Solving Recurrent MIPs with Semi-supervised Graph Neural Networks

TL;DR

This paper introduces a semi-supervised graph neural network model that predicts variable values to efficiently solve mixed-integer programs, especially in sequential, real-world scenarios like transportation and routing.

Contribution

It is the first to leverage the sequential nature of problem instances and train with unlabeled data, improving solution speed and accuracy for MIPs.

Findings

Outperforms existing ML-based optimization methods.

Effective in semi-supervised training with unlabeled instances.

Provides a systematic way to convert probabilistic predictions into integral solutions.

Abstract

We propose an ML-based model that automates and expedites the solution of MIPs by predicting the values of variables. Our approach is motivated by the observation that many problem instances share salient features and solution structures since they differ only in few (time-varying) parameters. Examples include transportation and routing problems where decisions need to be re-optimized whenever commodity volumes or link costs change. Our method is the first to exploit the sequential nature of the instances being solved periodically, and can be trained with ``unlabeled'' instances, when exact solutions are unavailable, in a semi-supervised setting. Also, we provide a principled way of transforming the probabilistic predictions into integral solutions. Using a battery of experiments with representative binary MIPs, we show the gains of our model over other ML-based optimization approaches.