@book{AbbinkBaermannBešinovicetal.2018, author = {Abbink, Erwin and B{\"a}rmann, Andreas and Bešinovic, Nikola and Bohlin, Markus and Cacchiani, Valentina and Caimi, Gabrio and de Fabris, Stefano and Dollevoet, Twan and Fischer, Frank and F{\"u}genschuh, Armin and Galli, Laura and Goverde, Rob M.P. and Hansmann, Ronny and Homfeld, Henning and Huisman, Dennis and Johann, Marc and Klug, Torsten and T{\"o}rnquist Krasemann, Johanna and Kroon, Leo and Lamorgese, Leonardo and Liers, Frauke and Mannino, Carlo and Medeossi, Giorgio and Pacciarelli, Dario and Reuther, Markus and Schlechte, Thomas and Schmidt, Marie and Sch{\"o}bel, Anita and Sch{\"u}lldorf, Hanno and Stieber, Anke and Stiller, Sebastian and Toth, Paolo and Zimmermann, Uwe}, title = {Handbook of Optimization in the Railway Industry}, volume = {268}, editor = {Bornd{\"o}rfer, Ralf and Klug, Torsten and Lamorgese, Leonardo and Mannino, Carlo and Reuther, Markus and Schlechte, Thomas}, publisher = {Springer Verlag}, isbn = {978-3-319-72152-1}, doi = {10.1007/978-3-319-72153-8}, year = {2018}, abstract = {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}, language = {en} } @article{VierhausFuegenschuhGottwaldetal.2017, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin and Gottwald, Robert Lion and Gr{\"o}sser, Stefan}, title = {Using white-box nonlinear optimization methods in system dynamics policy improvement}, volume = {33}, journal = {System Dynamics Review}, number = {2}, doi = {10.1002/sdr.1583}, pages = {138 -- 168}, year = {2017}, abstract = {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.}, language = {en} } @incollection{SchenkerVierhausBorndoerferetal.2017, author = {Schenker, Sebastian and Vierhaus, Ingmar and Bornd{\"o}rfer, Ralf and F{\"u}genschuh, Armin and Skutella, Martin}, title = {Optimisation Methods in Sustainable Manufacturing}, booktitle = {Sustainable Manufacturing}, editor = {Stark, Rainer and Seliger, G{\"u}nther and Bonvoisin, J{\´e}r{\´e}my}, publisher = {Springer International Publishing}, isbn = {978-3-319-48514-0}, doi = {10.1007/978-3-319-48514-0_15}, pages = {239 -- 253}, year = {2017}, abstract = {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.}, language = {en} } @article{HumpolaFuegenschuhKoch2016, author = {Humpola, Jesco and F{\"u}genschuh, Armin and Koch, Thorsten}, title = {Valid inequalities for the topology optimization problem in gas network design}, 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}, year = {2016}, 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} } @article{BorndoerferFuegenschuhKlugetal.2016, author = {Bornd{\"o}rfer, Ralf and F{\"u}genschuh, Armin and Klug, Torsten and Schang, Thilo and Schlechte, Thomas and Sch{\"u}lldorf, Hanno}, title = {The Freight Train Routing Problem for Congested Railway Networks with Mixed Traffic}, volume = {50}, journal = {Transportation Science}, number = {2}, doi = {10.1287/trsc.2015.0656}, pages = {408 -- 423}, year = {2016}, abstract = {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.}, language = {en} } @article{HumpolaFuegenschuh2015, author = {Humpola, Jesco and F{\"u}genschuh, Armin}, title = {Convex reformulations for solving a nonlinear network design problem}, volume = {62}, journal = {Computational Optimization and Applications}, number = {3}, publisher = {Springer US}, doi = {10.1007/s10589-015-9756-2}, pages = {717 -- 759}, year = {2015}, 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} } @incollection{HumpolaFuegenschuhHilleretal.2015, 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}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, year = {2015}, 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{FuegenschuhJunoszaSzaniawskiKlugetal.2015, 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}, year = {2015}, 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} } @inproceedings{KlugJunoszaSzaniawskiKwasiborskietal.2015, author = {Klug, Torsten and Junosza-Szaniawski, Konstanty and Kwasiborski, Slawomir and F{\"u}genschuh, Armin and Schlechte, Thomas}, title = {Fastest, Average and Quantile Schedule}, 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}, year = {2015}, 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} } @article{HumpolaLehmannFuegenschuh2015, author = {Humpola, Jesco and Lehmann, Thomas and F{\"u}genschuh, Armin}, title = {A primal heuristic for optimizing the topology of gas networks based on dual information}, volume = {3}, journal = {EURO Journal on Computational Optimization}, number = {1}, doi = {10.1007/s13675-014-0029-0}, pages = {53 -- 78}, year = {2015}, abstract = {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.}, language = {en} } @inproceedings{VierhausFuegenschuh2015, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin}, title = {Global and Local Optimal Control of a Resource Utilization Problem}, booktitle = {Proceedings of the 33rd International Conference of the System Dynamics Society}, year = {2015}, abstract = {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.}, language = {en} } @article{PfetschFuegenschuhGeissleretal.2014, 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}, journal = {Optimization Methods and Software}, publisher = {Taylor \& Francis}, doi = {10.1080/10556788.2014.888426}, year = {2014}, 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 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.}, language = {en} } @misc{VierhausFuegenschuhGottwaldetal.2014, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin and Gottwald, Robert Lion and Gr{\"o}sser, Stefan N.}, title = {Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-48159}, year = {2014}, 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 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.}, language = {en} } @inproceedings{VierhausFuegenschuhGottwaldetal.2014, 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}, booktitle = {Proceedings of the 32nd International Conference of the System Dynamics Society}, year = {2014}, 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} } @misc{BorndoerferFuegenschuhKlugetal.2013, author = {Bornd{\"o}rfer, Ralf and F{\"u}genschuh, Armin and Klug, Torsten and Schang, Thilo and Schlechte, Thomas and Sch{\"u}lldorf, Hanno}, title = {The Freight Train Routing Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18991}, year = {2013}, abstract = {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.}, language = {en} } @misc{BroseFuegenschuhGausemeieretal.2013, author = {Brose, Achim and F{\"u}genschuh, Armin and Gausemeier, Pia and Vierhaus, Ingmar and Seliger, G{\"u}nther}, title = {A System Dynamic Enhancement for the Scenario Technique}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18150}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{FuegenschuhvanVeldhuizenVierhaus2013, author = {F{\"u}genschuh, Armin and van Veldhuizen, Roel and Vierhaus, Ingmar}, title = {Production Planning for Non-Cooperating Companies with Nonlinear Optimization}, booktitle = {11th Global Conference on Sustainable Manufacturing : Proceedings}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, pages = {536 -- 541}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{FuegenschuhVierhaus2013, author = {F{\"u}genschuh, Armin and Vierhaus, Ingmar}, title = {System Dynamic Optimization in the Sustainability Assessment of a World-Model}, booktitle = {11th Global Conference on Sustainable Manufacturing : Proceedings}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, pages = {530 -- 535}, year = {2013}, 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 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.}, language = {en} } @inproceedings{BroseFuegenschuhGausemeieretal.2013, author = {Brose, Achim and F{\"u}genschuh, Armin and Gausemeier, Pia and Vierhaus, Ingmar and Seliger, G{\"u}nther}, title = {A System Dynamic Enhancement for the Scenario Technique}, booktitle = {Proc. 11th Global Conference on Sustainable Manufacturing}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, pages = {561 -- 566}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{ScheumannVierhausChangetal.2013, author = {Scheumann, Ren{\´e} and Vierhaus, Ingmar and Chang, Ya-Ju and F{\"u}genschuh, Armin and Finkbeiner, Matthias}, title = {Identification of trade-offs for sustainable manufacturing of a Bamboo Bike by System Dynamics}, booktitle = {Proceedings of the 27. Conference on Environmental Informatics - Informatics for Environmental Protection, Sustainable Development and Risk Management}, pages = {523 -- 531}, year = {2013}, abstract = {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.}, language = {en} }