Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming
It provides a review of incremental advancements for researchers and practitioners in optimization and machine learning, focusing on improving solver performance for real-life applications.
This paper surveys the integration of machine learning algorithms to enhance branch-and-bound efficiency in solving Mixed Integer Linear Programming (MILP) problems, addressing tasks like primal heuristics and branching, but does not present new experimental results or concrete numerical improvements.
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.