Modeling Disjunctive Constraints via Junction Trees
Hicks, Illya V.; Huchette, Joseph A.
Master of Arts
In this thesis, we study the independent-branching (IB) framework of disjunctive constraints and identify a class of pairwise IB-representable disjunctive constraints: disjunctive constraints with junction trees. For this class of constraints, the existence of junction trees can be recognized in polynomial time. We also present a polynomial-time heuristic algorithm for the minimum biclique cover problem on the associated conflict graphs to build small and strong mixed-integer programming (MIP) formulations. Additionally, we apply the heuristic to find a smaller MIP formulation of generalized special ordered set with less variables and constraints than Huchette and Vielma . In computational experiments, we compare the proposed heuristic with other methods on a large set of artificially generated disjunctive constraints with junction trees. The new method significantly reduces the numbers of binary variables and constraints required for the MIP formulations than those of vertex cover approach.
Mixed-integer Programming; Disjunctive Constraints; Minimum Biclique Cover Problem