Backdoor Branching

We present an exact mixed-integer programming (MIP) solution scheme where a set-covering model is used to find a small set of first-choice branching variables. In a preliminary “sampling” phase, our method quickly collects a number of relevant low-cost fractional solutions that qualify as obstacles for the linear programming (LP) relaxation bound improvement. Then a set covering model is solved to detect a small subset of variables (a “backdoor,” in the artificial intelligence jargon) that “cover the fractionality” of the collected fractional solutions. These backdoor variables are put in a priority branching list, and a black-box MIP solver is eventually run—in its default mode—by taking this list into account, thus avoiding any other interference with its highly optimized internal mechanisms. Computational results on a large set of instances from the literature are presented, showing that some speedup can be achieved even with respect to a state-of-the-art solver such as IBM ILOG CPLEX 12.2.