@misc{BurgschweigerGnaedigSteinbach2005, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8657}, number = {05-31}, year = {2005}, abstract = {Mathematical decision support for operative planning in water supply systems is highly desirable but leads to very difficult optimization problems. We propose a nonlinear programming approach that yields practically satisfactory operating schedules in acceptable computing time even for large networks. Based on a carefully designed model supporting gradient-based optimization algorithms, this approach employs a special initialization strategy for convergence acceleration, special minimum up and down time constraints together with pump aggregation to handle switching decisions, and several network reduction techniques for further speed-up. Results for selected application scenarios at Berliner Wasserbetriebe demonstrate the success of the approach.}, language = {en} } @misc{BurgschweigerGnaedigSteinbach2005, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Optimierte Tagesplanung im Berliner Trinkwassernetz}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8668}, number = {05-32}, year = {2005}, abstract = {Der Artikel beschreibt ein mathematisches Optimierungssystem zur Betriebsplanung in großen Wassernetzen, das bei den Berliner Wasserbetrieben eingesetzt wird. F{\"u}r das Berliner Versorgungsnetz werden Optimierungsergebnisse vorgestellt.}, language = {de} } @misc{Steinbach2004, author = {Steinbach, Marc}, title = {On PDE Solution in Transient Optimization of Gas Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8215}, number = {04-46}, year = {2004}, abstract = {Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions---or as relaxation in a branch and bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse local projections, based on the KKT systems' structual properties induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a control space method and with the multifrontal solver MA27 are provided.}, language = {en} } @misc{BurgschweigerGnaedigSteinbach2004, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Optimization Models for Operative Planning in Drinking Water Networks}, doi = {10.1007/s11081-008-9040-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8237}, number = {04-48}, year = {2004}, abstract = {The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.}, language = {en} } @misc{Steinbach2005, author = {Steinbach, Marc}, title = {Topological Index Criteria in DAE for Water Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8821}, number = {05-49}, year = {2005}, abstract = {The dynamics of pressurized water distribution networks are naturally modeled by differential algebraic equations (DAE). This paper investigates fundamental structural properties of such a DAE model under weak regularity assumptions. The usual partial derivative-based index-1 condition is shown to be necessary and sufficient for several index concepts, as well as sufficient for solvability in a strong sense. Using the physical properties of nonlinear network elements and the inherent saddle point structure of network hydraulics, we then derive purely topological index criteria based on the network graph and the choice of control variables. Several examples illustrate the theoretical results and explore different non-index-1 situations. A brief discussion of the implications for operative planning by discrete time DAE boundary value problems concludes the paper.}, language = {en} } @misc{Steinbach1997, author = {Steinbach, Marc}, title = {Optimal Motion Design Using Inverse Dynamics.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2818}, number = {SC-97-12}, year = {1997}, abstract = {Increasing demands on industrial robot operation call for optimal motion planning based on dynamic models. The resulting mathematical problems can be handled efficiently by sparse direct boundary value problem methods. Within this framework we propose a new solution technique that is closely related to the conventional kinematic approach: it eliminates the need for numerical integration of differential equations. First optimization results on a real life transport maneuver demonstrate that the technique may save over 50\,\\%\ computation time.}, language = {en} } @misc{SteinbachBockKostinetal.1997, author = {Steinbach, Marc and Bock, H. Georg and Kostin, Georgii V. and Longman, Richard W.}, title = {Mathematical Optimization in Robotics: Towards Automated High Speed Motion Planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2722}, number = {SC-97-03}, year = {1997}, abstract = {\def\KukaRob {{\sf KUKA IR\,761}} {\small Industrial robots have greatly enhanced the performance of automated manufacturing processes during the last decades. International competition, however, creates an increasing demand to further improve both the accuracy of off-line programming and the resulting cycle times on production lines. To meet these objectives, validated dynamic robot models are required. We describe in detail the development of a generic dynamic model, specialize it to an actual industrial robot \KukaRob, and discuss the problem of dynamic calibration. Efficient and robust trajectory optimization algorithms are then presented which, when integrated into a CAD system, are suitable for routine application in an industrial environment. Our computational results for the \KukaRob\ robot performing a real life transport maneuver show that considerable gains in productivity can be achieved by minimizing the cycle time.}}, language = {en} } @misc{Steinbach1998, author = {Steinbach, Marc}, title = {Recursive Direct Algorithms for Multistage Stochastic Programs in Financial Engineering}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3661}, number = {SC-98-23}, year = {1998}, abstract = {Multistage stochastic programs can be seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree. To exploit that structure, we propose a highly efficient dynamic programming recursion for the computationally intensive task of KKT systems solution within an interior point method. Test runs on a multistage portfolio selection problem demonstrate the performance of the algorithm.}, language = {en} } @misc{Steinbach1998, author = {Steinbach, Marc}, title = {Recursive Direct Optimization and Successive Refinement in Multistage Stochastic Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3706}, number = {SC-98-27}, year = {1998}, abstract = {The paper presents a new algorithmic approach for multistage stochastic programs which are seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree. To exploit that structure, we propose a highly efficient dynamic programming recursion for the computationally intensive task of KKT systems solution within a primal-dual interior point method. Convergence is drastically enhanced by a successive refinement technique providing both primal and dual initial estimates. Test runs on a multistage portfolio selection problem demonstrate the performance of the method.}, language = {en} } @misc{Steinbach2000, author = {Steinbach, Marc}, title = {Autos, Ziegen und Streith{\"a}hne}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6087}, number = {00-40}, year = {2000}, abstract = {Das aus den Medien bekannte umstrittene Ziegenproblem (auch Drei-T{\"u}ren-Problem genannt) wird vollst{\"a}ndig analysiert und gel{\"o}st. In der Streitfrage spielen sprachliche Mehrdeutigkeiten der Problemformulierung eine wesentliche Rolle; zudem werden Zufallsereignisse mit willk{\"u}rlicher Information {\"u}ber deren Ergebnisse verwechselt. Tats{\"a}chlich erweisen sich beide strittigen L{\"o}sungen als teilweise richtige Bestandteile der Gesamtl{\"o}sung. Die Argumentation wird in allgemeinverst{\"a}ndlicher Sprache gef{\"u}hrt und anschliessend durch eine formale mathematische Betrachtung erg{\"a}nzt.}, language = {de} }