Compressing Branch-and-Bound Trees
Abstract
A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same (or stronger) bound by either (1) applying a different disjunction at some node in T or (2) removing leaves from T? We believe such post-hoc analysis of BB trees may assist in identifying helpful general disjunctions in BB algorithms. We initiate our study by considering computational complexity and limitations of TCP. We then conduct experiments to evaluate the compressibility of realistic branch-and-bound trees generated by commonly-used branching strategies, using both an exact and a heuristic compression algorithm.
Keywords
Cite
@article{arxiv.2211.02727,
title = {Compressing Branch-and-Bound Trees},
author = {Gonzalo Muñoz and Joseph Paat and Álinson S. Xavier},
journal= {arXiv preprint arXiv:2211.02727},
year = {2023}
}
Comments
A short version of this article was accepted for publication at IPCO 2023. This extended version contains more detailed discussions and proofs, and new computational contributions and experiments