Code and Data Repository for Non-monotonicity of Branching Rules with Respect to Linear Relaxations

The goal of this software is to computationally ascertain how common it is for the strong branching rule to exhibit non-monotonicity in practice. We do so by applying cover cuts on randomly generated multi-dimensional knapsacks as well as by considering cuts applied by SCIP on MIPLIB 2017 benchmark set. Our main insight from these experiments is that if the gap closed by cuts is small, change in tree size is difficult to predict, and often increases, possibly due to inherent non-monotonicity. However, when a sufficiently large gap is closed, a significant decrease in tree size may be expected.