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Machine Learning for Cutting Planes in Integer Programming: A Survey
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We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to the linear programming (LP) relaxation at a given node of the branch-and-bound (B&B) tree has defied both formal and heuristic solutions to date. ML offers a promising approach for improving the cut selection process by using data to identify promising cuts that accelerate the solution of MILP instances. This paper presents an overview of the topic, highlighting recent advances in the literature, common approaches to data collection, evaluation, and ML model architectures. We analyze the empirical results in the literature in an attempt to quantify the progress that has been made and conclude by suggesting avenues for future research.
Forward citations
Cited by 2 Pith papers
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Learning to Optimize at Scale: A Benders Decomposition-TransfORmers Framework for Stochastic Combinatorial Optimization
A Transformer trained on T=90 deterministic lot-sizing instances predicts setup decisions inside Benders decomposition, yielding 3.55% average gap at T=90 and 19.6% at T=270 without reported subproblem infeasibility.
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How hard is learning to cut? Trade-offs and sample complexity
Learning to cut requires at least as many samples as learning any generic target from the same concept class, for both gap closed and branch-and-cut tree size scores.
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