Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods

TL;DR

Distributional MIPLIB is a comprehensive multi-domain library of MILP problem distributions designed to advance machine learning-guided optimization methods, enabling more robust evaluation and improved performance across diverse real-world and synthetic instances.

Contribution

The paper introduces Distributional MIPLIB, a standardized, multi-domain MILP problem library that facilitates research and evaluation of ML-guided MILP solving techniques.

Findings

ML-guided variable branching performance varies across distributions.

Learning from mixed distributions improves generalization and performance.

The library enables more comprehensive and realistic benchmarking.

Abstract

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. In this paper, we introduce Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used, and classify them into different hardness levels. It will facilitate research in this area by enabling comprehensive evaluation on diverse and realistic domains. We empirically illustrate the benefits of using Distributional MIPLIB as a research vehicle in two ways. We evaluate the performance of ML-guided variable branching on previously unused distributions to identify potential areas for improvement. Moreover, we propose to learn branching policies from a mix of distributions, demonstrating that mixed distributions achieve better performance compared to homogeneous distributions when there is limited data and generalize well to larger instances. The dataset is publicly available at https://sites.google.com/usc.edu/distributional-miplib/home.