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

•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 dec...

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Bibliographic Details
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
Online Access:	Get full text
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Abstract	•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.
AbstractList	•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.
Author	Lodi, Andrea Prouvost, Antoine Bengio, Yoshua
Author_xml	– sequence: 1 givenname: Yoshua surname: Bengio fullname: Bengio, Yoshua email: yoshua.bengio@mila.quebec organization: Mila, Institut Québecois d’Intelligence Artificielle, Pavillon André-Aisenstadt 2920, Chemin de la TourMontreal, Qc, H3T 1J4 Canada – sequence: 2 givenname: Andrea surname: Lodi fullname: Lodi, Andrea email: andrea.lodi@polymtl.ca organization: Canada Excellence Research Chair in Data Science for Decision Making, École Polytechnique de Montréal, Pavillon André-Aisenstadt 2920, Chemin de la TourMontreal, Qc, H3T 1J4 Canada – sequence: 3 givenname: Antoine surname: Prouvost fullname: Prouvost, Antoine email: antoine.prouvost@polymtl.ca organization: Canada Excellence Research Chair in Data Science for Decision Making, École Polytechnique de Montréal, Pavillon André-Aisenstadt 2920, Chemin de la TourMontreal, Qc, H3T 1J4 Canada
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SubjectTerms	Branch and bound Combinatorial optimization Machine learning Mixed-integer programming solvers
Title	Machine learning for combinatorial optimization: A methodological tour d’horizon
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