@article{BertholdFrancobaldiHendel2025,
  author    = {Berthold, Timo and Francobaldi, Matteo and Hendel, Gregor},
  title     = {Learning to use local cuts},
  journal   = {Mathematical Programming Computation},
  volume    = {17},
  number    = {3},
  publisher = {Springer Science and Business Media LLC},
  issn      = {1867-2949},
  doi       = {10.1007/s12532-025-00278-y},
  pages     = {437 -- 450},
  year      = {2025},
  abstract  = {An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear pro- gramming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B\&B) solver as there is always the trade-off between the efficiency of the cuts and their overhead, given that they tend to slow down the solution time of the relaxation. One of the most crucial questions is: Should cuts only be generated globally at the root or also locally at nodes of the tree? We address this question by a machine learning approach for which we train a regression forest to predict the speed-up (or slow-down) provided by using local cuts. We demonstrate with an open implementation that this helps to improve the perfor- mance of the FICO Xpress MIP solver on a public test set of general MIP instances. We further report on the impact of a practical implementation inside Xpress on a large, diverse set of real-world industry MIPs.},
  language  = {en}
}