Dr. Kai-Helge Becker

becker@zib.de


Projects as a member

  • MI10

    Acyclic network flows

    Dr. Benjamin Hiller / Prof. Dr. Thorsten Koch / Prof. Dr. Martin Skutella

    Project heads: Dr. Benjamin Hiller / Prof. Dr. Thorsten Koch / Prof. Dr. Martin Skutella
    Project members: Dr. Kai-Helge Becker
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    Utility and infrastructure networks are at the heart of our daily life and we are taking their proper working for granted. To provide this service, network operators face difficult planning and operational problems. The complexity of the considered optimization problems increases for several reasons, for instance because geographically bigger networks are considered or the detail level is increased. For large networks, providing globally optimal solutions or at least good bounds for assessing solution quality is still a big challenge. This project addresses this challenge for so-called potential-driven nonlinear network flow problems that are a key model for infrastructure networks for fluids, e.g. water and gas. These problems feature a so-called potential for each node, and the flow on an arc is related to the difference of the potential of its end nodes. In particular, flow is always directed from higher to lower potential, i.e. the potentials induce an acylic orientation of the arcs. This observation is the motivation for this project: We study network flow problems with the additional requirement of acyclic flows: If each network arc is oriented in the direction of flow over this arc, then there is no directed cycle in the resulting network. This is an interesting combinatorial structure that arises from nonconvex nonlinear constraints and thus links combinatorial and continuous optimization. The aim of this project is to develop algorithmic techniques to exploit this structure to improve global optimization methods for large-scale nonlinear flow problems.

Projects as a guest