  Branch-and-bound approaches in integer programming require ordering portions
of the space to explore next, a problem known as node comparison. We propose a
new siamese graph neural network model to tackle this problem, where the nodes
are represented as bipartite graphs with attributes. Similar to prior work, we
train our model to imitate a diving oracle that plunges towards the optimal
solution. We evaluate our method by solving the instances in a plain framework
where the nodes are explored according to their rank. On three NP-hard
benchmarks chosen to be particularly primal-difficult, our approach leads to
faster solving and smaller branch- and-bound trees than the default ranking
function of the open-source solver SCIP, as well as competing machine learning
methods. Moreover, these results generalize to instances larger than used for
training. Code for reproducing the experiments can be found at
https://github.com/ds4dm/learn2comparenodes.
