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! 🔥
• 2025.10.11 - With the assistance of several OR experts, we systematically performed an item-by-item examination and revision of the IndustryOR dataset to correct all question errors.. Users can access the full, corrected version here IndustryOR_fixedV2.
• 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.
• 2025.05.17 - SIRL paper published on arXiv: Solver-Informed Reinforcement Learning for Optimization Modeling.

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, SIRL-Qwen2.5-7B-COPT, SIRL-Qwen2.5-32B-Gurobi and SIRL-Qwen2.5-32B-COPT 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	SIRL-Qwen2.5-7B-Gurobi
Gurobi-32B	SIRL-Qwen2.5-32B-Gurobi	SIRL-Qwen2.5-32B-Gurobi
COPT-7B	SIRL-Qwen2.5-7B-COPT	SIRL-Qwen2.5-7B-COPT
COPT-32B	SIRL-Qwen2.5-32B-COPT	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 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%	38.0%	30.5%	58.0%	61.0%
Gruobi-32B	SIRL-Qwen2.5-32B-Gurobi	98.0%	94.6%	61.1%	48.0%	45.8%	67.4%	69.2%
COPT-7B	SIRL-Qwen2.5-7B-COPT	95.1%	92.1%	53.1%	35.0%	29.5%	58.3%	59.6%
COPT-32B	SIRL-Qwen2.5-32B-COPT	98.4%	94.7%	72.4%	46.0%	39.8%	64.1%	69.2%

Note: Values marked with "*" are from original or reproduced papers with the criterion: relative error < 10⁻⁶.

• The code to reproduce the results of Gurobi version can be found in our Jupyter Notebook for Gurobi.
• The code to reproduce the results of COPT version can be found in our Jupyter Notebook for COPT.

Inference

Setup

To get started, clone SIRL and install the required packages:

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:

from transformers import AutoTokenizer
from rule_prompt_utils import gurobi_prompt_temp,copt_prompt_temp
from utils import extract_code_block, extract_obj
from vllm import SamplingParams, LLM
from langchain.prompts import PromptTemplate
import subprocess

sovler_name = 'gurobi'
# solver_name = 'copt'
# Load model and parameters for Gurobi
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=0.9,
            max_tokens=8192,
            repetition_penalty=1.02
        )
# Load model and parameters for COPT
#model = LLM("chenyitian-shanshu/SIRL-COPT",            
#            tensor_parallel_size=1,
#            trust_remote_code=True)
#tokenizer = AutoTokenizer.from_pretrained("chenyitian-shanshu/SIRL-COPT")
#sampling_params = SamplingParams(
#            n=1,
#            temperature=0.5,
#            top_p=0.9,
#            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 for Gurobi
zeroshot_prompt_system = PromptTemplate.from_template(gurobi_prompt_temp['system'])
zeroshot_prompt_user = PromptTemplate.from_template(gurobi_prompt_temp['user'])

# Load prompt template for COPT
#zeroshot_prompt_system = PromptTemplate.from_template(copt_prompt_temp['system'])
#zeroshot_prompt_user = PromptTemplate.from_template(copt_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,solver_name)
result = subprocess.run(['python3', '-c', code_snippet], capture_output=True, text=True, timeout=100)
obj = extract_obj(result.stdout,solver_name)
print(response_text)
print('optimal value is', obj)

Test Dataset

Our model's performance is evaluated using the following benchmark datasets: NL4OPT, IndustryOR, MAMO-EasyLP, MAMO-ComplexLP, OptMATH, and Optibench. We performed a quick review and correction on the NL4OPT, IndustryOR, MAMO-ComplexLP, and MAMO-EasyLP dataset. Table 1 summarizes the sample counts for each dataset before and after our revisions.

Dataset	Number Before Correction	Number After Correction
NL4OPT	245	245
MAMO_EasyLP	652	642
MAMO_ComplexLP	211	203
IndustryOR	100	100
OptMATH	166	166
Optibench	605	605

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:

{
    "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:

@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}
}