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Combinatorial acyclicity models for potential‐based flows

Habeck, Oliver ; Pfetsch, Marc E. (2024)
Combinatorial acyclicity models for potential‐based flows.
In: Networks, 2021, 79 (1)
doi: 10.26083/tuprints-00020137
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Combinatorial acyclicity models for potential‐based flows
Language: English
Date: 13 February 2024
Place of Publication: Darmstadt
Year of primary publication: 2021
Place of primary publication: New York
Publisher: Wiley
Journal or Publication Title: Networks
Volume of the journal: 79
Issue Number: 1
DOI: 10.26083/tuprints-00020137
Corresponding Links:
Origin: Secondary publication DeepGreen

Potential‐based flows constitute a basic model to represent physical behavior in networks. Under natural assumptions, the flow in such networks must be acyclic. The goal of this article is to exploit this property for the solution of corresponding optimization problems. To this end, we introduce several combinatorial models for acyclic flows, based on binary variables for flow directions. We compare these models and introduce a particular model that tries to capture acyclicity together with the supply/demand behavior. We analyze properties of this model, including variable fixing rules. Our computational results show that the usage of the corresponding constraints speeds up solution times by about a factor of 3 on average and a speed‐up of a factor of almost 5 for the time to prove optimality.

Uncontrolled Keywords: acyclic flows, gas networks, mixed‐integer program, network optimization, potential‐based flows, valid inequalities
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-201379
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Optimization
Date Deposited: 13 Feb 2024 10:30
Last Modified: 13 Feb 2024 10:30
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/20137
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