Branch-and-Bound versus Lift-and-Project Relaxations in Combinatorial Optimization
Optimization and Control
2023-11-02 v1 Data Structures and Algorithms
Abstract
In this paper, we consider a theoretical framework for comparing branch-and-bound with classical lift-and-project hierarchies. We simplify our analysis of streamlining the definition of branch-and-bound. We introduce "skewed -trees" which give a hierarchy of relaxations that is incomparable to that of Sherali-Adams, and we show that it is much better for some instances. We also give an example where lift-and-project does very well and branch-and-bound does not. Finally, we study the set of branch-and-bound trees of height at most and effectively "squeeze" their effectiveness between two well-known lift-and-project procedures.
Cite
@article{arxiv.2311.00185,
title = {Branch-and-Bound versus Lift-and-Project Relaxations in Combinatorial Optimization},
author = {Gérard Cornuéjols and Yatharth Dubey},
journal= {arXiv preprint arXiv:2311.00185},
year = {2023}
}