OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning

Abstract

Optimization modeling and solving are fundamental to the application of Operations Research (OR) in real-world decision making, yet the process of translating natural language problem descriptions into formal models and solver code remains highly expertise intensive. While recent advances in large language models (LLMs) have opened new opportunities for automation, the generalization ability and data efficiency of existing LLM-based methods are still limited, asmost require vast amounts of annotated or synthetic data, resulting in high costs and scalability barriers. In this work, we present OR-R1, a data-efficient training framework for automated optimization modeling and solving. OR-R1 first employs supervised fine-tuning (SFT) to help the model acquire the essential reasoning patterns for problem formulation and code generation from limited labeled data. In addition, it improves the capability and consistency through Test-Time Group Relative Policy Optimization (TGRPO). This two-stage design enables OR-R1 to leverage both scarce labeled and abundant unlabeled data for effective learning. Experiments show that OR-R1 achieves state-of-the-art performance with an average solving accuracy of 67.7%, using only 1/10 the synthetic data required by prior methods such as ORLM, exceeding ORLM’s solving accuracy by up to 4.2%. Remarkably, OR-R1 outperforms ORLM by over 2.4% with just 100 synthetic samples. Furthermore, TGRPO contributes an additional 3.1%–6.4% improvement in accuracy, significantly narrowing the gap between single-attempt (Pass@1) and multi-attempt (Pass@8) performance from 13% to 7%. Extensive evaluations across diverse real-world benchmarks demonstrate that OR-R1 provides a robust, scalable, and cost-effective solution for automated OR optimization problem modeling and solving, lowering the expertise and data barriers for industrial OR applications.