OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling

TL;DR

OptiTree introduces a hierarchical tree search method that adaptively decomposes complex optimization problems into simpler subproblems, significantly improving modeling accuracy for operations research tasks using large language models.

Contribution

It presents a novel tree search approach for hierarchical problem decomposition, enhancing LLM-based optimization modeling for complex OR problems.

Findings

Achieves over 10% improvement in modeling accuracy on benchmarks.

Effectively decomposes complex problems into simpler subproblems.

Outperforms state-of-the-art methods in OR modeling accuracy.

Abstract

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10\% improvements on the challenging benchmarks. The code is released at https://github.com/MIRALab-USTC/OptiTree/tree/main.