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 lowcost 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 AI 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 highlyoptimized 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.