Computational benefit of non-root cutting planes in MILP

Determine whether applying cutting planes at non-root nodes within branch-and-bound (i.e., using branch-and-cut beyond the root) yields computational benefits compared to root-only cut strategies for mixed integer linear programming, with performance measured by metrics such as total solving time, search tree size, and numerical stability across standard benchmarks and solver configurations.

Background

Modern MILP solvers typically apply cutting planes heavily at the root node, and many learning-based cut selection methods focus there. While branch-and-cut allows adding cuts in non-root nodes, excessive cuts can slow LP solving and cause numerical instability, raising concerns about overall performance. The survey explicitly notes uncertainty about whether using cuts outside the root node is computationally beneficial, highlighting the need for a clear evaluation across instances and solver settings.

The question is central to integrating ML-driven cut selection beyond the root: if non-root cuts improve bound tightening but degrade LP performance or stability, the net effect on solving time could be negative—making a principled, empirical determination necessary.