Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching

TL;DR

This paper introduces PreMIO, a data-driven framework that uses probabilistic multi-variable branching to accelerate mixed integer program solving, combining machine learning with theoretical guarantees.

Contribution

It presents a simple, flexible, and provably justified multi-variable branching method for MIP solving that leverages offline data and concentration inequalities.

Findings

Outperforms traditional MIP solvers on benchmark datasets.

Efficiently solves real-life MIP instances.

Provides theoretical guarantees for the branching procedure.

Abstract

In this paper, we propose a Pre-trained Mixed Integer Optimization framework (PreMIO) that accelerates online mixed integer program (MIP) solving with offline datasets and machine learning models. Our method is based on a data-driven multi-variable cardinality branching procedure that splits the MIP feasible region using hyperplanes chosen by the concentration inequalities. Unlike most previous ML+MIP approaches that either require complicated implementation or suffer from a lack of theoretical justification, our method is simple, flexible, provable, and explainable. Numerical experiments on both classical OR benchmark datasets and real-life instances validate the efficiency of our proposed method.