Learning To Branch In Mixed Integer Programming
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Learning To Branch In Mixed Integer Programming
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 play an important role in solving mixed-integer linear programs (MILPs)%2C 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%2C machine learning carries the potential to learn more effective heuristics. However%2C many existing learning-based methods learn which cuts to prefer%2C neglecting the importance of learning how many cuts to select. Moreover%2C we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges%2C we propose a novel hierarchical sequence%2Fset model (HEM) to learn cut selection policies. Specifically%2C HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select%2C (2) and a lower-level module -- that formulates the cut selection as a sequence%2Fset 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%2C 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%2C including two Huawei's real problems. "Learning To Cut Via Hierarchical Sequence Set Model For Efficient Mixed")
Learning To Cut Via Hierarchical Sequence Set Model For Efficient Mixed