LLM4Branch: Large Language Model for Discovering Efficient Branching Policies of Integer Programs

TL;DR

This paper introduces LLM4Branch, a framework using Large Language Models to automatically discover efficient branching policies for MILP solvers, outperforming traditional heuristics and rivaling GPU-based models.

Contribution

The paper presents a novel LLM-based approach that generates executable branching policies optimized through end-to-end feedback, reducing reliance on expert demonstrations.

Findings

LLM4Branch achieves state-of-the-art results on MILP benchmarks.

The method is competitive with advanced GPU-based models.

Codes are publicly available at the provided GitHub link.

Abstract

Efficient branching policies are essential for accelerating Mixed Integer Linear Programming (MILP) solvers. Their design has long relied on hand-crafted heuristics, and now machine learning has emerged as a promising paradigm to automate this process. However, existing learning-based methods are often hindered by their dependence on expensive expert demonstrations and the gap between training objectives and the solver's end-to-end performance. In this work, we propose LLM4Branch, a novel framework that leverages Large Language Models (LLMs) to automate the discovery of efficient branching policies. Specifically, the discovered policy is an executable program with a program skeleton generated by the LLM and a parameter vector, which is optimized via a zeroth-order method over a few instances with their end-to-end performance feedback. Extensive experiments on standard MILP benchmarks demonstrate that LLM4Branch establishes a new state-of-the-art among CPU-based methods and achieves performance competitive with advanced GPU-based models. Codes are available at https://github.com/hzn18/LLM4Branch.