Configuring Mixed-Integer Linear Programming Solvers with Deep Metric Learning

Abdelrahman Hosny, Sherief Reda

Keywords: Mixed Integer Linear Programming, Metric Learning, Algorithm Configuration

TL;DR: We learn similarities among MILP problem instances using deep metric learning to predict an instance-specific solver configuration

Abstract: Mixed Integer Linear Programming (MILP) solvers expose a large number of configuration parameters for their internal algorithms. Solutions, and their associated costs or runtimes, are significantly affected by the choice of the configuration parameters, even when problem instances are coming from the same distribution. On one hand, using the default solver configuration leads to poor suboptimal solutions. On the other hand, searching and evaluating an exponential number of configurations for every problem instance is time-consuming and in some cases infeasible. In this work, we propose MILPTune -- a machine learning-based approach to predict an instance-aware parameters configuration for MILP solvers. It enables avoiding the expensive search of configuration parameters for each new problem instance, while tuning the solver's behavior for the given instance. Our method trains a metric learning model based on a graph neural network to project problem instances to a space where instances with similar costs are closer to each other. At inference time, and given a new problem instance, we first embed the instance to the learned metric space, and then predict a parameters configuration using nearest neighbor data. Empirical results on real-world problem benchmarks show that our method predicts configuration parameters that improve solutions' costs by 10-67% compared to the baselines and previous approaches.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Optimization (eg, convex and non-convex optimization)