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Volume 6 Issue 5
Sep.  2019

IEEE/CAA Journal of Automatica Sinica

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Reza Asadi and Solmaz S. Kia, "Cycle Flow Formulation of Optimal Network Flow Problems and Respective Distributed Solutions," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1251-1260, Sept. 2019. doi: 10.1109/JAS.2019.1911705
Citation: Reza Asadi and Solmaz S. Kia, "Cycle Flow Formulation of Optimal Network Flow Problems and Respective Distributed Solutions," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1251-1260, Sept. 2019. doi: 10.1109/JAS.2019.1911705

Cycle Flow Formulation of Optimal Network Flow Problems and Respective Distributed Solutions

doi: 10.1109/JAS.2019.1911705
Funds:  This work was supported by National Science Foundation award ECCS-1653838
More Information
  • In this paper, we use the cycle basis from graph theory to reduce the size of the decision variable space of optimal network flow problems by eliminating the aggregated flow conservation constraint. We use a minimum cost flow problem and an optimal power flow problem with generation and storage at the nodes to demonstrate our decision variable reduction method. The main advantage of the proposed technique is that it retains the natural sparse/decomposable structure of network flow problems. As such, the reformulated problems are still amenable to distributed solutions. We demonstrate this by proposing a distributed alternating direction method of multipliers (ADMM) solution for a minimum cost flow problem. We also show that the communication cost of the distributed ADMM algorithm for our proposed cycle-based formulation of the minimum cost flow problem is lower than that of a distributed ADMM algorithm for the original arc-based formulation.


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  • 1Resources are generically categorized as CPUs (number of independent computational units), primary storage (amount of memory/RAM), secondary storage (disk, cloud, etc.).
    2An articulation point of an undirected connected graph is a node whose removal along with its incident edges disconnects the graph [32].
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    • Cycle basis from graph theory is used to reduce the size of the decision variable space of optimal network flow problem.
    • Proposed technique retains the natural sparse/decomposable structure of network flow problems.
    • The reformulated problems are still amenable to distributed solutions.
    • A cycle based distributed ADMM solution is demonstrated for a minimum cost flow problem.


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