Branching on nonchimerical fractionalities

In this paper we address methods for selecting the branching variable in an enumerative exact algorithm for Mixed-Integer Programs|a crucial step for the eectiveness of the resulting method. Many branching rules have been proposed in the literature, most of which are based on the impact of branching constraints on the LP solution values at the child nodes. Among them, strong branching turns out to be the most eective strategy in reducing the number of branching nodes, though its associated overhead may be substantial in most cases. In this paper we present heuristics to speed-up the strong branching computation, and also to reduce the set of candidate branching variables by removing the variables whose fractionality is just chimerical, in the sense that it can be xed by allowing for a little worsening of the objective function. Extensive computational results on instances from the literature are presented, showing that an average speedup of two can be achieved with respect to a standard full strong branching implementation. This is particularly encouraging if one considers the proof-of-concept nature of our implementation.