Information-theoretic approaches to branching in search

Deciding what question to branch on at each node is a key element of search algorithms. In this paper, we describe a collection of techniques for branching decisions that are motivated from an information-theoretic perspective. The idea is to drive the search to reduce the uncertainty (entropy) in the current subproblem. We present four families of methods for branch question selection in mixed integer programming that use this idea. In the first, a variable to branch on is selected based on lookahead. This method performs comparably to strong branching on MIPLIB, and better than strong branching on hard real-world procurement optimization instances on which CPLEX’s default strong branching outperforms CPLEX’s default branching strategy. The second family combines this idea with strong branching. The third family does not use lookahead, but instead exploits the tie between indicator variables and the variables they govern. This significantly outperforms the state-of-the-art branching strategies on both combinatorial procurement problems and facility location problems. The fourth family concerns branching using carefully constructed linear inequality constraints over sets of variables.