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Combinatorial acyclicity models for potential‐based flows
Author(s) -
Habeck Oliver,
Pfetsch Marc E.
Publication year - 2022
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.22038
Subject(s) - exploit , computer science , variable (mathematics) , binary number , mathematical optimization , flow (mathematics) , directed acyclic graph , property (philosophy) , flow network , factor (programming language) , theoretical computer science , algorithm , mathematics , mathematical analysis , philosophy , geometry , computer security , arithmetic , epistemology , programming language
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.