@inproceedings{BorndoerferSchenkerSkutellaetal., author = {Bornd{\"o}rfer, Ralf and Schenker, Sebastian and Skutella, Martin and Strunk, Timo}, title = {PolySCIP}, series = {Mathematical Software - ICMS 2016, 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings}, volume = {9725}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings}, editor = {Greuel, G.-M. and Koch, Thorsten and Paule, Peter and Sommese, Andrew}, edition = {Mathematical Software - ICMS 2016}, publisher = {Springer International Publishing}, isbn = {978-3-319-42431-6}, doi = {10.1007/978-3-319-42432-3_32}, pages = {259 -- 264}, abstract = {PolySCIP is a new solver for multi-criteria integer and multi-criteria linear programs handling an arbitrary number of objectives. It is available as an official part of the non-commercial constraint integer programming framework SCIP. It utilizes a lifted weight space approach to compute the set of supported extreme non-dominated points and unbounded non-dominated rays, respectively. The algorithmic approach can be summarized as follows: At the beginning an arbitrary non-dominated point is computed (or it is determined that there is none) and a weight space polyhedron created. In every next iteration a vertex of the weight space polyhedron is selected whose entries give rise to a single-objective optimization problem via a combination of the original objectives. If the ptimization of this single-objective problem yields a new non-dominated point, the weight space polyhedron is updated. Otherwise another vertex of the weight space polyhedron is investigated. The algorithm finishes when all vertices of the weight space polyhedron have been investigated. The file format of PolySCIP is based on the widely used MPS format and allows a simple generation of multi-criteria models via an algebraic modelling language.}, language = {en} } @misc{VierhausFuegenschuhGottwaldetal., 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}, 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{BroseFuegenschuhGausemeieretal., 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}, series = {Proc. 11th Global Conference on Sustainable Manufacturing}, booktitle = {Proc. 11th Global Conference on Sustainable Manufacturing}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, pages = {561 -- 566}, 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., 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}, series = {Proceedings of the 27. Conference on Environmental Informatics - Informatics for Environmental Protection, Sustainable Development and Risk Management}, booktitle = {Proceedings of the 27. Conference on Environmental Informatics - Informatics for Environmental Protection, Sustainable Development and Risk Management}, pages = {523 -- 531}, 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} } @inproceedings{FuegenschuhvanVeldhuizenVierhaus, author = {F{\"u}genschuh, Armin and van Veldhuizen, Roel and Vierhaus, Ingmar}, title = {Production Planning for Non-Cooperating Companies with Nonlinear Optimization}, series = {11th Global Conference on Sustainable Manufacturing : Proceedings}, booktitle = {11th Global Conference on Sustainable Manufacturing : Proceedings}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, pages = {536 -- 541}, 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{FuegenschuhVierhaus, author = {F{\"u}genschuh, Armin and Vierhaus, Ingmar}, title = {System Dynamic Optimization in the Sustainability Assessment of a World-Model}, series = {11th Global Conference on Sustainable Manufacturing : Proceedings}, booktitle = {11th Global Conference on Sustainable Manufacturing : Proceedings}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, pages = {530 -- 535}, 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{ScheumannFuegenschuhSchenkeretal., author = {Scheumann, Ren{\´e} 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}, series = {Proceedings of the 10th Global Conference on Sustainable Manufacturing}, booktitle = {Proceedings of the 10th Global Conference on Sustainable Manufacturing}, editor = {Seliger, G{\"u}nther}, isbn = {978-605-63463-1-6}, pages = {538 -- 545}, language = {en} } @incollection{SchenkerVierhausBorndoerferetal., 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}, series = {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}, 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} } @inproceedings{VierhausFuegenschuh, author = {Vierhaus, Ingmar and F{\"u}genschuh, Armin}, title = {Global and Local Optimal Control of a Resource Utilization Problem}, series = {Proceedings of the 33rd International Conference of the System Dynamics Society}, booktitle = {Proceedings of the 33rd International Conference of the System Dynamics Society}, 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} } @misc{FuegenschuhVierhaus, author = {F{\"u}genschuh, Armin and Vierhaus, Ingmar}, title = {System Dynamic Optimization in the Sustainability Assessment of a World-Model}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18148}, 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} } @misc{BroseFuegenschuhGausemeieretal., 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}, 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} } @misc{FuegenschuhvanVeldhuizenVierhaus, author = {F{\"u}genschuh, Armin and van Veldhuizen, Roel and Vierhaus, Ingmar}, title = {Production Planning for Non-Cooperating Companies with Nonlinear Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18163}, 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{BuchertNeugebauerSchenkeretal., author = {Buchert, Tom and Neugebauer, Sabrina and Schenker, Sebastian and Lindow, Kai and Stark, Rainer}, title = {Multi-criteria Decision Making as a Tool for Sustainable Product Development - Benefits and Obstacles}, series = {Procedia CIRP}, volume = {26}, booktitle = {Procedia CIRP}, doi = {10.1016/j.procir.2014.07.110}, pages = {70 -- 75}, language = {en} } @inproceedings{GausemeierSeligerSchenkeretal., author = {Gausemeier, Pia and Seliger, G{\"u}nther and Schenker, Sebastian and Bornd{\"o}rfer, Ralf}, title = {Nachhaltige Technologiepfade f{\"u}r unterschiedliche Entwicklungsniveaus mithilfe mehrkriterieller Entscheidungsfindung}, series = {Vorausschau und Technologieplanung}, volume = {334}, booktitle = {Vorausschau und Technologieplanung}, isbn = {978-3-942647-53-3}, pages = {65 -- 94}, language = {de} } @inproceedings{SproesserSchenkerPittneretal., author = {Spr{\"o}sser, Gunther and Schenker, Sebastian and Pittner, Andreas and Bornd{\"o}rfer, Ralf and Rethmeier, Michael and Chang, Ya-Ju and Finkbeiner, Matthias}, title = {Sustainable Welding Process Selection based on Weight Space Partitions}, series = {Procedia CIRP}, volume = {40}, booktitle = {Procedia CIRP}, doi = {10.1016/j.procir.2016.01.077}, pages = {127 -- 132}, language = {en} } @inproceedings{SchenkerSteingrimssonBorndoerferetal., author = {Schenker, Sebastian and Steingr{\´i}msson, J{\´o}n Garðar and Bornd{\"o}rfer, Ralf and Seliger, G{\"u}nther}, title = {Modelling of Bicycle Manufacturing via Multi-criteria Mixed Integer Programming}, series = {Procedia CIRP}, volume = {26}, booktitle = {Procedia CIRP}, doi = {10.1016/j.procir.2014.07.068}, pages = {276 -- 280}, 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} } @masterthesis{Wirsching, type = {Bachelor Thesis}, author = {Wirsching, Marie}, title = {Der Einfluss von Langzahlarithmetik auf das Gewichtsraumpolyeder in mehrkriterieller Optimierung}, pages = {59}, abstract = {Die Arbeit befasst sich mit einem gewichtsraumbasierten Algorithmus, der ganzzahlige und lineare Optimierungsprobleme mit mehreren Zielfunktionen l{\"o}st und die Menge der unterst{\"u}tzt nicht dominierten Punkte ermittelt. Die dabei erzeugten Gewichtsraumpolyeder sind das entscheidende Mittel, um die gesuchte L{\"o}sungsmenge zu bestimmen. Aus softwaretechnischer Sicht sind numerische Ungenauigkeiten potentielle Fehlerquellen, die sich negativ auf das Endergebnis auswirken. Aus diesem Grund untersuchen wir anhand von Zuweisungs- und Rucksackinstanzen mit 3 Zielfunktionen, inwieweit der Gebrauch von Langzahlarithmetik die Gewichtsraumpolyeder und die damit verbundene Menge der unterst{\"u}tzt nicht dominierten Punkte beeinflusst.}, language = {de} } @misc{SchenkerBorndoerferSkutella, author = {Schenker, Sebastian and Bornd{\"o}rfer, Ralf and Skutella, Martin}, title = {A novel partitioning of the set of non-dominated points}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61286}, abstract = {We consider a novel partitioning of the set of non-dominated points for general multi-objective integer programs with \$k\$ objectives. The set of non-dominated points is partitioned into a set of non-dominated points whose efficient solutions are also efficient for some restricted subproblem with one less objective; the second partition comprises the non-dominated points whose efficient solutions are inefficient for any of the restricted subproblems. We show that the first partition has the nice property that it yields finite rectangular boxes in which the points of the second partition are located.}, 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} } @misc{GamrathFischerGallyetal., author = {Gamrath, Gerald and Fischer, Tobias and Gally, Tristan and Gleixner, Ambros and Hendel, Gregor and Koch, Thorsten and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Vigerske, Stefan and Weninger, Dieter and Winkler, Michael and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 3.2}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57675}, abstract = {The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.}, language = {en} }