Random sampling and machine learning to understand good decompositions

Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIPs), we address a fundamental research question, that is how to exploit data-driven techniques to obtain automatic decomposition methods. We preliminary investigate the link between static properties of MIP input instances and good decomposition patterns. We devise a random sampling algorithm, considering a set of generic MIP base instances, and generate a large, balanced and well diversified set of decomposition patterns, that we analyze with machine learning tools. We also propose and test a minimal proof of concept framework performing data-driven automatic decomposition. The use of supervised techniques highlights interesting structures of random decompositions, as well as proving (under certain conditions) that data-driven methods are fruitful in our context, triggering at the same time perspectives for future research.