Machine Learning Augmented for Mixed-Integer Linear Programming

Title: Machine Learning Augmented for Mixed-Integer Linear Programming

Abstract:  Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving MILPs, and many commercial and academic software packages exist. Nevertheless, the availability of data, both from problem instances and from solvers, and the desire to solve new problems and larger (real-life) instances, trigger the need for continuing algorithmic development. MILP solvers use branch and bound as their main component. In recent years, there has been an explosive development in the use of machine learning algorithms for enhancing all main tasks involved in the branch-and-bound algorithm, such as primal heuristics, branching, cutting planes, node selection and solver configuration decisions. This paper presents a survey of such approaches, addressing the vision of integration of machine learning and mathematical optimization as complementary technologies, and how this integration can benefit MILP solving. In particular, we give detailed attention to machine learning algorithms that automatically optimize some metric of branch-and-bound efficiency. We also address how to represent MILPs in the context of applying learning algorithms, MILP benchmarks and software.

Bio:  Andrea is an Andrew H. and Ann R. Tisch Professor at the Jacobs Technion-Cornell Institute at Cornell Tech and the Technion. He is a member of the Operations Research and Information Engineering field at Cornell University. Before joining Cornell, he was a Herman Goldstine Fellow at the IBM Mathematical Sciences Department, NY in 2005–2006, full professor of Operations Research at DEI, University of Bologna 2007-2015 and Canada Excellence Research Chair in “Data Science for Real-time Decision Making” at Polytechnique Montréal 2015-2022. His main research interests are in Mixed-Integer Linear and Nonlinear Programming and Data Science and his work has received several recognitions including the IBM and Google faculty awards. Andrea is the recipient of the INFORMS Optimization Society 2021 Farkas Prize and has been elected an INFORMS Fellow in 2023. Andrea has been the principal investigator of scientific projects (often involving industrial partners) for Italy, European Union, Canada and USA. In the period 2006-2021, he was a consultant of the IBM CPLEX research and development team, developing CPLEX, one of the leading software for Mixed-Integer Optimization.