English

Modeling Combinatorial Disjunctive Constraints via Junction Trees

Optimization and Control 2022-05-17 v1

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 (SOSk\text{SOS} k) can be modeled by CDCs admitting junction trees and we also obtain MIP formulations of SOSk\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.

Keywords

Cite

@article{arxiv.2205.06916,
  title  = {Modeling Combinatorial Disjunctive Constraints via Junction Trees},
  author = {Bochuan Lyu and Illya V. Hicks and Joey Huchette},
  journal= {arXiv preprint arXiv:2205.06916},
  year   = {2022}
}
R2 v1 2026-06-24T11:17:04.594Z