Information-theoretic Approaches to Branching in Search

Andrew Gilpin, Tuomas Sandholm

Deciding what question to branch on at each node is a key element of search algorithms. We introduce the information-theoretic paradigm for branching question selection. The idea is to drive the search to reduce uncertainty (entropy) in the current subproblem. We present four families of methods that fall within this paradigm. 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 other variables they govern. This significantly outperforms the state-of-the-art branching strategies. The fourth family is about branching using carefully constructed linear inequality constraints over sets of variables.