9%* | 88.3%* | 50.2% | 37.0%* | 44.0% | **71.6%*** | 64.5%* |
| | DeepSeek-R1 | 82.4% | 87.2% | **67.9%** | **45.0%** | 40.4% | 66.4% | 61.9% |
| | OpenAI-O3 | 69.4% | 77.1% | 51.2% | 44.0% | 44.0% | 58.6% | 57.38% |
| Agent-based | OptiMUS | 78.8%* | 77.0%* | 43.6%* | 31.0%* | 20.2%* | 45.8%* | 49.4%* |
| Offline-learning | ORLM-LLaMA-3-8B | 85.7%* | 82.3%* | 37.4%* | 24.0%* | 2.6%* | 51.1%* | 47.2%* |
| | LLMOpt-Qwen2.5-14B | 80.3%* | 89.5%* | 44.1%* | 29.0%* | 12.5%* | 53.8%* | 51.1%* |
| | OptMATH-Qwen2.5-7B | 94.7%* | 86.5%* | 40.8% | 20.0%* | 24.4%* | 57.9%* | 55.8%* |
| | OptMATH-Qwen2.5-32B | 95.9%| 89.9%| 54.1%| 31.0% |34.7% |66.1% |62.0% |
| Gurobi-7B | SIRL-Qwen2.5-7B-Gurobi | 96.3%* | 91.7% | 51.7% | 33.0% | 30.5% | 58.0% | 60.2% |
| Gruobi-32B | SIRL-Qwen2.5-32B-Gurobi | 98.0% | 94.6%| 61.1% |42.0% |**45.8%** |67.4% |68.2% |
| COPT-7B | SIRL-Qwen2.5-7B-COPT| 95.1% | 92.1% | 53.1% | 31.0% | 29.5% | 58.3% | 58.9%|
| COPT-32B | SIRL-Qwen2.5-32B-COPT | **98.4%** | **94.7%** | **72.4%** | 41.0% | 39.8% | 64.1% | **68.4%** |
*Note:* Values marked with "*" are from original or reproduced papers with the criterion: relative error < 10⁻⁶.
The code to reproduce these results can be found in our [Jupyter Notebook](https://github.com/Cardinal-Operations/SIRL/blob/main/reproduce_gurobi.ipynb).
## Inference
### Setup
To get started, clone SIRL and install the required packages in the github:
```shell
pip install -r requirements.txt
```
Make sure that you have already apply for the license of solvers such as Gurobi or COPT.
We recommend using the following prompt template which can be found in [rule_prompt_utils.py](https://github.com/Cardinal-Operations/SIRL/blob/main/rule_prompt_utils.py). Please replace the {question} with any natural language OR question.
### Quick start
Below is a simple example for model inference:
```python
from transformers import AutoTokenizer
from rule_prompt_utils import gurobi_prompt_temp
from utils import extract_code_block, extract_obj
from vllm import SamplingParams, LLM
from langchain.prompts import PromptTemplate
import subprocess
# Load model and parameters
model = LLM("chenyitian-shanshu/SIRL-Gurobi",
tensor_parallel_size=1,
trust_remote_code=True)
tokenizer = AutoTokenizer.from_pretrained("chenyitian-shanshu/SIRL-Gurobi")
sampling_params = SamplingParams(
n=1,
temperature=0.5,
top_p=0.95,
max_tokens=8192,
repetition_penalty=1.02
)
# Load question. Here is just an example. Users can replace this with datasets they want to test
question = "An industrial tire company delivers large tires for equipment to remote engineering sites either by cargo planes or ultrawide trucks. Each cargo plane can transport 10 tires per trip and costs $1000. Each ultrawide truck can transport 6 tires per trip and costs $700. The company needs to transport at least 200 tires and has available $22000. Because most remote sites don't have proper airports, the number of plane trips cannot exceed the number of ultrawide truck trips. How many trips of each should be done to minimize the total number of trips?"
# Load prompt templete
zeroshot_prompt_system = PromptTemplate.from_template(gurobi_prompt_temp['system'])
zeroshot_prompt_user = PromptTemplate.from_template(gurobi_prompt_temp['user'])
prompt =[{"role": "system",
"content": zeroshot_prompt_system.format().strip() },
{"role": "user",
"content": zeroshot_prompt_user.format(question=question).strip() }]
# Generate Response
text = tokenizer.apply_chat_template(prompt, tokenize=False, add_generation_prompt=True)
response = model.generate(text,sampling_params)
response_text = response[0].outputs[0].text
code_snippet = extract_code_block(response_text,'gurobi')
result = subprocess.run(['python3', '-c', code_snippet], capture_output=True, text=True, timeout=100)
obj = extract_obj(result.stdout,'gurobi')
print(response_text)
print('optimal value is', obj)
```
## Test Dataset
We evaluate the performance of our trained model on multiple datasets
which include NL4OPT, MAMO, IndustryOR, OptMATH.
Minor errors exist within these testing datasets.
To address this, we rigorously reviewed and corrected the test sets of these benchmarks, updating the questions and corresponding answers to ensure the integrity of our evaluation, with a specific focus on the NL4OPT and IndustryOR dataset. The datasets are available at [https://github.com/Cardinal-Operations/SIRL/tree/main/test_data](https://github.com/Cardinal-Operations/SIRL/tree/main/test_data).
### Data Structure
Each dataset is organized in a `jsonl` file, with each line containing an independent data entry. Each entry includes:
- `en_question`: A string description of the optimization problem.
- `en_answer`: The ground truth objective function value (float). The answers of infeasible problems are "No Best Solution" or "-99999"
An example from NL4OPT:
```json
{
"en_question": "A company needs to minimize shipping costs across 5 warehouses with varying demands...",
"en_answer": 1250.50,
}
```
## Citation
If you find SILR useful or relevant to your research, please consider citing our paper:
```bibtex
@article{chen2025solver,
title={Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling},
author={Chen, Yitian and Xia, Jingfan and Shao, Siyu and Ge, Dongdong and Ye, Yinyu},
journal={arXiv preprint arXiv:2505.11792},
year={2025}
}
```

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