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

arXiv: https://arxiv.org/abs/2411.17404 · HTML: https://mlsanity.com/paper/2411.17404/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [TaskBench: Benchmarking Large Language Models for Task Automation](https://mlsanity.com/paper/2311.18760/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [Leveraging Large Language Models for Solving Rare MIP Challenges](https://mlsanity.com/paper/2409.04464/) (2024)

## Built on by (most cited first, 15 of 15)

- [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://mlsanity.com/paper/2509.22558/) (2025)
- [Towards Hierarchical Multi-Step Reward Models for Enhanced Reasoning in Large Language Models](https://mlsanity.com/paper/2503.13551/) (2025)
- [Ontology-Guided Reverse Thinking Makes Large Language Models Stronger on Knowledge Graph Question Answering](https://mlsanity.com/paper/2502.11491/) (2025)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [ColorBrowserAgent: Complex Long-Horizon Browser Agent with Adaptive Knowledge Evolution](https://mlsanity.com/paper/2601.07262/) (2026)
- [SAGE: Strategy-Adaptive Generation Engine for Query Rewriting](https://mlsanity.com/paper/2506.19783/) (2025)
- [Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization](https://mlsanity.com/paper/2508.18091/) (2025)
- [OSCAR: Optimization-Steered Agentic Planning for Composed Image Retrieval](https://mlsanity.com/paper/2602.08603/) (2026)
- [Automated Reformulation of Robust Optimization via Memory-Augmented Large Language Models](https://mlsanity.com/paper/2605.11813/) (2026)
- [StarOR: Synergizing Tree Search and Test-Time Reinforcement Learning for Optimization Modeling](https://mlsanity.com/paper/2606.15197/) (2026)
- [MiniOpt: Reasoning to Model and Solve General Optimization Problems with Limited Resources](https://mlsanity.com/paper/2606.25832/) (2026)
- [Domain-Specialized Tree of Thought through Plug-and-Play Predictors](https://mlsanity.com/paper/2603.20267/) (2026)
- [Beyond Fixed Budgets: Characterizing the Inelasticity and Limitations of Tree-of-Thought Reasoning Strategies](https://mlsanity.com/paper/2606.20599/) (2026)
- [Beyond Verified Answers: Solver-Informed Self-Distillation for Bootstrapping Operations Research Language Models](https://mlsanity.com/paper/2609.09957/) (2026)
- [OptiSkill: A Hierarchical and Evolving SkillBank for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2609.22987/) (2026)

## Abstract (arXiv)

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.