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Combinatorial Acyclicity Models for Potential-based Flows

  • 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 paper 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.

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Metadaten
Author:Oliver Habeck, Marc E. Pfetsch
Document Type:Preprint
Language:English
Date of Publication (online):2020/04/22
Date of first Publication:2020/04/22
Release Date:2020/04/22
Tag:Network Optimization; Potential networks; Potential-based flows; acyclic flows
Institutes:Technische Universität Darmstadt
Subprojects:A01
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International