Learning to Select Cutting Planes in Mixed Integer Linear Programming Solving

Abstract: Cutting planes (cuts) are crucial for solving Mixed Integer Linear Programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and cannot be generalized for different scales of MILP problems. Therefore, learning-based methods for cut selection are considered a promising direction. State-of-the-art learning-based methods formulate cut selection as a sequence-to-sequence problem, easily handled by sequence models. However, the existing sequence models need help with the following issues: (1) the model only captures cut information while neglecting the Linear Programming (LP) relaxation; (2) the sequence model utilizes positional information of the input sequence, which may influence cut selection. To address these challenges, we design a novel learning model HGTSM for better select cuts. We encode MILP problem state as a heterogeneous tripartite graph, utilizing heterogeneous graph networks to fully capture the underlying structure of MILP problems. Simultaneously, we propose a novel sequence model whose architecture is tailored to handle inputs in different orders. Experimental results demonstrate that our model outperforms heuristic methods and learning-based baselines on multiple challenging MILP datasets. Additionally, the model exhibits stability and the ability to generalize to different types of problems.