Information-theoretic approaches to branching in search

Deciding what to branch on at each node is a key element of search algorithms. We present four families of methods for selecting what question to branch on. They are all information-theoretically motivated to reduce uncertainty in remaining subproblems. In the first family, a good variable to branch on is selected based on lookahead. In real-world procurement optimization, this entropic branching method outperforms default CPLEX and strong branching. The second family combines this idea with strong branching. The third family does not use lookahead, but instead exploits features of the underlying structure of the problem. Experiments show that this family significantly outperforms the state-of-the-art branching strategy when the problem includes indicator variables as the key driver of complexity. The fourth family is about branching using carefully constructed linear inequality constraints over sets of variables.