Machine learning for combinatorial optimization: A methodological tour d’horizon

• Published in: European journal of operational research Vol. 290; no. 2; pp. 405 - 421
• Main Authors: Bengio, Yoshua, Lodi, Andrea, Prouvost, Antoine
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.04.2021
• Subjects: Branch and bound; Combinatorial optimization; Machine learning; Mixed-integer programming solvers; Mixed-integer programming solvers; Branch and bound; Combinatorial optimization; Machine learning
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2020.07.063

•This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems.•Given the hard nature of these problems, state-of-the-art algorithms rely on handcrafted heuristics for making decisions which are otherwise too expensive to compute or mathematically not well-defined. Thus, machine learning looks like a natural candidate to make such decisions in a more principled and optimized way. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail a methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task. This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art algorithms rely on handcrafted heuristics for making decisions that are otherwise too expensive to compute or mathematically not well defined. Thus, machine learning looks like a natural candidate to make such decisions in a more principled and optimized way. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail a methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.