Research Paper On Integer Linear Programming
%20play%20an%20important%20role%20in%20solving%20mixed-integer%20linear%20programs%20(MILPs)%2C%20which%20formulate%20many%20important%20real-world%20applications.%20Cut%20selection%20heavily%20depends%20on%20(P1)%20which%20cuts%20to%20prefer%20and%20(P2)%20how%20many%20cuts%20to%20select.%20Although%20modern%20MILP%20solvers%20tackle%20(P1)-(P2)%20by%20human-designed%20heuristics%2C%20machine%20learning%20carries%20the%20potential%20to%20learn%20more%20effective%20heuristics.%20However%2C%20many%20existing%20learning-based%20methods%20learn%20which%20cuts%20to%20prefer%2C%20neglecting%20the%20importance%20of%20learning%20how%20many%20cuts%20to%20select.%20Moreover%2C%20we%20observe%20that%20(P3)%20what%20order%20of%20selected%20cuts%20to%20prefer%20significantly%20impacts%20the%20efficiency%20of%20MILP%20solvers%20as%20well.%20To%20address%20these%20challenges%2C%20we%20propose%20a%20novel%20hierarchical%20sequence%2Fset%20model%20(HEM)%20to%20learn%20cut%20selection%20policies.%20Specifically%2C%20HEM%20is%20a%20bi-level%20model:%20(1)%20a%20higher-level%20module%20that%20learns%20how%20many%20cuts%20to%20select%2C%20(2)%20and%20a%20lower-level%20module%20--%20that%20formulates%20the%20cut%20selection%20as%20a%20sequence%2Fset%20to%20sequence%20learning%20problem%20--%20to%20learn%20policies%20selecting%20an%20ordered%20subset%20with%20the%20cardinality%20determined%20by%20the%20higher-level%20module.%20To%20the%20best%20of%20our%20knowledge%2C%20HEM%20is%20the%20first%20data-driven%20methodology%20that%20well%20tackles%20(P1)-(P3)%20simultaneously.%20Experiments%20demonstrate%20that%20HEM%20significantly%20improves%20the%20efficiency%20of%20solving%20MILPs%20on%20eleven%20challenging%20MILP%20benchmarks%2C%20including%20two%20Huawei's%20real%20problems.)
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