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
 | There is a more recent version of this item available. |
Abstract
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2024 |
| Creators: | Habeck, Oliver ; Pfetsch, Marc E. |
| 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 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/20137 |
| Corresponding Links: | |
| Origin: | Secondary publication DeepGreen |
| Abstract: | 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 04 Department of Mathematics > Optimization |
| Date Deposited: | 13 Feb 2024 10:30 |
| Last Modified: | 15 Feb 2024 14:02 |
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| Suche nach Titel in: | TUfind oder in Google |
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