Surrogate Branching: Parametric Relaxation for Mixed Integer Optimization

Surrogate Branching (SB) methods in mixed integer optimization provide a staged parametric relaxation of customary branching methods used in branch-and-bound and branch-and-cut algorithms. SB methods operate by forming surrogate constraints composed of non-negative linear combinations of component inequalities of three types: (1) ordinary branching inequalities, (2) redundant inequalities involving bounds on variables, and (3) the strictly redundant inequality 0 ≤ 1. The usefulness of surrogate constraint relaxations and their associated duality theory in mixed integer optimization acquires a new scope through these surrogate branching inequalities, by allowing branching decisions to be progressively compounded, and parametrically staged in strength, as a function of the degree of separation desired.