  Many real-world problems can be efficiently modeled as Mixed Integer Linear
Programs (MILPs) and solved with the Branch-and-Bound method. Prior work has
shown the existence of MILP backdoors, small sets of variables such that
prioritizing branching on them when possible leads to faster running times.
However, finding high-quality backdoors that improve running times remains an
open question. Previous work learns to estimate the relative solver speed of
randomly sampled backdoors through ranking and then decide whether to use the
highest-ranked backdoor candidate. In this paper, we utilize the Monte-Carlo
tree search method to collect backdoors for training, rather than relying on
random sampling, and adapt a contrastive learning framework to train a Graph
Attention Network model to predict backdoors. Our method, evaluated on several
common MILP problem domains, demonstrates performance improvements over both
Gurobi and previous models.
