@misc{Fuegenschuh2006, author = {F{\"u}genschuh, Armin}, title = {Optimale Schulanfangszeiten}, publisher = {Bild der Wissenschaft 11/2006, Sonderbeilage zum Klaus-Tschira-Preis}, year = {2006}, language = {en} } @article{Fuegenschuh2006, author = {F{\"u}genschuh, Armin}, title = {Optimal verkn{\"u}pft - Schulanfangszeiten und {\"o}ffentlicher Personennahverkehr}, series = {thema forschung}, volume = {1}, journal = {thema forschung}, pages = {82 -- 85}, year = {2006}, language = {en} } @article{Fuegenschuh2006, author = {F{\"u}genschuh, Armin}, title = {Mathematische Modelle zur betrieblichen Optimierung}, series = {Z! - das Zukunftsmagazin}, volume = {1}, journal = {Z! - das Zukunftsmagazin}, pages = {3}, year = {2006}, language = {en} } @inproceedings{EisenblaetterKochMartinetal.2003, author = {Eisenbl{\"a}tter, Andreas and Koch, Thorsten and Martin, Alexander and Achterberg, Tobias and F{\"u}genschuh, Armin and Koster, Arie M.C.A. and Wegel, Oliver and Wess{\"a}ly, Roland}, title = {Modelling Feasible Network Configurations for UMTS}, series = {Telecommunications Network Design and Management}, booktitle = {Telecommunications Network Design and Management}, editor = {Anandalingam, G. and Raghavan, S.}, publisher = {Kluver}, year = {2003}, language = {en} } @inproceedings{EisenblaetterFuegenschuhGeerdesetal.2003, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Geerdes, Hans-Florian and Junglas, Daniel and Koch, Thorsten and Martin, Alexander}, title = {Optimisation Methods for UMTS Radio Network Planning}, series = {Operation Research Proceedings 2003}, booktitle = {Operation Research Proceedings 2003}, editor = {Ahr, Dino and Fahrion, Roland and Oswald, Marcus and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-17022-5_5}, pages = {31 -- 38}, year = {2003}, language = {en} } @article{EisenblaetterFuegenschuhFledderusetal.2003, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Fledderus, E. and Geerdes, Hans-Florian and Heideck, B. and Junglas, Daniel and Koch, Thorsten and K{\"u}rner, T. and Martin, Alexander}, title = {Mathematical Methods for Automatic Optimization of UMTS Radio Networks}, number = {D4.3}, editor = {Martin, Alexander}, publisher = {IST-2000-28088 MOMENTUM}, year = {2003}, language = {en} } @inproceedings{FuegenschuhHomfeldMartin2007, author = {F{\"u}genschuh, Armin and Homfeld, Henning and Martin, Alexander}, title = {Leitwegeplanung}, series = {Mathematik f{\"u}r Innovationen in Industrie und Dienstleistungen}, booktitle = {Mathematik f{\"u}r Innovationen in Industrie und Dienstleistungen}, year = {2007}, language = {en} } @inproceedings{VierhausFuegenschuh, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin}, title = {A Global Approach to the Optimal Control of System Dynamics Models}, series = {Proceedings of the 31st International Conference of the System Dynamics Society}, booktitle = {Proceedings of the 31st International Conference of the System Dynamics Society}, abstract = {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.}, language = {en} } @inproceedings{VierhausFuegenschuhGottwaldetal., author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin and Gottwald, Robert Lion and Gr{\"o}sser, Stefan}, title = {Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models}, series = {Proceedings of the 32nd International Conference of the System Dynamics Society}, booktitle = {Proceedings of the 32nd International Conference of the System Dynamics Society}, abstract = {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.}, language = {en} } @incollection{HumpolaFuegenschuhHilleretal., author = {Humpola, Jesco and F{\"u}genschuh, Armin and Hiller, Benjamin and Koch, Thorsten and Lehmann, Thomas and Lenz, Ralf and Schwarz, Robert and Schweiger, Jonas}, title = {The Specialized MINLP Approach}, series = {Evaluating Gas Network Capacities}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, abstract = {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.}, language = {en} } @misc{HumpolaFuegenschuhLehmann, author = {Humpola, Jesco and F{\"u}genschuh, Armin and Lehmann, Thomas}, title = {A Primal Heuristic for MINLP based on Dual Information}, issn = {1438-0064}, doi = {10.1007/s13675-014-0029-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43110}, abstract = {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.}, language = {en} } @article{HumpolaFuegenschuh, author = {Humpola, Jesco and F{\"u}genschuh, Armin}, title = {Convex reformulations for solving a nonlinear network design problem}, series = {Computational Optimization and Applications}, volume = {62}, journal = {Computational Optimization and Applications}, number = {3}, publisher = {Springer US}, doi = {10.1007/s10589-015-9756-2}, pages = {717 -- 759}, abstract = {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.}, language = {en} } @article{HumpolaFuegenschuhKoch, author = {Humpola, Jesco and F{\"u}genschuh, Armin and Koch, Thorsten}, title = {Valid inequalities for the topology optimization problem in gas network design}, series = {OR Spectrum}, volume = {38}, journal = {OR Spectrum}, number = {3}, publisher = {Springer}, address = {Berlin Heidelberg}, doi = {https://doi.org/10.1007/s00291-015-0390-2}, pages = {597 -- 631}, abstract = {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.}, language = {en} } @misc{FuegenschuhJunoszaSzaniawskiKlugetal., author = {F{\"u}genschuh, Armin and Junosza-Szaniawski, Konstanty and Klug, Torsten and Kwasiborski, Slawomir and Schlechte, Thomas}, title = {Fastest, average and quantile schedule}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53592}, abstract = {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.}, language = {en} } @misc{PfetschFuegenschuhGeissleretal., author = {Pfetsch, Marc and F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Geißler, Nina and Gollmer, Ralf and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Morsi, Antonio and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Vigerske, Stefan and Willert, Bernhard}, title = {Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions}, issn = {1438-0064}, doi = {10.1080/10556788.2014.888426}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16531}, abstract = {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.}, language = {en} } @inproceedings{KlugJunoszaSzaniawskiKwasiborskietal., author = {Klug, Torsten and Junosza-Szaniawski, Konstanty and Kwasiborski, Slawomir and F{\"u}genschuh, Armin and Schlechte, Thomas}, title = {Fastest, Average and Quantile Schedule}, series = {SOFSEM 2015: Theory and Practice of Computer Science}, booktitle = {SOFSEM 2015: Theory and Practice of Computer Science}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/978-3-662-46078-8_17}, pages = {201 -- 216}, abstract = {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.}, language = {en} } @misc{FuegenschuhHaynMichaels, author = {F{\"u}genschuh, Armin and Hayn, Christine and Michaels, Dennis}, title = {Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16862}, abstract = {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.}, language = {en} } @misc{ScheumannFuegenschuhSchenkeretal., author = {Scheumann, Rene and F{\"u}genschuh, Armin and Schenker, Sebastian and Vierhaus, Ingmar and Bornd{\"o}rfer, Ralf and Finkbeiner, Matthias}, title = {Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15703}, abstract = {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.}, language = {en} } @misc{FuegenschuhGroesserVierhaus, author = {F{\"u}genschuh, Armin and Gr{\"o}sser, Stefan N. and Vierhaus, Ingmar}, title = {A Global Approach to the Control of an Industry Structure System Dynamics Model}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42932}, abstract = {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.}, language = {en} }