BPP-Search: Enhancing Tree of Thought Reasoning for Mathematical Modeling Problem Solving

TL;DR

This paper introduces BPP-Search, a reinforcement learning-based algorithm that enhances tree-of-thought reasoning for mathematical modeling, supported by a new comprehensive dataset, StructuredOR, to improve accuracy and efficiency in problem solving.

Contribution

The paper presents BPP-Search, a novel tree search algorithm integrating reinforcement learning with beam search and preference modeling, and releases StructuredOR, a detailed dataset for mathematical modeling tasks.

Findings

BPP-Search outperforms state-of-the-art methods in accuracy and efficiency.

StructuredOR dataset enables better training and evaluation of reasoning models.

BPP-Search achieves faster retrieval of correct solutions in complex datasets.

Abstract

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.