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

混合整数线性规划（MILP）是建模组合优化问题的基本工具。最近，越来越多的研究使用机器学习加速MILP求解。尽管这种方法越来越受欢迎，但缺乏一个提供不同领域、不同难度级别、标准化测试集的类似MILP实例分布的共同存储库。本文介绍了分布式MIPLIB，这是一个多领域问题分布库，用于推进ML引导的MILP方法。我们从现有工作和未使用的实际问题中策划MILP分布，并将它们分类为不同的难度级别。它将通过在不同和现实领域上进行全面评估来促进这一领域的研究。我们通过两种方式实证了使用分布式MIPLIB作为研究工具的好处。我们评估了ML引导变量分支在以前未使用的分布上的性能，以确定潜在的改进领域。此外，我们建议从不同的分布中学习分支策略，证明混合分布相对于同质分布在数据有限且对更大的实例具有良好的推广能力时具有更好的性能。

Distributional MIPLIB: A Multi-Domain Library of Problem Distributions for Machine Learning-Guided MILP

The paper introduces Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods, which curates MILP distributions from existing work and real-world problems and classifies them into different hardness levels. The paper proposes to use Distributional MIPLIB as a research vehicle to evaluate the performance of ML-guided variable branching on previously unused distributions and to learn branching policies from a mix of distributions.

The paper provides a common repository of MILP instances across different domains and hardness levels, facilitating comprehensive evaluation on diverse and realistic domains. The paper empirically illustrates the benefits of using Distributional MIPLIB as a research vehicle by evaluating the performance of ML-guided variable branching and proposing to learn branching policies from a mix of distributions. The paper also discusses the limitations of the current approach and suggests future research directions.

Recent related work includes 'Learning to Branch in Mixed Integer Programming' by Khalil et al., 'Learning Combinatorial Optimization Algorithms over Graphs' by Bello et al., and 'Accelerating Branch-and-Bound via Reinforcement Learning' by Jin et al.