The matching relaxation for a class of generalized set partitioning problems
Abstract
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.
Cite
@article{arxiv.1606.09279,
title = {The matching relaxation for a class of generalized set partitioning problems},
author = {Phillippe Samer and Evellyn Cavalcante and Sebastián Urrutia and Johan Oppen},
journal= {arXiv preprint arXiv:1606.09279},
year = {2022}
}
Comments
33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematics