A Combinatorial Cut-and-Lift Procedure with an Application to 0-1 Second-Order Conic Programming
Abstract
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a binary decision diagram (BDD) encoding of their constraints. We present a general framework that can be applied to a wide range of binary optimization problems and show its applicability for second-order conic inequalities. We identify conditions for which our lifted inequalities are facet-defining and derive a new BDD-based cut generation linear program. Such a model serves as a basis for a max-flow combinatorial algorithm over the BDD that can be applied to derive valid cuts more efficiently. Our numerical results show encouraging performance when incorporated into a state-of-the-art mathematical programming solver, significantly reducing the root node gap, increasing the number of problems solved, and reducing the run-time by a factor of three on average.
Cite
@article{arxiv.2003.06363,
title = {A Combinatorial Cut-and-Lift Procedure with an Application to 0-1 Second-Order Conic Programming},
author = {Margarita P. Castro and Andre A. Cire and J. Christopher Beck},
journal= {arXiv preprint arXiv:2003.06363},
year = {2022}
}