@misc{FrankFuegenschuhHertyetal., author = {Frank, Martin and F{\"u}genschuh, Armin and Herty, Michael and Schewe, Lars}, title = {The Coolest Path Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11571}, number = {09-37}, abstract = {We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.}, language = {en} } @inproceedings{FuegenschuhGoettlichHerty2007, author = {F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Herty, Michael}, title = {A new modeling approach for an integrated simulation and optimization of production networks}, series = {Management logistischer Netzwerke}, booktitle = {Management logistischer Netzwerke}, editor = {G{\"u}nther, H.-O. and Mattfeld, D. and Suhl, L.}, pages = {45 -- 60}, year = {2007}, language = {en} } @inproceedings{FuegenschuhGoettlichHerty2007, author = {F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Herty, Michael}, title = {Water Contamination Detection}, series = {eOrganisation}, booktitle = {eOrganisation}, editor = {Oberweis, A. and Weinhardt, C. and Gimpel, H. and Koschmider, A. and Pankratius, V. and Schnizler, B.}, pages = {501 -- 518}, year = {2007}, language = {en} } @article{FrankFuegenschuhHertyetal.2010, author = {Frank, Martin and F{\"u}genschuh, Armin and Herty, Michael and Schewe, Lars}, title = {The Coolest Path Problem}, series = {Networks and Heterogeneous Media}, volume = {5}, journal = {Networks and Heterogeneous Media}, number = {1}, pages = {143 -- 162}, year = {2010}, language = {en} } @article{FuegenschuhGoettlichKirchneretal.2009, author = {F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Kirchner, Claus and Herty, Michael and Martin, Alexander}, title = {Efficient Reformulation and Solution of a Nonlinear PDE-Controlled Flow Network Model}, series = {Computing}, volume = {85}, journal = {Computing}, number = {3}, pages = {245 -- 265}, year = {2009}, language = {en} } @article{DittelFuegenschuhGoettlichetal.2009, author = {Dittel, Agnes and F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Herty, Michael}, title = {MIP Presolve Techniques for a PDE-based Supply Chain Model}, series = {Optimization Methods \& Software}, volume = {24}, journal = {Optimization Methods \& Software}, number = {3}, pages = {427 -- 445}, year = {2009}, language = {en} } @article{FuegenschuhGoettlichHertyetal.2008, author = {F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Herty, Michael and Klar, Alexander and Martin, Alexander}, title = {A Discrete Optimization Approach to Large Scale Supply Networks Based on Partial Differential Equations}, series = {SIAM Journal on Scientific Computing}, volume = {30}, journal = {SIAM Journal on Scientific Computing}, number = {3}, pages = {1490 -- 1507}, year = {2008}, language = {en} } @article{FuegenschuhHertyKlaretal.2006, author = {F{\"u}genschuh, Armin and Herty, Michael and Klar, Axel and Martin, Alexander}, title = {Combinatorial and Continuous Models and Optimization for Traffic Flow on Networks}, series = {SIAM Journal on Optimization}, volume = {16}, journal = {SIAM Journal on Optimization}, number = {4}, pages = {1155 -- 1176}, year = {2006}, language = {en} }