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

Abstract

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.