Large Language Models (LLMs) have demonstrated strong mathematical reasoning abilities through supervised fine-tuning and reinforcement learning. However, existing Process Reward Models (PRMs) are vulnerable to reward hacking and require expensive, large-scale annotation of reasoning steps, limiting their reliability and scalability. To address the first problem, we propose a novel reward model approach, Hierarchical Reward Model (HRM), which evaluates both individual and consecutive reasoning steps from fine-grained and coarse-grained level. HRM excels at assessing multi-step mathematical reasoning coherence, particularly in cases where a flawed step is later corrected through self-reflection. Furthermore, to address the inefficiency of autonomously annotating PRM training data via Monte Carlo Tree Search (MCTS), we propose a lightweight data augmentation strategy, Hierarchical Node Compression (HNC), which merges consecutive reasoning steps within the tree structure. Applying HNC to MCTS-generated reasoning trajectories increases the diversity and robustness of HRM training data, while introducing controlled noise with minimal computational overhead. Empirical results on the PRM800K dataset demonstrate that HRM, in conjunction with HNC, achieves superior stability and reliability in evaluation compared to PRM. Furthermore, cross-domain evaluations on MATH500 and GSM8K dataset confirm HRM’s superior generalization and robustness across diverse mathematical reasoning tasks.

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, an algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions. The StructuredOR dataset is available on Huggingface https://huggingface.co/datasets/LLM4OR/StructuredOR and GitHub https://github.com/LLM4OR/StructuredOR.