Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling
Updates
2025.09.19 - Our paper has been accepted for a poster presentation at NeurIPS 2025! 🔥
2025.09.28 - SIRL-Qwen2.5-32B-COPT, 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 across all optimization benchmarks.
2025.09.09 - SIRL-Qwen2.5-32B-Gurobi, 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. 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 ,which leverages the COPT optimization solver, is publicly available on Hugging Face and ModelScope.
2025.05.20 - SIRL-Qwen2.5-7B-Gurobi ,which leverages the Gurobi optimization solver, is publicly available on Hugging Face and ModelScope.
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.
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 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.
Inference
Setup
To get started, clone SIRL and install the required packages in the github:
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. Please replace the {question} with any natural language OR question.
Quick start
Below is a simple example for model inference:
python
1from transformers import AutoTokenizer
2from rule_prompt_utils import gurobi_prompt_temp
3from utils import extract_code_block, extract_obj
4from vllm import SamplingParams, LLM
5from langchain.prompts import PromptTemplate
6import subprocess
78# Load model and parameters9model = LLM("chenyitian-shanshu/SIRL-COPT",10 tensor_parallel_size=1,11 trust_remote_code=True)12tokenizer = AutoTokenizer.from_pretrained("chenyitian-shanshu/SIRL-COPT")13sampling_params = SamplingParams(14 n=1,15 temperature=0.5,16 top_p=0.95,17 max_tokens=8192,18 repetition_penalty=1.0219)2021# Load question. Here is just an example. Users can replace this with datasets they want to test22question ="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?"2324# Load prompt templete25zeroshot_prompt_system = PromptTemplate.from_template(gurobi_prompt_temp['system'])26zeroshot_prompt_user = PromptTemplate.from_template(gurobi_prompt_temp['user'])27prompt =[{"role":"system",28"content": zeroshot_prompt_system.format().strip()},29{"role":"user",30"content": zeroshot_prompt_user.format(question=question).strip()}]3132# Generate Response33text = tokenizer.apply_chat_template(prompt, tokenize=False, add_generation_prompt=True)34response = model.generate(text,sampling_params)35response_text = response[0].outputs[0].text
36code_snippet = extract_code_block(response_text,'gurobi')37result = subprocess.run(['python3','-c', code_snippet], capture_output=True, text=True, timeout=100)38obj = extract_obj(result.stdout,'gurobi')39print(response_text)40print('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.
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
1{2"en_question":"A company needs to minimize shipping costs across 5 warehouses with varying demands...",3"en_answer":1250.50,4}
Citation
If you find SILR useful or relevant to your research, please consider citing our paper:
bibtex
1@article{chen2025solver,
2 title={Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling},
3 author={Chen, Yitian and Xia, Jingfan and Shao, Siyu and Ge, Dongdong and Ye, Yinyu},
4 journal={arXiv preprint arXiv:2505.11792},
5 year={2025}
6}
