Permutatorial Optimization via the Permutahedron
Optimization and Control
2022-07-27 v2
Abstract
A water company decides to expand its network with a set of water lines, but it cannot build them all at once. However, it starts reaping benefits from a partial expansion. In what order should the company build the lines? We formalize a class of permutatorial problems with combinatorial/continuous subproblems capturing applications of incremental deployment. We show that, for additive/linear objective functions, efficient polyhedral methods for the subproblems extend to the permutatorial problem. Our main technical ingredient is the permutahedron.
Cite
@article{arxiv.2203.00735,
title = {Permutatorial Optimization via the Permutahedron},
author = {J. Carlos Martinez Mori and Samitha Samaranayake},
journal= {arXiv preprint arXiv:2203.00735},
year = {2022}
}