Faster integer-feasibility in mixed-integer linear programs by branching to force change

Branching in mixed-integer (or integer) linear programming requires choosing both the branching variable and the branching direction. This paper develops a number of new methods for making those two decisions either independently or together with the goal of reaching the first integer-feasible solution quickly. These new methods are based on estimating the probability of satisfying a constraint at the child node given a variable/direction pair. The surprising result is that the first integer-feasible solution is usually found much more quickly when the variable/direction pair with the smallest probability of satisfying the constraint is chosen. This is because this selection forces change in many candidate variables simultaneously, leading to an integer-feasible solution sooner. Extensive empirical results are given.