Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-2928 Wissenschaftlicher Artikel Fügenschuh, Armin; Fügenschuh, Marzena Integer Linear Programming Models for Topology Optimization in Sheet Metal Design 2008 18 Mathematical Methods of Operations Research 68 2 313 331 Mathematical Optimization
OPUS4-1157 misc Frank, Martin; Fügenschuh, Armin; Herty, Michael; Schewe, Lars The Coolest Path Problem 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. urn:nbn:de:0297-zib-11571 Mathematical Optimization
OPUS4-1234 misc Fügenschuh, Armin; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Schwarz, Robert; Schweiger, Jonas; Szabó, Jácint Gas Network Topology Optimization for Upcoming Market Requirements Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed. urn:nbn:de:0297-zib-12348 10.1109/EEM.2011.5953035 Mathematical Optimization
OPUS4-1257 misc Dittel, Agnes; Fügenschuh, Armin; Martin, Alexander Polyhedral Aspects of Self-Avoiding Walks 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. urn:nbn:de:0297-zib-12576 Mathematical Optimization
OPUS4-683 misc Eisenblätter, Andreas; Fügenschuh, Armin; Koch, Thorsten; Koster, Arie; Martin, Alexander; Pfender, Tobias; Wegel, Oliver; Wessäly, Roland Modelling Feasible Network Configurations for UMTS A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations. urn:nbn:de:0297-zib-6837 ZIB Allgemein
OPUS4-763 misc Eisenblätter, Andreas; Fügenschuh, Armin; Geerdes, Hans-Florian; Junglas, Daniel; Koch, Thorsten; Martin, Alexander Optimization Methods for UMTS Radio Network Planning The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results. urn:nbn:de:0297-zib-7637 ZIB Allgemein
OPUS4-2933 Wissenschaftlicher Artikel Fügenschuh, Armin; Herty, Michael; Klar, Axel; Martin, Alexander Combinatorial and Continuous Models and Optimization for Traffic Flow on Networks 2006 21 SIAM Journal on Optimization 16 4 1155 1176 Mathematical Optimization
OPUS4-2934 Wissenschaftlicher Artikel Fügenschuh, Armin; Stöveken, Peter Integrierte Optimierung des ÖPNV-Angebots und der Schulanfangszeiten 2005 6 Straß enverkehrstechnik 49 6 281 287 Mathematical Optimization
OPUS4-2935 Konferenzveröffentlichung Fügenschuh, Armin; Homfeld, Henning; Schülldorf, Hanno; Vigerske, Stefan Rodrigues, H. Mixed-Integer Nonlinear Problems in Transportation Applications 2010 Proceedings of the 2nd International Conference on Engineering Optimization (+CD-rom) Mathematical Optimization
OPUS4-2936 Konferenzveröffentlichung Fügenschuh, Armin; Gausemeier, Pia; Seliger, Günther; Severengiz, Semih Dangelmaier, W. Scenario Technique with Integer Programming for Sustainability in Manufacturing 2010 11 8th International Heinz Nixdorf Symposium, Changing Paradigms 320 331 Mathematical Optimization
OPUS4-2937 Konferenzveröffentlichung Fügenschuh, Armin; Defterli, Özlem; Weber, Gehard-Wilhelm New Discretization and Optimization Techniques with Results in the Dynamics of Gene-Environment Networks 2010 3rd Global Conference on Power Control and Optimization (PCO 2010) Mathematical Optimization
OPUS4-2938 Konferenzveröffentlichung Fügenschuh, Armin; Homfeld, Henning; Schülldorf, Hanno Barnhart, C.; Clausen, U.; Lauther, U.; Möhring, R. Single Car Routing in Rail Freight Transport 2009 Dagstuhl Seminar Proceedings 09261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Deutschland Mathematical Optimization
OPUS4-2939 Konferenzveröffentlichung Fügenschuh, Armin; ler, Björn; Martin, Alexander; Morsi, Antonio Barnhart, C.; Clausen, U.; Lauther, U.; Möhring, R. The Transport PDE and Mixed-Integer Linear Programming 2009 Dagstuhl Seminar Proceedings 09261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Deutschland Mathematical Optimization
OPUS4-2940 Konferenzveröffentlichung Dsoki, Chalid; Fügenschuh, Armin; Hanselka, Holger; Hochbaum, Dorit; Hernandez-Magallanes, Irma; Moreno-Centeno, Erick; Peter, Andrea Groche, P. Das ANSLC-Programm und das SDM im Vergleich 2008 9 Sonderforschungsbereich 666 97 106 Mathematical Optimization
OPUS4-2941 Konferenzveröffentlichung Fügenschuh, Armin; Hess, Wolfgang; Schewe, Lars; Martin, Alexander; Ulbrich, Stefan Groche, P. Verfeinerte Modelle zur Topologie- und Geometrie-Optimierung von Blechprofilen mit Kammern 2008 11 Sonderforschungsbereich 666 17 28 Mathematical Optimization
OPUS4-2942 Konferenzveröffentlichung Balaprakash, Prasanna; Fügenschuh, Armin; Homfeld, Henning; Schoch, Michael; Stützle, Thomas; Yuan, Zhi Aguilera, M.J. Iterated Greedy Algorithms for a Real-World Cyclic Train Scheduling Problem 2008 10 Hybrid Metaheuristics, 4th International Workshop, HM 2008, Malaga, Spain, October 8-9, 2008 21 31 Mathematical Optimization
OPUS4-2943 Konferenzveröffentlichung Fügenschuh, Armin; Martin, Alexander Mixed-integer models for topology optimization in sheet metal design 2007 1 Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007 2060049 2060050 Mathematical Optimization
OPUS4-2944 Konferenzveröffentlichung Fügenschuh, Armin; Prick, Matthias; Stöveken, Peter Ausschreibung von Linienbündeln versus Schulzeitkoordinierung? 2007 VWT Conference e-Proceedings Mathematical Optimization
OPUS4-2945 Konferenzveröffentlichung Birkhofer, Herbert; Fügenschuh, Armin; Martin, Alexander; Wäldele, Martin Algorithmenbasierte Produktentwicklung für integrale Blechbauweisen höherer Verzweigungsordnung 2007 Optimierung in der Produktentwicklung, 5. Geimeinsames Kolloquium Konstruktionstechnik Mathematical Optimization
OPUS4-2946 Konferenzveröffentlichung Fügenschuh, Armin; Göttlich, Simone; Herty, Michael Günther, H.-O.; Mattfeld, D.; Suhl, L. A new modeling approach for an integrated simulation and optimization of production networks 2007 15 Management logistischer Netzwerke 45 60 Mathematical Optimization
OPUS4-2947 Konferenzveröffentlichung Fügenschuh, Armin; Göttlich, Simone; Herty, Michael Oberweis, A.; Weinhardt, C.; Gimpel, H.; Koschmider, A.; Pankratius, V.; Schnizler, B. Water Contamination Detection 2007 17 eOrganisation 501 518 Mathematical Optimization
OPUS4-2948 Konferenzveröffentlichung Fügenschuh, Armin; Hess, Wolfgang; Martin, Alexander; Ulbrich, Stefan Groche, P. Diskrete und kontinuierliche Modelle zur Topologie- und Geometrie-Optimierung von Blechprofilen 2007 10 Sonderforschungsbereich 666 37 47 Mathematical Optimization
OPUS4-2949 Konferenzveröffentlichung Fügenschuh, Armin Waldmann, K.-H.; Stocker, U. Scheduling Buses and School Starting Times 2007 5 Operations Research Proceedings 17 22 Mathematical Optimization
OPUS4-2950 Konferenzveröffentlichung Birkhofer, Herbert; Fügenschuh, Armin; Günther, Ute; Junglas, Daniel; Martin, Alexander; Sauer, Thorsten; Ulbrich, Stefan; Wäldele, Martin; Walter, Stephan Haasis, H.; Kopfer, H.; Schönberger, J. Topology- and shape-optimization of branched sheet metal products 2006 9 Operations Research Proceedings 327 336 Mathematical Optimization
OPUS4-2951 Konferenzveröffentlichung Fügenschuh, Armin; Höfler, Benjamin Gottlieb, J.; Raidl, G. Parametrized GRASP Heuristics for Three-Index Assignment 2006 11 Evolutionary Computation in Combinatorial Optimization 61 72 Mathematical Optimization
OPUS4-2952 Konferenzveröffentlichung Fügenschuh, Armin; Homfeld, Henning; Huck, Andreas; Martin, Alexander Jacob, R.; Müller-Hannemann, M. Locomotive and Wagon Scheduling in Freight Transport 2006 Proceedings of the ATMOS06 Mathematical Optimization
OPUS4-2953 Konferenzveröffentlichung Fügenschuh, Armin; Martin, Alexander; Stöveken, Peter Fleuren, H.; den Hertog, D.; Kort, P. Integrated Optimization of School Starting Times and Public Bus Services 2005 7 Operations Research Proceedings 150 157 Mathematical Optimization
OPUS4-2954 Konferenzveröffentlichung Fügenschuh, Armin; Martin, Alexander; Mehlert, Christian; Stöveken, Peter Günther, H.-O.; Mattfeld, D.; Suhl, L. Ein Planungstool zur Schulzeitstaffelung 2005 17 Supply Chain Management und Logistik 419 436 Mathematical Optimization
OPUS4-2955 Konferenzveröffentlichung Fügenschuh, Armin; Stöveken, Peter Integrierte Optimierung der Schulanfangszeit und des Nahverkehrs-Angebots 2005 13 Tagungsband der Heureka’05 – Optimierung in Verkehr und Transport 265 278 Mathematical Optimization
OPUS4-2956 Konferenzveröffentlichung Fügenschuh, Armin Aguilera, M.J.; Blum, C.; Roli, A.; Sampels, M. Parametrized Greedy Heuristics in Theory and Practice 2005 10 Hybrid Metaheuristics, Second International Workshop, HM 2005, Barcelona 21 31 Mathematical Optimization
OPUS4-2957 Konferenzveröffentlichung Fügenschuh, Armin Jaszkiewicz, A.; Kaczmarek, M.; Zak, J.; Kubiak, M. Scheduling Buses in Rural Areas 2005 5 Advanced OR and AI Methods in Transportation, 10th EWGT / 16th Mini-Euro Conference Proceedings, Poznan 706 711 Mathematical Optimization
OPUS4-2958 Konferenzveröffentlichung Eisenblätter, Andreas; Fügenschuh, Armin; Geerdes, Hans-Florian; Junglas, Daniel; Koch, Thorsten; Martin, Alexander Integer Programming Methods for UMTS Radio Network Planning 2004 Proceedings of the WiOpt’04, Cambridge, UK Mathematical Optimization
OPUS4-2959 Konferenzveröffentlichung Fügenschuh, Armin; Martin, Alexander; Stöveken, Peter Bixby, R.; Simchi-Levi, D.; Martin, A.; Zimmermann, U. Integrated Optimization of School Starting Times and Public Bus Services 2004 Mathematics in the Supply Chain Mathematical Optimization
OPUS4-2961 Teil eines Buches Fügenschuh, Armin; Martin, Alexander Aardal, K.; Nemhauser, G.; Weismantel, R. Computational Integer Programming and Cutting Planes North-Holland 2005 53 Handbooks in Operations Research and Management Science, Vol. 12 69 122 Mathematical Optimization
OPUS4-2962 Teil eines Buches Fügenschuh, Armin Görts, W. Von Mikrochips, Proteinen und Schulbussen - Projektproseminare im Mathematikstudium UVW UniversitätsVerlagWebler, Bielefeld 2003 22 Projektveranstaltungen in Mathematik, Informatik und Ingenieurwissenschaften 21 43 Mathematical Optimization
OPUS4-2963 Teil eines Buches Eisenblätter, Andreas; Fügenschuh, Armin; Koch, Thorsten; Koster, Ari; Martin, Alexander; Pfender, Tobias; Wegel, Oliver; Wessäly, Roland G. Anandalingam, S. Mathematical Model of Feasible Network Configurations for UMTS Kluwer 2002 23 Telecommunications network design and management 1 24 Mathematical Optimization
OPUS4-2892 Konferenzveröffentlichung Fügenschuh, Armin; Homfeld, Henning; Martin, Alexander Leitwegeplanung 2007 Mathematik für Innovationen in Industrie und Dienstleistungen Mathematical Optimization
OPUS4-2964 Wissenschaftlicher Artikel Dür, Mirjam; Fügenschuh, Armin; Martin, Alexander; Schabel, Samuel; Schönberger, Christine; Villforth, Klaus Steuerung einer Sortieranlage, z.B. für Altpapier 2010 Europäische Patentanmeldung EP 09 718 564.9 Mathematical Optimization
OPUS4-2965 Wissenschaftlicher Artikel Dür, Mirjam; Fügenschuh, Armin; Martin, Alexander; Schabel, Samuel; Schönberger, Christine; Villforth, Klaus Verfahren zum Einstellen und/oder Optimieren einer einen Gutstoff von einem Schlechtstoff trennenden Sortieranlage und Sortieranlage 2008 Deutsches Patent DE 10 2008 013 034 Mathematical Optimization
OPUS4-2966 Wissenschaftlicher Artikel Dür, Mirjam; Fügenschuh, Armin; Martin, Alexander; Ulbrich, Stefan Verfahren und Vorrichtung zum Auswuchten von wellenelastischen Rotoren 2006 Deutsche Patentanmeldung DE 10 2006 060 583.7 Mathematical Optimization
OPUS4-2967 Wissenschaftlicher Artikel Fügenschuh, Armin; Martin, Alexander Verfahren und Vorrichtung zur automatischen Optimierung von Schulanfangszeiten und des öffentlichen Personenverkehrs und entsprechendes Computerprogramm 2004 Deutsche Patentanmeldung DE 10 2004 020 786.0 Mathematical Optimization
OPUS4-2969 misc Eisenblätter, Andreas; Fügenschuh, Armin; Geerdes, Hans-Florian; Koch, Thorsten; Türke, Ulrich; Meijerink, Ellen XML Data Specification and Documentation IST-2000-28088 MOMENTUM Technical Report 2003 Mathematical Optimization
OPUS4-2970 Wissenschaftlicher Artikel Fügenschuh, Armin Scheduling School Starting Times and Public Buses 2009 5 SIAG/OPT Views-and-News 20 1 1 6 Mathematical Optimization
OPUS4-2971 Wissenschaftlicher Artikel Fügenschuh, Armin Spalten am Stück - Maschinenbauer, Materialwissenschaftler und Mathematiker erfinden die Blechbearbeitung neu 2007 hoch$^3$ 2 19 Mathematical Optimization
OPUS4-2972 Wissenschaftlicher Artikel Fügenschuh, Armin Bestes Blech - Der hochkomplexe unsichtbare Weg zum präzisen und belastbaren Bauteil 2007 hoch$^3$ 2 20 Mathematical Optimization
OPUS4-2973 Wissenschaftlicher Artikel Fügenschuh, Armin Optimierte Schulanfangszeiten 2006 2 OR News 28 25 27 Mathematical Optimization
OPUS4-2974 Wissenschaftlicher Artikel Dür, Mirjam; Fügenschuh, Armin; Huhn, Petra; Klamroth, Kathrin; Saliba, Sleman; Tammer, Christiane EURO Summer Institute 2006 in Wittenberg 2006 1 OR News 28 71 72 Mathematical Optimization
OPUS4-2923 Wissenschaftlicher Artikel Frank, Martin; Fügenschuh, Armin; Herty, Michael; Schewe, Lars The Coolest Path Problem 2010 19 Networks and Heterogeneous Media 5 1 143 162 Mathematical Optimization
OPUS4-2924 Wissenschaftlicher Artikel Fügenschuh, Armin; Göttlich, Simone; Kirchner, Claus; Herty, Michael; Martin, Alexander Efficient Reformulation and Solution of a Nonlinear PDE-Controlled Flow Network Model 2009 20 Computing 85 3 245 265 Mathematical Optimization
OPUS4-2925 Wissenschaftlicher Artikel Dittel, Agnes; Fügenschuh, Armin; Göttlich, Simone; Herty, Michael MIP Presolve Techniques for a PDE-based Supply Chain Model 2009 18 Optimization Methods & Software 24 3 427 445 Mathematical Optimization
OPUS4-2926 Wissenschaftlicher Artikel Fügenschuh, Armin Solving a School Bus Scheduling Problem with Integer Programming 2009 17 European Journal of Operational Research 193 3 867 884 Mathematical Optimization
OPUS4-2927 Wissenschaftlicher Artikel Fügenschuh, Armin; Homfeld, Henning; Huck, Andreas; Martin, Alexander; Yuan, Zhi Scheduling Locomotives and Car Transfers in Freight Transport 2008 13 Transportation Science 42 4 1 14 Mathematical Optimization
OPUS4-2929 Wissenschaftlicher Artikel Fügenschuh, Armin; Göttlich, Simone; Herty, Michael; Klar, Alexander; Martin, Alexander A Discrete Optimization Approach to Large Scale Supply Networks Based on Partial Differential Equations 2008 17 SIAM Journal on Scientific Computing 30 3 1490 1507 Mathematical Optimization
OPUS4-2930 Wissenschaftlicher Artikel Fügenschuh, Armin; Martin, Alexander A Multicriterial Approach for Optimizing Bus Schedules and School Starting Times 2006 17 Annals of Operations Research 147 1 199 216 Mathematical Optimization
OPUS4-2931 Wissenschaftlicher Artikel Fügenschuh, Armin The Vehicle Routing Problem with Coupled Time Windows 2006 19 Central European Journal of Operations Research 14 2 157 176 Mathematical Optimization
OPUS4-2932 Wissenschaftlicher Artikel Fügenschuh, Armin; Martin, Alexander Welche Gemeinsamkeiten haben Jugendliche und Groß banken? 2006 4 mathematiklehren 129 50 54 Mathematical Optimization
OPUS4-2921 Buch (Monographie) Fügenschuh, Armin The Integrated Optimization of School Starting Times and Public Bus Services Logos Verlag Berlin 2005 Mathematical Optimization
OPUS4-2922 Masterarbeit / Diplomarbeit Fügenschuh, Armin Zur Bergman-Vollständigkeit hyperkonvexer Gebiete 2000 Mathematical Optimization
OPUS4-2975 misc Fügenschuh, Armin Optimale Schulanfangszeiten Bild der Wissenschaft 11/2006, Sonderbeilage zum Klaus-Tschira-Preis 2006 Mathematical Optimization
OPUS4-2976 Wissenschaftlicher Artikel Fügenschuh, Armin Optimal verknüpft - Schulanfangszeiten und öffentlicher Personennahverkehr 2006 3 thema forschung 1 82 85 Mathematical Optimization
OPUS4-2977 Wissenschaftlicher Artikel Fügenschuh, Armin Mathematische Modelle zur betrieblichen Optimierung 2006 Z! - das Zukunftsmagazin 1 3 Mathematical Optimization
OPUS4-2978 misc Fügenschuh, Armin Einsatzplanung von ÖPNV-Bussen Mathematische Modellierung mit Schülern - Die Modellierungswoche im Kloster Höchst. M. Kiehl, A. Schich, S. Purpus (Hrsg.). Zentrum für Mathematik, Bensheim 2002 Mathematical Optimization
OPUS4-2979 misc Fügenschuh, Armin Proteinfaltung Mathematische Modellierung mit Schülern - Die Modellierungswoche im Kloster Höchst. M. Kiehl, A. Schich, S. Purpus (Hrsg.). Zentrum für Mathematik, Bensheim 2001 Mathematical Optimization
OPUS4-3244 Konferenzveröffentlichung Eisenblätter, Andreas; Koch, Thorsten; Martin, Alexander; Achterberg, Tobias; Fügenschuh, Armin; Koster, Arie; Wegel, Oliver; Wessäly, Roland Anandalingam, G.; Raghavan, S. Modelling Feasible Network Configurations for UMTS Kluver 2003 Telecommunications Network Design and Management
OPUS4-3246 Konferenzveröffentlichung Eisenblätter, Andreas; Fügenschuh, Armin; Geerdes, Hans-Florian; Junglas, Daniel; Koch, Thorsten; Martin, Alexander Ahr, D.; Fahrion, R.; Oswald, M.; Reinelt, G. Optimisation Methods for UMTS Radio Network Planning Springer 2003 7 Operation Research Proceedings 2003 31 38 10.1007/978-3-642-17022-5_5
OPUS4-5759 Konferenzveröffentlichung Klug, Torsten; Junosza-Szaniawski, Konstanty; Kwasiborski, Slawomir; Fügenschuh, Armin; Schlechte, Thomas Fastest, Average and Quantile Schedule We consider problems concerning the scheduling of a set of trains on a single track. For every pair of trains there is a minimum headway, which every train must wait before it enters the track after another train. The speed of each train is also given. Hence for every schedule - a sequence of trains - we may compute the time that is at least needed for all trains to travel along the track in the given order. We give the solution to three problems: the fastest schedule, the average schedule, and the problem of quantile schedules. The last problem is a question about the smallest upper bound on the time of a given fraction of all possible schedules. We show how these problems are related to the travelling salesman problem. We prove NP-completeness of the fastest schedule problem, NP-hardness of quantile of schedules problem, and polynomiality of the average schedule problem. We also describe some algorithms for all three problems. In the solution of the quantile problem we give an algorithm, based on a reverse search method, generating with polynomial delay all Eulerian multigraphs with the given degree sequence and a bound on the number of such multigraphs. A better bound is left as an open question. Springer Berlin Heidelberg 15 SOFSEM 2015: Theory and Practice of Computer Science 201 216 10.1007/978-3-662-46078-8_17 Mathematical Optimization
OPUS4-4940 Habilitation Fügenschuh, Armin Computational aspects of time in scheduling and dynamic flow problems Mathematical Optimization
OPUS4-4816 Konferenzveröffentlichung Brose, Achim; Fügenschuh, Armin; Gausemeier, Pia; Vierhaus, Ingmar; Seliger, Günther A System Dynamic Enhancement for the Scenario Technique The Scenario Technique is a strategic planning method that aims to describe and analyze potential developments of a considered system in the future. Its application consists of several steps, from an initial problem analysis over an influence analysis to projections of key factors and a definition of the scenarios to a final interpretation of the results. The technique itself combines qualitative and quantitative methods and is an enhancement of the standard Scenario Technique. We use the numerical values gathered during the influence analysis, and embed them in a System Dynamics framework. This yields a mathematically rigorous way to achieve predictions of the system's future behavior from an initial impulse and the feedback structure of the factors. The outcome of our new method is a further way of projecting the present into the future, which enables the user of the Scenario Technique to obtain a validation of the results achieved by the standard method. Berlin Universitätsverlag der TU Berlin 5 Proc. 11th Global Conference on Sustainable Manufacturing 561 566 Mathematical Optimization
OPUS4-4817 Konferenzveröffentlichung Scheumann, René; Vierhaus, Ingmar; Chang, Ya-Ju; Fügenschuh, Armin; Finkbeiner, Matthias Identification of trade-offs for sustainable manufacturing of a Bamboo Bike by System Dynamics We develop a generic System Dynamic model to simulate the production, machines, employees, waste, and capital flows of a manufacturing company. In a second step, this model is specialised by defining suit-able input data to represent a bicycle manufacturing company in a developing country. We monitor a set of sustainability indicators to understand the social, environmental and economic impact of the company, and to estimate managerial decisions to be taken in order to improve on these criteria. We show that the social and environmental situation can be improved over time without sacrificing the economic success of the company's business. 8 Proceedings of the 27. Conference on Environmental Informatics - Informatics for Environmental Protection, Sustainable Development and Risk Management 523 531 Mathematical Optimization
OPUS4-4822 Konferenzveröffentlichung Fügenschuh, Armin; van Veldhuizen, Roel; Vierhaus, Ingmar Production Planning for Non-Cooperating Companies with Nonlinear Optimization We consider a production planning problem where two competing companies are selling their items on a common market. Moreover, the raw material used in the production is a limited non-renewable resource. The revenue per item sold depends on the total amount of items produced by both players. If they collaborate they could apply a production strategy that leads to the highest combined revenue. Usually the formation of such syndicates is prohibited by law; hence we assume that one company does not know how much the other company will produce. We formulate the problem for company A to find an optimal production plan without information on the strategy of company B as a nonlinear mathematical optimization problem. In its naive formulation the model is too large, making its solution practically impossible. After a reformulation we find a much smaller model, which we solve by spatial branch-and-cut methods and linear programming. We discuss the practical implications of our solutions. Berlin Universitätsverlag der TU Berlin 5 11th Global Conference on Sustainable Manufacturing : Proceedings 536 541 Mathematical Optimization
OPUS4-4823 Konferenzveröffentlichung Fügenschuh, Armin; Vierhaus, Ingmar System Dynamic Optimization in the Sustainability Assessment of a World-Model The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually nonlinear. Therefore seemingly simple systems can show a nonintuitive, nonpredictable behavior over time. Controlling a dynamical system means to define a desired final state in which the system should be, and to specify potential interventions from outside that should keep the system on the right track. The central question is how to compute such globally optimal control for a given SD model. We propose a branch-and-bound approach that is based on a bound propagation method, primal heuristics, and spatial branching. We apply our new SD-control method to a small System Dynamics model, that describes the evolution of a social-economic system over time. We examine the problem of steering this system on a sustainable consumption path. Berlin Universitätsverlag der TU Berlin 5 11th Global Conference on Sustainable Manufacturing : Proceedings 530 535 Mathematical Optimization
OPUS4-4832 Konferenzveröffentlichung Fügenschuh, Armin; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Schwarz, Robert; Schweiger, Jonas; Szabo, Jacint Gas Network Topology Optimization for Upcoming Market Requirements Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed. 5 International Conference on the European Energy Market (EEM) 346 351 10.1109/EEM.2011.5953035 Mathematical Optimization
OPUS4-4718 Wissenschaftlicher Artikel Pfetsch, Marc. E; Fügenschuh, Armin; Geißler, Björn; Geißler, Nina; Gollmer, Ralf; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Martin, Alexander; Morsi, Antonio; Rövekamp, Jessica; Schewe, Lars; Schmidt, Martin; Schultz, Rüdiger; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Steinbach, Marc C.; Vigerske, Stefan; Willert, Bernhard M. Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before. Taylor & Francis Optimization Methods and Software 10.1080/10556788.2014.888426 Mathematical Optimization
OPUS4-4738 Wissenschaftlicher Artikel Fügenschuh, Armin; Geißler, Björn; Gollmer, Ralf; Hayn, Christine; Henrion, René; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Martin, Alexander; Mirkov, Radoslava; Morsi, Antonio; Römisch, Werner; Rövekamp, Jessica; Schewe, Lars; Schmidt, Martin; Schultz, Rüdiger; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Steinbach, Marc C.; Willert, Bernhard M. Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network's capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations. Berlin Springer Berlin Heidelberg 24 Energy Systems 5 3 449 473 10.1007/s12667-013-0099-8 Mathematical Optimization
OPUS4-5376 Wissenschaftlicher Artikel Humpola, Jesco; Fügenschuh, Armin; Koch, Thorsten Valid inequalities for the topology optimization problem in gas network design One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euro per km extending the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. Unfortunately, current mathematical methods are not capable of solving the arising network design problems due to their size and complexity. In this article, we will show how to apply optimization methods that can converge to a proven global optimal solution. By introducing a new class of valid inequalities that improve the relaxation of our mixed-integer nonlinear programming model, we are able to speed up the necessary computations substantially. Berlin Heidelberg Springer OR Spectrum 10.1007/s00291-015-0390-2 Mathematical Optimization
OPUS4-5345 Teil eines Buches Humpola, Jesco; Fügenschuh, Armin; Hiller, Benjamin; Koch, Thorsten; Lehmann, Thomas; Lenz, Ralf; Schwarz, Robert; Schweiger, Jonas The Specialized MINLP Approach 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. SIAM Evaluating Gas Network Capacities 9781611973686 Mathematical Optimization
OPUS4-5467 Wissenschaftlicher Artikel Humpola, Jesco; Fügenschuh, Armin Convex reformulations for solving a nonlinear network design problem 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. Springer US Computational Optimization and Applications 10.1007/s10589-015-9756-2 Mathematical Optimization
OPUS4-1653 misc Pfetsch, Marc E.; Fügenschuh, Armin; Geißler, Björn; Geißler, Nina; Gollmer, Ralf; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Martin, Alexander; Morsi, Antonio; Rövekamp, Jessica; Schewe, Lars; Schmidt, Martin; Schultz, Rüdiger; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Steinbach, Marc C.; Vigerske, Stefan; Willert, Bernhard M. Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously. urn:nbn:de:0297-zib-16531 10.1080/10556788.2014.888426 Mathematical Optimization
OPUS4-1782 misc Fügenschuh, Armin; Geißler, Björn; Gollmer, Ralf; Hayn, Christine; Henrion, Rene; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Martin, Alexander; Mirkov, Radoslava; Morsi, Antonio; Römisch, Werner; Rövekamp, Jessica; Schewe, Lars; Schmidt, Martin; Schultz, Rüdiger; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Steinbach, Marc C.; Willert, Bernhard M. Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined. urn:nbn:de:0297-zib-17821 10.1007/s12667-013-0099-8 Mathematical Optimization
OPUS4-6274 Konferenzveröffentlichung Vierhaus, Ingmar; Fügenschuh, Armin Global and Local Optimal Control of a Resource Utilization Problem System Dynamic models describe physical, technical, economical, or social systems using differential and algebraic equations. In their purest form, these models are intended to describe the evolution of a system from a given initial state. In many applications, it is possible to intervene with the system in order to obtain a desired dynamic or a certain outcome in the end. On the mathematical side, this leads to control problems, where aside from the simulation one has to find optimal intervention functions over time that maximize a specific objective function. Using a dynamical model for the utilization of a natural nonrenewable resource of Behrens as a demonstrator example, we present two main mathematical solution strategies. They are distinguished by the quality certificate on their respective solution: one leads to proven local optimal solution, and the other technique yields proven global optimal solutions. We present implementational and numerical issues, and a comparison of both methods. Proceedings of the
33rd International Conference of the System Dynamics Society Mathematical Optimization
OPUS4-5302 Konferenzveröffentlichung Vierhaus, Ingmar; Fügenschuh, Armin A Global Approach to the Optimal Control of System Dynamics Models The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually ordinary differential equations and nonlinear algebraic constraints. Seemingly simple systems can show a nonintuitive, unpredictable behavior over time. Controlling a dynamical system means to specify potential interventions from outside that should keep the system on the desired track, and to define an evaluation schema to compare different controls among each other, so that a ``best'' control can be defined in a meaningful way. The central question is how to compute such globally optimal control for a given SD model, that allows the transition of the system into a desired state with minimum effort. We propose a mixed-integer nonlinear programming (MINLP) reformulation of the System Dynamics Optimization (SDO) problem. MINLP problems can be solved by linear programming based branch-and-bound approach. We demonstrate that standard MINLP solvers are not able to solve SDO problem. To overcome this obstacle, we introduce a special-tailored bound propagation method. Numerical results for these test cases are presented. Proceedings of the 31st International Conference of the System Dynamics Society Mathematical Optimization
OPUS4-5303 Konferenzveröffentlichung Vierhaus, Ingmar; Fügenschuh, Armin; Gottwald, Robert; Grösser, Stefan Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models We study System Dynamics models with several free parameters that can be altered by the user. We assume that the user's goal is to achieve a certain dynamic behavior of the model by varying these parameters. In order to find best possible combination of parameter settings, several automatic parameter tuning methods are described in the literature and readily available within existing System Dynamic software packages. We give a survey on the available techniques in the market and describe their theoretical background. Some of these methods are already six decades old, and meanwhile newer and more powerful optimization methods have emerged in the mathematical literature. One major obstacle for their direct use are tabled data in System Dynamics models, which are usually interpreted as piecewise linear functions. However, modern optimization methods usually require smooth functions which are twice continuously differentiable. We overcome this problem by a smooth spline interpolation of the tabled data. We use a test set of three complex System Dynamic models from the literature, describe their individual transition into optimization problems, and demonstrate the applicability of modern optimization algorithms to these System Dynamics Optimization problems. Proceedings of the 32nd International Conference of the System Dynamics Society Mathematical Optimization
OPUS4-5249 Wissenschaftlicher Artikel Humpola, Jesco; Lehmann, Thomas; Fügenschuh, Armin A primal heuristic for optimizing the topology of gas networks based on dual information We present a novel heuristic to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point of a nonlinear relaxation. Based on the information from the KKT point we alter some of the binary variables in a locally promising way exploiting our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP. EURO Journal on Computational Optimization 10.1007/s13675-014-0029-0 Mathematical Optimization
OPUS4-5812 Wissenschaftlicher Artikel Borndörfer, Ralf; Fügenschuh, Armin; Klug, Torsten; Schang, Thilo; Schlechte, Thomas; Schülldorf, Hanno The Freight Train Routing Problem for Congested Railway Networks with Mixed Traffic We consider the following freight train routing problem (FTRP). Given is a transportation network with fixed routes for passenger trains and a set of freight trains (requests), each defined by an origin and destination station pair. The objective is to calculate a feasible route for each freight train such that the sum of all expected delays and all running times is minimal. Previous research concentrated on microscopic train routings for junctions or inside major stations. Only recently approaches were developed to tackle larger corridors or even networks. We investigate the routing problem from a strategic perspective, calculating the routes in a macroscopic transportation network of Deutsche Bahn AG. In this context, macroscopic refers to an aggregation of complex and large real-world structures into fewer network elements. Moreover, the departure and arrival times of freight trains are approximated. The problem has a strategic character since it asks only for a coarse routing through the network without the precise timings. We provide a mixed-integer nonlinear programming (MINLP) formulation for the FTRP, which is a multicommodity flow model on a time-expanded graph with additional routing constraints. The model's nonlinearities originate from an algebraic approximation of the delays of the trains on the arcs of the network by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model (MILP) by piecewise linear approximation. The latter is solved by a state-of-the art MILP solver for various real-world test instances. Transportation Science 10.1287/trsc.2015.0656 Mathematical Optimization
OPUS4-1899 misc Borndörfer, Ralf; Fügenschuh, Armin; Klug, Torsten; Schang, Thilo; Schlechte, Thomas; Schülldorf, Hanno The Freight Train Routing Problem We consider the following freight train routing problem (FTRP). Given is a transportation network with fixed routes for passenger trains and a set of freight trains (requests), each defined by an origin and destination station pair. The objective is to calculate a feasible route for each freight train such that a sum of all expected delays and all running times is minimal. Previous research concentrated on microscopic train routings for junctions or inside major stations. Only recently approaches were developed to tackle larger corridors or even networks. We investigate the routing problem from a strategic perspective, calculating the routes in a macroscopic transportation network of Deutsche Bahn AG. Here macroscopic refers to an aggregation of complex real-world structures are into fewer network elements. Moreover, the departure and arrival times of freight trains are approximated. The problem has a strategic character since it asks only for a coarse routing through the network without the precise timings. We give a mixed-integer nonlinear programming~(MINLP) formulation for FTRP, which is a multi-commodity flow model on a time-expanded graph with additional routing constraints. The model's nonlinearities are due to an algebraic approximation of the delays of the trains on the arcs of the network by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model~(MILP) by piecewise linear approximation. The latter is solved by a state of the art MILP solver for various real-world test instances. urn:nbn:de:0297-zib-18991 Mathematical Optimization
OPUS4-5359 misc Fügenschuh, Armin; Junosza-Szaniawski, Konstanty; Klug, Torsten; Kwasiborski, Slawomir; Schlechte, Thomas Fastest, average and quantile schedule We consider problems concerning the scheduling of a set of trains on a single track. For every pair of trains there is a minimum headway, which every train must wait before it enters the track after another train. The speed of each train is also given. Hence for every schedule - a sequence of trains - we may compute the time that is at least needed for all trains to travel along the track in the given order. We give the solution to three problems: the fastest schedule, the average schedule, and the problem of quantile schedules. The last problem is a question about the smallest upper bound on the time of a given fraction of all possible schedules. We show how these problems are related to the travelling salesman problem. We prove NP-completeness of the fastest schedule problem, NP-hardness of quantile of schedules problem, and polynomiality of the average schedule problem. We also describe some algorithms for all three problems. In the solution of the quantile problem we give an algorithm, based on a reverse search method, generating with polynomial delay all Eulerian multigraphs with the given degree sequence and a bound on the number of such multigraphs. A better bound is left as an open question. urn:nbn:de:0297-zib-53592 Mathematical Optimization
OPUS4-1777 misc Humpola, Jesco; Fügenschuh, Armin A New Class of Valid Inequalities for Nonlinear Network Design Problems We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. 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. Assume that there does not exist a feasible flow that fulfills all physical constraints and meets the desired entry and exit amounts. Then a natural question is where to extend the network by adding pipes in the most economic way such that this flow becomes feasible. Answering this question is computationally demanding because of the difficult problem structure. We use mixed-integer nonlinear programming techniques that rely on an outer approximation of the overall problem, and a branching on decision variables. We formulate a new class of valid inequalities (or cutting planes) which reduce the overall solution time when added to the formulation. We demonstrate the computational merits of our approach on test instances. urn:nbn:de:0297-zib-17771 10.1007/s00291-015-0390-2 Mathematical Optimization
OPUS4-1686 misc Fügenschuh, Armin; Hayn, Christine; Michaels, Dennis Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt the production process. For the mechanical separation process of fibers from stickies a separator screen is used. This machine has one input feed and two output streams, called the accept and the reject. In the accept the fibers are concentrated, whereas the reject has a higher concentration of stickies. The machine can be controlled by setting its reject rate. But even when the reject rate is set properly, after just a single screening step, the accept still has too many stickies, or the reject too many fibers. To get a proper separation, several separators have to be assembled into a network. From a mathematical point of view this problem can be seen as a multi-commodity network flow design problem with a nonlinear, controllable distribution function at each node. We present a nonlinear mixed-integer programming model for the simultaneous selection of a subset of separators, the network's topology, and the optimal setting of each separator. Numerical results are obtained via different types of linearization of the nonlinearities and the use of mixed-integer linear solvers, and compared with state-of-the-art global optimization software. urn:nbn:de:0297-zib-16862 Mathematical Optimization
OPUS4-1814 misc Fügenschuh, Armin; Vierhaus, Ingmar System Dynamic Optimization in the Sustainability Assessment of a World-Model The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually nonlinear. Therefore seemingly simple systems can show a nonintuitive, nonpredictable behavior over time. Controlling a dynamical system means to define a desired final state in which the system should be, and to specify potential interventions from outside that should keep the system on the right track. The central question is how to compute such globally optimal control for a given SD model. We propose a branch-and-bound approach that is based on a bound propagation method, primal heuristics, and spatial branching. We apply our new SD-control method to a small System Dynamics model, that describes the evolution of a social-economic system over time. We examine the problem of steering this system on a sustainable consumption path. urn:nbn:de:0297-zib-18148 Mathematical Optimization
OPUS4-4293 misc Fügenschuh, Armin; Grösser, Stefan N.; Vierhaus, Ingmar A Global Approach to the Control of an Industry Structure System Dynamics Model We consider a system dynamics model that describes the effect of human activity on natural resources. The central stocks are the accumulated profit, the industry structures, and the water resources. The model can be controlled through two time-dependent parameters. The goal in this paper is to find a parameter setting that leads to a maximization of a performance index, which reflects both environmental and economic aspects. Thus, the goal is to identify the most sustainable stock of industry structures within the model's constraints and assumptions. In order to find a proven global optimal parameter set, we formulate the System Dynamics Optimization model as a mixed-integer nonlinear problem that is accessible for numerical solvers. Due to the dynamic structure of the model, certain steps of the solution process must be handled with greater care, compared to standard non-dynamic problems. We describe our approach of solving the industry structure model and present computational results. In addition, we discuss the limitations of the approach and next steps. urn:nbn:de:0297-zib-42932 Mathematical Optimization
OPUS4-4311 misc Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas A Primal Heuristic for MINLP based on Dual Information We present a novel heuristic algorithm to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point for a nonlinear relaxation. Based on the information from the KKT point we alter some of the integer variables in a locally promising way. We describe this heuristic for general MINLPs and then show how to tailor the heuristic to exploit our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP. urn:nbn:de:0297-zib-43110 10.1007/s13675-014-0029-0 Mathematical Optimization
OPUS4-1885 misc Fügenschuh, Armin; Humpola, Jesco A Unified View on Relaxations for a Nonlinear Network Flow Problem We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. 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 how to numerically compute this flow and pressures. We review an existing approach of Maugis (1977) and extend it to the case of networks with active elements (for example, compressors). We further examine different ways of relaxations for the nonlinear network flow model. We compare different approaches based on nonlinear optimization numerically on a set of test instances. urn:nbn:de:0297-zib-18857 Mathematical Optimization
OPUS4-1860 misc Fügenschuh, Armin; Vierhaus, Ingmar A Global Approach to the Optimal Control of System Dynamics Models The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually ordinary differential equations and nonlinear algebraic constraints. Therefore seemingly simple systems can show a nonintuitive, unpredictable behavior over time. Controlling a dynamical system means to specify potential interventions from outside that should keep the system on the desired track, and to define an evaluation schema to compare different controls among each other, so that a "best" control can be defined in a meaningful way. The central question is how to compute such globally optimal control for a given SD model, that allows the transition of the system into a desired state with minimum effort. We propose a mixed-integer nonlinear programming (MINLP) reformulation of the System Dynamics Optimization (SDO) problem. MINLP problems can be solved by linear programming based branch-and-bound approach. We demonstrate that standard MINLP solvers are not able to solve SDO problem. To overcome this obstacle, we introduce a special-tailored bound propagation method. We apply our new method to a predator-prey model with additional hunting activity as control, and to a mini-world model with the consumption level as control. Numerical results for these test cases are presented. urn:nbn:de:0297-zib-18600 Mathematical Optimization
OPUS4-1815 misc Brose, Achim; Fügenschuh, Armin; Gausemeier, Pia; Vierhaus, Ingmar; Seliger, Günther A System Dynamic Enhancement for the Scenario Technique The Scenario Technique is a strategic planning method that aims to describe and analyze potential developments of a considered system in the future. Its application consists of several steps, from an initial problem analysis over an influence analysis to projections of key factors and a definition of the scenarios to a final interpretation of the results. The technique itself combines qualitative and quantitative methods and is an enhancement of the standard Scenario Technique. We use the numerical values gathered during the influence analysis, and embed them in a System Dynamics framework. This yields a mathematically rigorous way to achieve predictions of the system's future behavior from an initial impulse and the feedback structure of the factors. The outcome of our new method is a further way of projecting the present into the future, which enables the user of the Scenario Technique to obtain a validation of the results achieved by the standard method. urn:nbn:de:0297-zib-18150 Mathematical Optimization
OPUS4-1816 misc Fügenschuh, Armin; van Veldhuizen, Roel; Vierhaus, Ingmar Production Planning for Non-Cooperating Companies with Nonlinear Optimization We consider a production planning problem where two competing companies are selling their items on a common market. Moreover, the raw material used in the production is a limited non-renewable resource. The revenue per item sold depends on the total amount of items produced by both players. If they collaborate they could apply a production strategy that leads to the highest combined revenue. Usually the formation of such syndicates is prohibited by law; hence we assume that one company does not know how much the other company will produce. We formulate the problem for company A to find an optimal production plan without information on the strategy of company B as a nonlinear mathematical optimization problem. In its naive formulation the model is too large, making its solution practically impossible. After a reformulation we find a much smaller model, which we solve by spatial branch-and-cut methods and linear programming. We discuss the practical implications of our solutions. urn:nbn:de:0297-zib-18163 Mathematical Optimization
OPUS4-4815 misc Vierhaus, Ingmar; Fügenschuh, Armin; Gottwald, Robert Lion; Grösser, Stefan N. Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models We study System Dynamics models with several free parameters that can be altered by the user. We assume that the user's goal is to achieve a certain dynamic behavior of the model by varying these parameters. In order to the find best possible combination of parameter settings, several automatic parameter tuning methods are described in the literature and readily available within existing System Dynamic software packages. We give a survey on the available techniques in the market and describe their theoretical background. Some of these methods are already six decades old, and meanwhile newer and more powerful optimization methods have emerged in the mathematical literature. One major obstacle for their direct use are tabled data in System Dynamics models, which are usually interpreted as piecewise linear functions. However, modern optimization methods usually require smooth functions which are twice continuously differentiable. We overcome this problem by a smooth spline interpolation of the tabled data. We use a test set of three complex System Dynamic models from the literature, describe their individual transition into optimization problems, and demonstrate the applicability of modern optimization algorithms to these System Dynamics Optimization problems. urn:nbn:de:0297-zib-48159 Mathematical Optimization
OPUS4-1889 misc Scheumann, René; Vierhaus, Ingmar; Chang, Ya-Ju; Fügenschuh, Armin; Finkbeiner, Matthias Identification of trade-offs for sustainable manufacturing of a Bamboo Bike by System Dynamics We develop a generic System Dynamic model to simulate the production, machines, employees, waste, and capital flows of a manufacturing company. In a second step, this model is specialised by defining suit-able input data to represent a bicycle manufacturing company in a developing country. We monitor a set of sustainability indicators to understand the social, environmental and economic impact of the company, and to estimate managerial decisions to be taken in order to improve on these criteria. We show that the social and environmental situation can be improved over time without sacrificing the economic success of the company's business. urn:nbn:de:0297-zib-18895 Mathematical Optimization
OPUS4-6753 Wissenschaftlicher Artikel Vierhaus, Ingmar; Fügenschuh, Armin; Gottwald, Robert Lion; Grösser, Stefan Using white-box nonlinear optimization methods in system dynamics policy improvement We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white-box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published "towards a global equilibrium" run with equal cost of intervention. 30 System Dynamics Review 33 2 138 168 10.1002/sdr.1583 Mathematical Optimization
OPUS4-4800 Konferenzveröffentlichung Scheumann, René; Fügenschuh, Armin; Schenker, Sebastian; Vierhaus, Ingmar; Borndörfer, Ralf; Finkbeiner, Matthias Seliger, Günther Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation 7 Proceedings of the 10th Global Conference on Sustainable Manufacturing 978-605-63463-1-6 538 545 Mathematical Optimization
OPUS4-6188 Teil eines Buches Schenker, Sebastian; Vierhaus, Ingmar; Borndörfer, Ralf; Fügenschuh, Armin; Skutella, Martin Stark, Rainer; Seliger, Günther; Bonvoisin, Jérémy Optimisation Methods in Sustainable Manufacturing Sustainable manufacturing is driven by the insight that the focus on the economic dimension in current businesses and lifestyles has to be broadened to cover all three pillars of sustainability: economic development, social development, and environmental protection. Springer International Publishing 14 Sustainable Manufacturing 978-3-319-48514-0 239 253 10.1007/978-3-319-48514-0_15 Mathematical Optimization
OPUS4-1570 misc Scheumann, Rene; Fügenschuh, Armin; Schenker, Sebastian; Vierhaus, Ingmar; Borndörfer, Ralf; Finkbeiner, Matthias Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation It is clear that a transformation to sustainable value creation is needed, because business as usual is not an option for preserving competitive advantages of leading industries. What does that mean? This contribution proposes possible approaches for a shift in existing manufacturing paradigms. In a first step, sustainability aspects from the German Sustainability Strategy and from the tools of life cycle sustainability assessment are chosen to match areas of a value creation process. Within these aspects are indicators, which can be measured within a manufacturing process. Once these data are obtained they can be used to set up a mathematical linear pulse model of manufacturing in order to analyse the evolution of the system over time, that is the transition process, by using a system dynamics approach. An increase of technology development by a factor of 2 leads to an increase of manufacturing but also to an increase of climate change. Compensation measures need to be taken. This can be done by e.g. taking money from the GDP (as an indicator of the aspect ``macroeconomic performance''). The value of the arc from that building block towards climate change must then be increased by a factor of 10. The choice of independent and representative indicators or aspects shall be validated and double-checked for their significance with the help of multi-criteria mixed-integer programming optimisation methods. urn:nbn:de:0297-zib-15703 Mathematical Optimization
OPUS4-6655 Buch (Monographie) Abbink, Erwin; Bärmann, Andreas; Besinovic, Nikola; Bohlin, Markus; Cacchiani, Valentina; Caimi, Gabrio; Dollevot, Twan; de Fabris, Stefano; Fischer, Frank; Fügenschuh, Armin; Galli, Laura; Goverde, Rob M.P.; Hansmann, Ronny; Homfeld, Henning; Huisman, Dennis; Johann, Marc; Klug, Torsten; Kroon, Leo; Lamorgese, Leonardo; Liers, Frauke; Mannino, Carlo; Medeossi, Giorgio; Pacciarelli, Dario; Reuther, Markus; Schlechte, Thomas; Schmidt, Marie; Schöbel, Anita; Schülldorf, Hanno; Stieber, Anke; Stiller, Sebastian; Törnquist Krasemann, Johanna; Toth, Paolo; Zimmermann, Uwe T. Borndörfer, Ralf; Klug, Torsten; Lamorgese, Leonardo; Mannino, Carlo; Reuther, Markus; Schlechte, Thomas Handbook of Optimization in the Railway Industry This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation 1 Springer International Publishing 338 268 978-3-319-72152-1 10.1007/978-3-319-72153-8 Mathematical Optimization