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Cutting planes (cuts) are important for solving mixed-integer linear programs(MILPs), which formulate a wide range of important real-world applications. Cutselection -- which aims to select a proper subset of the candidate cuts toimprove the efficiency of solving MILPs -- heavily depends on (P1) which cutsshould be preferred, and (P2) how many cuts should be selected. Although manymodern MILP solvers tackle (P1)-(P2) by manually designed heuristics, machinelearning offers a promising approach to learn more effective heuristics fromMILPs collected from specific applications. However, many existinglearning-based methods focus on learning which cuts should be preferred,neglecting the importance of learning the number of cuts that should beselected. Moreover, we observe from extensive empirical results that (P3) whatorder of selected cuts should be preferred has a significant impact on theefficiency of solving MILPs as well. To address this challenge, we propose anovel hierarchical sequence model (HEM) to learn cut selection policies viareinforcement learning. Specifically, HEM consists of a two-level model: (1) ahigher-level model to learn the number of cuts that should be selected, (2) anda lower-level model -- that formulates the cut selection task as a sequence tosequence learning problem -- to learn policies selecting an ordered subset withthe size determined by the higher-level model. To the best of our knowledge,HEM is the first method that can tackle (P1)-(P3) in cut selectionsimultaneously from a data-driven perspective. Experiments show that HEMsignificantly improves the efficiency of solving MILPs compared tohuman-designed and learning-based baselines on both synthetic and large-scalereal-world MILPs, including MIPLIB 2017. Moreover, experiments demonstrate thatHEM well generalizes to MILPs that are significantly larger than those seenduring training.

Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model