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

Pierre Bonami(pierre.bonami***at***es.ibm.com)
Andrea Lodi(andrea.lodi***at***polymtl.ca)
Giulia Zarpellon(giulia.zarpellon***at***polymtl.ca)

Abstract: We translate the algorithmic question of whether to linearize convex Mixed-Integer Quadratic Programming problems (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 learned predictions and Mixed-Integer Programming technology.

Keywords: mixed-integer quadratic programming, machine learning, classification, linearization

Category 1: Integer Programming

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Optimization Software and Modeling Systems (Optimization Software Design Principles )

Citation: Technical Report, Polytechnique Montreal, March 2020

Download: [PDF]

Entry Submitted: 03/04/2020
Entry Accepted: 03/04/2020
Entry Last Modified: 03/04/2020

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