A Classifier to Decide on the Linearization of Mixed-Integer Quadratic Problems in CPLEX

With the aim of fully embedding learned predictions in the algorithmic design of a mixed-integer quadratic programming (MIQP) solver, we translate the algorithmic question of whether to linearize convex MIQPs into a classification task and use machine learning (ML) techniques to tackle it. We represent MIQPs and the linearization decision by careful target and feature engineering. Computational experiments and evaluation metrics are designed to further incorporate the optimization knowledge in the learning pipeline. As a practical result, a classifier deciding on MIQP linearization is successfully deployed in CPLEX 12.10.0: to the best of our knowledge, we establish the first example of an end-to-end integration of ML into a commercial optimization solver and ultimately contribute a general-purpose methodology for combining ML-based decisions and mixed-integer programming technology.