A knapsack intersection hierarchy

We introduce a knapsack intersection hierarchy for strengthening linear programming relaxations of packing integer programs. In level t of the hierarchy, all valid cuts are added for the integer hull of the intersection of all t-row relaxations. This model captures the maximum possible strength of t...

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Bibliographic Details
Published inOperations research letters Vol. 51; no. 1; pp. 72 - 78
Main Authors Jozefiak, Adam, Shepherd, F. Bruce, Weninger, Noah
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2023
Subjects
All-or-nothing flow
Integer programming hierarchies
Knapsack problem
Packing integer program
Unsplittable flow
Packing integer program
All-or-nothing flow
Integer programming hierarchies
Unsplittable flow
Knapsack problem
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Summary:We introduce a knapsack intersection hierarchy for strengthening linear programming relaxations of packing integer programs. In level t of the hierarchy, all valid cuts are added for the integer hull of the intersection of all t-row relaxations. This model captures the maximum possible strength of t-row cuts, an approach often used by solvers for small t. We investigate the integrality gap of the strengthened formulations on the all-or-nothing flow problem in trees (also called unsplittable flow on trees).
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2022.12.001