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 - Homfeld, Henning A1 - Huck, Andreas A1 - Martin, Alexander A1 - Yuan, Zhi T1 - Scheduling Locomotives and Car Transfers in Freight Transport JF - Transportation Science Y1 - 2008 VL - 42 IS - 4 SP - 1 EP - 14 ER - TY - JOUR A1 - Fügenschuh, Armin T1 - Solving a School Bus Scheduling Problem with Integer Programming JF - European Journal of Operational Research Y1 - 2009 VL - 193 IS - 3 SP - 867 EP - 884 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - A Multicriterial Approach for Optimizing Bus Schedules and School Starting Times JF - Annals of Operations Research Y1 - 2006 VL - 147 IS - 1 SP - 199 EP - 216 ER - TY - JOUR A1 - Fügenschuh, Armin T1 - Optimal verknüpft - Schulanfangszeiten und öffentlicher Personennahverkehr JF - thema forschung Y1 - 2006 VL - 1 SP - 82 EP - 85 ER - TY - JOUR A1 - Fügenschuh, Armin T1 - Optimierte Schulanfangszeiten JF - OR News Y1 - 2006 VL - 28 SP - 25 EP - 27 ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Fledderus, E. A1 - Geerdes, Hans-Florian A1 - Heideck, B. A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Kürner, T. A1 - Martin, Alexander ED - Martin, Alexander T1 - Mathematical Methods for Automatic Optimization of UMTS Radio Networks Y1 - 2003 UR - http://momentum.zib.de/paper/momentum-d43.pdf IS - D4.3 PB - IST-2000-28088 MOMENTUM ER - TY - JOUR A1 - Fügenschuh, Armin T1 - Mathematische Modelle zur betrieblichen Optimierung JF - Z! - das Zukunftsmagazin Y1 - 2006 VL - 1 SP - 3 ER - TY - GEN A1 - Dittel, Agnes A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - Polyhedral Aspects of Self-Avoiding Walks N2 - In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this problem one is interested in optimal configurations, where an energy function measures the benefit if certain path elements are placed on adjacent vertices of the graph. The most prominent application of this problem is the protein folding problem in biochemistry. On a set of selected instances, we demonstrate the computational merits of our approach. T3 - ZIB-Report - 11-11 KW - Polyhedral Combinatorics KW - Integer Programming KW - Self-Avoiding Path KW - Protein Folding Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12576 ER - TY - JOUR A1 - Humpola, Jesco A1 - Fügenschuh, Armin T1 - Convex reformulations for solving a nonlinear network design problem JF - Computational Optimization and Applications N2 - We consider a nonlinear nonconvex network design problem that arises, for example, in natural gas or water transmission networks. Given is such a network with active and passive components, that is, valves, compressors, control valves (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes in the network. The active elements are associated with costs when used. Besides flow conservation constraints in the nodes, the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is to compute a cost minimal setting of the active components and numerical values for the flow and node potentials. We examine different (convex) relaxations for a subproblem of the design problem and benefit from them within a branch-and-bound approach. We compare different approaches based on nonlinear optimization numerically on a set of test instances. Y1 - 2015 U6 - https://doi.org/10.1007/s10589-015-9756-2 VL - 62 IS - 3 SP - 717 EP - 759 PB - Springer US ER - TY - CHAP A1 - Humpola, Jesco A1 - Fügenschuh, Armin A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Lenz, Ralf A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - The Specialized MINLP Approach T2 - Evaluating Gas Network Capacities N2 - We propose an approach to solve the validation of nominations problem using mixed-integer nonlinear programming (MINLP) methods. Our approach handles both the discrete settings and the nonlinear aspects of gas physics. Our main contribution is an innovative coupling of mixed-integer (linear) programming (MILP) methods with nonlinear programming (NLP) that exploits the special structure of a suitable approximation of gas physics, resulting in a global optimization method for this type of problem. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER -