Modeling Combinatorial Disjunctive Constraints via Junction Trees
Abstract
We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We present a novel pairwise IB-representable class of CDCs, CDCs admitting junction trees, and provide a combinatorial procedure to build MIP formulations for those constraints. Generalized special ordered sets (SOS k) can be modeled by CDCs admitting junction trees and we also obtain MIP formulations of SOS k. Furthermore, we provide a novel ideal extended formulation of any combinatorial disjunctive constraints with fewer auxiliary binary variables with an application in planar obstacle avoidance.
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