Learning generalized strong branching for set covering, set packing, and 0–1 knapsack problems

Branching on a set of variables, rather than on a single variable, can give tighter bounds at the child nodes and can result in smaller search trees. However, selecting a good set of variables to branch on is even more challenging than selecting a good single variable to branch on. Generalized strong branching extends the strong branching concepts developed for choosing a single variable to choosing a set of variables. As the computational requirements of a full implementation of strong branching are prohibitive, we use extreme gradient boosting to train a model to predict the ranking of (sets of) candidate variables. An extensive computational study using instances from three well-known classes of optimization problems demonstrates that branching on sets of variables outperforms branching on a single variable, that a learned model can be used effectively to select among (sets of) candidate variables, and that the learned strong branching strategies outperform the default branching strategy of state-of-the-art commercial solver CPLEX in terms of both the number of nodes explored in the search tree and the time it takes to explore the search tree.