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

Despite modern solvers being able to tackle mixed-integer quadratic programming problems (MIQPs) for several years, the theoretical and computational implications of the employed resolution techniques are not fully grasped yet. An interesting question concerns the choice of whether to linearize the quadratic part of a convex MIQP: although in theory no approach dominates the other, the decision is typically performed during the preprocessing phase and can thus substantially condition the downstream performance of the solver. In “A Classifier to Decide on the Linearization of Mixed-Integer Quadratic Problems in CPLEX,” Bonami, Lodi, and Zarpellon use machine learning (ML) to cast a prediction on this algorithmic choice. The whole experimental framework aims at integrating optimization knowledge in the learning pipeline and contributes a general methodology for using ML in MIP technology. The workflow is fine-tuned to enable online predictions in the IBM-CPLEX solver ecosystem, and, as a practical result, a classifier deciding on MIQP linearization is successfully deployed in CPLEX 12.10.0. 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.