Experiments with Branching using General Disjunctions

Branching is an important component of the branch-and-cut algorithm for solving mixed integer linear programs. Most solvers branch by imposing a disjunction of the form“xi ≤ k ∨ xi ≥ k + 1” for some integer k and some integer-constrained variable xi. A generalization of this branching scheme is to branch by imposing a more general disjunction of the form “πx ≤ π0 ∨ πx ≥ π0 + 1.” In this paper, we discuss the formulation of two optimization models for selecting such a branching disjunction and then describe methods of solution using a standard MILP solver. We report on computational experiments carried out to study the effects of branching on such disjunctions.