  Cutting planes (cuts) play an important role in solving mixed-integer linear
programs (MILPs), which formulate many important real-world applications. Cut
selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts
to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed
heuristics, machine learning carries the potential to learn more effective
heuristics. However, many existing learning-based methods learn which cuts to
prefer, neglecting the importance of learning how many cuts to select.
Moreover, we observe that (P3) what order of selected cuts to prefer
significantly impacts the efficiency of MILP solvers as well. To address these
challenges, we propose a novel hierarchical sequence/set model (HEM) to learn
cut selection policies. Specifically, HEM is a bi-level model: (1) a
higher-level module that learns how many cuts to select, (2) and a lower-level
module -- that formulates the cut selection as a sequence/set to sequence
learning problem -- to learn policies selecting an ordered subset with the
cardinality determined by the higher-level module. To the best of our
knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3)
simultaneously. Experiments demonstrate that HEM significantly improves the
efficiency of solving MILPs on eleven challenging MILP benchmarks, including
two Huawei's real problems.
