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Branch-and-bound approaches in integer programming require ordering portionsof the space to explore next, a problem known as node comparison. We propose anew siamese graph neural network model to tackle this problem, where the nodesare represented as bipartite graphs with attributes. Similar to prior work, wetrain our model to imitate a diving oracle that plunges towards the optimalsolution. We evaluate our method by solving the instances in a plain frameworkwhere the nodes are explored according to their rank. On three NP-hardbenchmarks chosen to be particularly primal-difficult, our approach leads tofaster solving and smaller branch- and-bound trees than the default rankingfunction of the open-source solver SCIP, as well as competing machine learningmethods. Moreover, these results generalize to instances larger than used fortraining. Code for reproducing the experiments can be found athttps://github.com/ds4dm/learn2comparenodes.

Learning to Compare Nodes in Branch and Bound with Graph Neural Networks