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arXiv · 2205.06916

Modeling Combinatorial Disjunctive Constraints via Junction Trees

Bochuan Lyu·Illya V. Hicks·Joey Huchette
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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 ($\text{SOS} k$) can be modeled by CDCs admitting junction trees and we also obtain MIP formulations of $\text{SOS} k$. 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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Bochuan Lyu, Illya V. Hicks, Joey Huchette. 2022-05-13. Modeling Combinatorial Disjunctive Constraints via Junction Trees. https://arxiv.org/abs/2205.06916

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