TY - GEN A1 - Frank, Martin A1 - Fügenschuh, Armin A1 - Herty, Michael A1 - Schewe, Lars T1 - The Coolest Path Problem N2 - 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. T3 - ZIB-Report - 09-37 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11571 SN - 1438-0064 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Göttlich, Simone A1 - Herty, Michael ED - Günther, H.-O. ED - Mattfeld, D. ED - Suhl, L. T1 - A new modeling approach for an integrated simulation and optimization of production networks T2 - Management logistischer Netzwerke Y1 - 2007 SP - 45 EP - 60 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Göttlich, Simone A1 - Herty, Michael ED - Oberweis, A. ED - Weinhardt, C. ED - Gimpel, H. ED - Koschmider, A. ED - Pankratius, V. ED - Schnizler, B. T1 - Water Contamination Detection T2 - eOrganisation Y1 - 2007 SP - 501 EP - 518 ER - TY - JOUR A1 - Frank, Martin A1 - Fügenschuh, Armin A1 - Herty, Michael A1 - Schewe, Lars T1 - The Coolest Path Problem JF - Networks and Heterogeneous Media Y1 - 2010 VL - 5 IS - 1 SP - 143 EP - 162 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Göttlich, Simone A1 - Kirchner, Claus A1 - Herty, Michael A1 - Martin, Alexander T1 - Efficient Reformulation and Solution of a Nonlinear PDE-Controlled Flow Network Model JF - Computing Y1 - 2009 VL - 85 IS - 3 SP - 245 EP - 265 ER - TY - JOUR A1 - Dittel, Agnes A1 - Fügenschuh, Armin A1 - Göttlich, Simone A1 - Herty, Michael T1 - MIP Presolve Techniques for a PDE-based Supply Chain Model JF - Optimization Methods & Software Y1 - 2009 VL - 24 IS - 3 SP - 427 EP - 445 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Göttlich, Simone A1 - Herty, Michael A1 - Klar, Alexander A1 - Martin, Alexander T1 - A Discrete Optimization Approach to Large Scale Supply Networks Based on Partial Differential Equations JF - SIAM Journal on Scientific Computing Y1 - 2008 VL - 30 IS - 3 SP - 1490 EP - 1507 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Herty, Michael A1 - Klar, Axel A1 - Martin, Alexander T1 - Combinatorial and Continuous Models and Optimization for Traffic Flow on Networks JF - SIAM Journal on Optimization Y1 - 2006 VL - 16 IS - 4 SP - 1155 EP - 1176 ER -