TY - GEN A1 - Fügenschuh, Armin A1 - Hayn, Christine A1 - Michaels, Dennis T1 - Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production N2 - 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. T3 - ZIB-Report - 12-44 KW - Mixed-Integer Linear Programming KW - Nonlinear Programming KW - Piecewise Linear Approximation KW - Topology Optimization KW - Network Design Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16862 SN - 1438-0064 ER - TY - GEN A1 - Scheumann, Rene A1 - Fügenschuh, Armin A1 - Schenker, Sebastian A1 - Vierhaus, Ingmar A1 - Borndörfer, Ralf A1 - Finkbeiner, Matthias T1 - Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation N2 - 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. T3 - ZIB-Report - 12-28 KW - Multi-Criteria Optimisation KW - Sustainability Indicator KW - System Dynamics KW - Value Creation Process Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15703 SN - 1438-0064 ER - TY - GEN A1 - Frank, Martin A1 - Fügenschuh, Armin A1 - Herty, Michael A1 - Schewe, Lars T1 - The Coolest Path Problem N2 - We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph. T3 - ZIB-Report - 09-37 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11571 SN - 1438-0064 ER - TY - CHAP A1 - Klug, Torsten A1 - Junosza-Szaniawski, Konstanty A1 - Kwasiborski, Slawomir A1 - Fügenschuh, Armin A1 - Schlechte, Thomas T1 - Fastest, Average and Quantile Schedule T2 - SOFSEM 2015: Theory and Practice of Computer Science N2 - 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. KW - scheduling KW - eulerian multigraphs Y1 - 2015 U6 - https://doi.org/10.1007/978-3-662-46078-8_17 SP - 201 EP - 216 PB - Springer Berlin Heidelberg ER - TY - CHAP A1 - Vierhaus, Ingmar A1 - Fügenschuh, Armin T1 - Global and Local Optimal Control of a Resource Utilization Problem T2 - Proceedings of the 33rd International Conference of the System Dynamics Society N2 - 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. Y1 - 2015 ER - TY - THES A1 - Fügenschuh, Armin T1 - Computational aspects of time in scheduling and dynamic flow problems Y1 - 2011 ER - TY - CHAP A1 - Schenker, Sebastian A1 - Vierhaus, Ingmar A1 - Borndörfer, Ralf A1 - Fügenschuh, Armin A1 - Skutella, Martin ED - Stark, Rainer ED - Seliger, Günther ED - Bonvoisin, Jérémy T1 - Optimisation Methods in Sustainable Manufacturing BT - Challenges, Solutions and Implementation Perspectives T2 - Sustainable Manufacturing N2 - 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. Y1 - 2017 SN - 978-3-319-48514-0 U6 - https://doi.org/10.1007/978-3-319-48514-0_15 SP - 239 EP - 253 PB - Springer International Publishing ER - TY - CHAP A1 - Vierhaus, Ingmar A1 - Fügenschuh, Armin T1 - A Global Approach to the Optimal Control of System Dynamics Models T2 - Proceedings of the 31st International Conference of the System Dynamics Society N2 - 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. Y1 - 2013 ER - TY - CHAP A1 - Vierhaus, Ingmar A1 - Fügenschuh, Armin A1 - Gottwald, Robert Lion A1 - Grösser, Stefan T1 - Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models T2 - Proceedings of the 32nd International Conference of the System Dynamics Society N2 - 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. Y1 - 2014 ER -