@misc{HillerKrumkeRambau, author = {Hiller, Benjamin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7928}, number = {04-17}, abstract = {Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100--150 vehicles and 400 requests in about ten seconds to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within ten seconds. One way-out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new model ZIBDIP{\footnotesize dummy} can keep up with ZIBDIP.}, language = {en} } @misc{HillerKrumkeSalibaetal., author = {Hiller, Benjamin and Krumke, Sven and Saliba, Sleman and Tuchscherer, Andreas}, title = {Randomized Online Algorithms for Dynamic Multi-Period Routing Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11132}, number = {09-03}, abstract = {The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of \$\frac{1+\sqrt{2}}{2}\$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.}, language = {en} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {On the optimality of Least Recently Used}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10928}, number = {08-39}, abstract = {It is well known that competitive analysis yields too pessimistic results when applied to the paging problem and it also cannot make a distinction between many paging strategies. Many deterministic paging algorithms achieve the same competitive ratio, ranging from inefficient strategies as flush-when-full to the good performing least-recently-used (LRU). In this paper, we study this fundamental online problem from the viewpoint of stochastic dominance. We show that when sequences are drawn from distributions modelling locality of reference, LRU is stochastically better than any other online paging algorithm.}, language = {en} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10726}, number = {08-18}, abstract = {This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.}, language = {en} } @misc{GroetschelHillerTuchscherer, author = {Gr{\"o}tschel, Martin and Hiller, Benjamin and Tuchscherer, Andreas}, title = {Combinatorial Online Optimization: Elevators \& Yellow Angels}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10360}, number = {07-36}, abstract = {In \emph{classical optimization} it is assumed that full information about the problem to be solved is given. This, in particular, includes that all data are at hand. The real world may not be so nice'' to optimizers. Some problem constraints may not be known, the data may be corrupted, or some data may not be available at the moments when decisions have to be made. The last issue is the subject of \emph{online optimization} which will be addressed here. We explain some theory that has been developed to cope with such situations and provide examples from practice where unavailable information is not the result of bad data handling but an inevitable phenomenon.}, language = {en} } @misc{FuegenschuhGeisslerGollmeretal., author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Rene and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner 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 Willert, Bernhard}, title = {Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets}, issn = {1438-0064}, doi = {10.1007/s12667-013-0099-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17821}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.}, language = {en} } @misc{FuegenschuhHillerHumpolaetal., author = {F{\"u}genschuh, Armin and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Schwarz, Robert and Schweiger, Jonas and Szab{\´o}, J{\´a}cint}, title = {Gas Network Topology Optimization for Upcoming Market Requirements}, doi = {10.1109/EEM.2011.5953035}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12348}, number = {11-09}, abstract = {Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed.}, language = {en} } @misc{HillerKlugTuchscherer, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups}, issn = {1438-0064}, doi = {10.1007/s10696-013-9175-6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16485}, abstract = {The task of an elevator control is to schedule the elevators of a group such that small waiting and travel times for the passengers are obtained. We present an exact reoptimization algorithm for this problem. A reoptimization algorithm computes a new schedule for the elevator group each time a new passenger arrives. Our algorithm uses column generation techniques and is, to the best of our knowledge, the first exact reoptimization algorithms for a group of passenger elevators. To solve the column generation problem, we propose a Branch \& Bound method.}, language = {en} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Stochastic dominance analysis of Online Bin Coloring algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16502}, abstract = {This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.}, language = {en} } @inproceedings{HillerTuchscherer2008, author = {Hiller, Benjamin and Tuchscherer, Andreas}, title = {Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers}, series = {Operations Research Proceedings}, booktitle = {Operations Research Proceedings}, editor = {Kalcsics, J{\"o}rg and Nickel, Stefan}, publisher = {Springer}, pages = {357 -- 362}, year = {2008}, language = {en} } @inproceedings{HillerKrumkeSalibaetal.2009, author = {Hiller, Benjamin and Krumke, Sven and Saliba, Sleman and Tuchscherer, Andreas}, title = {Randomized Online Algorithms for Dynamic Multi-Period Routing Problems}, series = {Proceedings of MAPSP}, booktitle = {Proceedings of MAPSP}, pages = {71 -- 73}, year = {2009}, language = {en} } @inproceedings{HillerKlugTuchscherer2009, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {Improving the performance of elevator systems using exact reoptimization algorithms}, series = {Proceedings of MAPSP}, booktitle = {Proceedings of MAPSP}, pages = {224 -- 226}, year = {2009}, language = {en} } @inproceedings{HillerKlugTuchscherer2010, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {Improved destination call elevator control algorithms for up peak traffic}, series = {Operations Research Proceedings 2010}, booktitle = {Operations Research Proceedings 2010}, publisher = {Springer}, year = {2010}, language = {en} } @book{KochHillerPfetschetal., author = {Koch, Thorsten and Hiller, Benjamin and Pfetsch, Marc and Schewe, Lars}, title = {Evaluating Gas Network Capacities}, publisher = {SIAM}, isbn = {978-1-611973-68-6}, pages = {xvi + 376 pages}, language = {en} } @article{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}, series = {Optimization Methods and Software}, journal = {Optimization Methods and Software}, publisher = {Taylor \& Francis}, doi = {10.1080/10556788.2014.888426}, 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} } @article{FuegenschuhGeisslerGollmeretal., author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Ren{\´e} and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner 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 Willert, Bernhard}, title = {Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets}, series = {Energy Systems}, volume = {5}, journal = {Energy Systems}, number = {3}, publisher = {Springer Berlin Heidelberg}, address = {Berlin}, doi = {10.1007/s12667-013-0099-8}, pages = {449 -- 473}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network's capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations.}, language = {en} } @misc{HillerSaitenmacherWalther, author = {Hiller, Benjamin and Saitenmacher, Ren{\´e} and Walther, Tom}, title = {Analysis of operating modes of complex compressor stations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61092}, abstract = {We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model.}, language = {en} } @inproceedings{HillerSaitenmacherWalther, author = {Hiller, Benjamin and Saitenmacher, Ren{\´e} and Walther, Tom}, title = {Analysis of operating modes of complex compressor stations}, series = {Proceedings of Operations Research 2016}, booktitle = {Proceedings of Operations Research 2016}, doi = {10.1007/978-3-319-55702-1_34}, pages = {251 -- 257}, abstract = {We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model.}, language = {en} } @article{HillerKlugTuchscherer, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups}, series = {Flexible Services and Manufacturing Journal}, journal = {Flexible Services and Manufacturing Journal}, doi = {10.1007/s10696-013-9175-6}, pages = {1 -- 24}, language = {en} } @inproceedings{FuegenschuhHillerHumpolaetal., author = {F{\"u}genschuh, Armin and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Schwarz, Robert and Schweiger, Jonas and Szabo, Jacint}, title = {Gas Network Topology Optimization for Upcoming Market Requirements}, series = {International Conference on the European Energy Market (EEM)}, booktitle = {International Conference on the European Energy Market (EEM)}, doi = {10.1109/EEM.2011.5953035}, pages = {346 -- 351}, abstract = {Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed.}, language = {en} } @inproceedings{MartinGeisslerHeynetal.2011, author = {Martin, Alexander and Geißler, Bj{\"o}rn and Heyn, Christine and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Steinbach, Marc and Willert, Bernhard}, title = {Optimierung Technischer Kapazit{\"a}ten in Gasnetzen}, series = {Optimierung in der Energiewirtschaft}, booktitle = {Optimierung in der Energiewirtschaft}, publisher = {VDI-Verlag, D{\"u}sseldorf}, pages = {105 -- 114}, year = {2011}, language = {en} } @incollection{GroetschelHillerTuchscherer2009, author = {Gr{\"o}tschel, Martin and Hiller, Benjamin and Tuchscherer, Andreas}, title = {Structuring a Dynamic Environment}, series = {Emergence, Analysis and Evolution of Structures. Concepts and Strategies Across Disciplines}, booktitle = {Emergence, Analysis and Evolution of Structures. Concepts and Strategies Across Disciplines}, editor = {Lucas, Klaus and Roosen, Peter}, publisher = {Springer}, doi = {10.1007/978-3-642-00870-2}, pages = {199 -- 214}, year = {2009}, language = {en} } @inproceedings{HillerVredeveld2008, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison}, series = {Proceedings of the 16th esa}, volume = {5193}, booktitle = {Proceedings of the 16th esa}, publisher = {Springer}, pages = {528 -- 539}, year = {2008}, language = {en} } @inproceedings{HillerVredeveld2009, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Stochastic dominance analysis of online bin coloring algorithms}, series = {9th Workshop on Models and Algorithms for Planning and Scheduling Problems}, booktitle = {9th Workshop on Models and Algorithms for Planning and Scheduling Problems}, year = {2009}, language = {en} } @article{HillerKrumkeRambau2006, author = {Hiller, Benjamin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC}, series = {DISAM}, volume = {154}, journal = {DISAM}, number = {13}, pages = {1897 -- 1907}, year = {2006}, language = {en} } @article{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Probabilistic alternatives for competitive analysis}, series = {Computer Science - Research and Development}, volume = {27}, journal = {Computer Science - Research and Development}, number = {3}, publisher = {Springer}, doi = {10.1007/s00450-011-0149-1}, pages = {189 -- 196}, language = {en} } @incollection{GeyerHillerMeinert2010, author = {Geyer, Markus and Hiller, Benjamin and Meinert, Sascha}, title = {Modeling}, series = {Algorithm Engineering}, volume = {5971}, booktitle = {Algorithm Engineering}, editor = {M{\"u}ller-Hannemann, Matthias and Schirra, Stefan}, publisher = {Springer}, pages = {16 -- 57}, year = {2010}, language = {en} } @incollection{BerberichHagenHilleretal.2010, author = {Berberich, Eric and Hagen, Matthias and Hiller, Benjamin and Moser, Hannes}, title = {Experiments}, series = {Algorithm Engineering}, volume = {5971}, booktitle = {Algorithm Engineering}, editor = {M{\"u}ller-Hannemann, Matthias and Schirra, Stefan}, publisher = {Springer}, pages = {325 -- 388}, year = {2010}, language = {en} } @misc{Hiller2003, author = {Hiller, Benjamin}, title = {Hochlastvarianten des Algorithmus ZIBDIP f{\"u}r die automatische Disposition von ADAC-Einsatzfahrzeugen}, publisher = {Studienarbeit TU Ilmenau\,/\,Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin}, year = {2003}, language = {en} } @misc{Hiller2004, type = {Master Thesis}, author = {Hiller, Benjamin}, title = {Bad Guys are Rare}, year = {2004}, language = {en} } @phdthesis{Hiller2009, author = {Hiller, Benjamin}, title = {Online Optimization}, year = {2009}, language = {en} } @inproceedings{HillerKrumkeRambau2004, author = {Hiller, Benjamin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC}, series = {Latin-American Conference on Combinatorics, Graphs and Applications, Santiago de Chile 2004}, volume = {18}, booktitle = {Latin-American Conference on Combinatorics, Graphs and Applications, Santiago de Chile 2004}, editor = {Liebling, T. and Duran, G. and Matamala, M.}, pages = {157 -- 163}, year = {2004}, language = {en} } @inproceedings{HillerTuchscherer2008, author = {Hiller, Benjamin and Tuchscherer, Andreas}, title = {Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers}, series = {Operations Research Proceedings 2007}, booktitle = {Operations Research Proceedings 2007}, publisher = {Springer}, pages = {357 -- 362}, year = {2008}, language = {en} } @article{DomschkeGrossHanteetal., author = {Domschke, Pia and Groß, Martin and Hante, Falk M. and Hiller, Benjamin and Schewe, Lars and Schmidt, Martin}, title = {Mathematische Modellierung, Simulation und Optimierung von Gastransportnetzwerken}, series = {gwf - Gas+Energie}, volume = {156}, journal = {gwf - Gas+Energie}, number = {11}, pages = {880 -- 885}, language = {de} } @incollection{HillerHumpolaLehmannetal., author = {Hiller, Benjamin and Humpola, Jesco and Lehmann, Thomas and Lenz, Ralf and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Willert, Bernhard}, title = {Computational results for validation of nominations}, series = {Evaluating Gas Network Capacities}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, abstract = {The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances.}, 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} } @incollection{GotzesHeineckeHilleretal., author = {Gotzes, Uwe and Heinecke, Nina and Hiller, Benjamin and R{\"o}vekamp, Jessica and Koch, Thorsten}, title = {Regulatory rules for gas markets in Germany and other European countries}, series = {Evaluating gas network capacities}, booktitle = {Evaluating gas network capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {978-1-611973-68-6}, pages = {45 -- 64}, language = {en} } @incollection{HillerHaynHeitschetal., author = {Hiller, Benjamin and Hayn, Christine and Heitsch, Holger and Henrion, Ren{\´e} and Le{\"o}vey, Hernan and M{\"o}ller, Andris and R{\"o}misch, Werner}, title = {Methods for verifying booked capacities}, series = {Evaluating gas network capacities}, booktitle = {Evaluating gas network capacities}, publisher = {Society for Industrial and Applied Mathematics}, pages = {291 -- 315}, language = {en} } @misc{BeckerHiller, author = {Becker, Kai-Helge and Hiller, Benjamin}, title = {ASTS Orientations on Undirected Graphs: Structural analysis and enumeration}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69632}, abstract = {All feasible flows in potential-driven networks induce an orientation on the undirected graph underlying the network. Clearly, these orientations must satisfy two conditions: they are acyclic and there are no "dead ends" in the network, i.e. each source requires outgoing flows, each sink requires incoming flows, and each transhipment vertex requires both an incoming and an outgoing flow. In this paper we will call orientations that satisfy these conditions acyclic source-transhipment-sink orientations (ASTS-orientation) and study their structure. In particular, we characterize graphs that allow for such an orientation, describe a way to enumerate all possible ASTS-orientations of a given graph, present an algorithm to simplify and decompose a graph before such an enumeration and shed light on the role of zero flows in the context of ASTS-orientations.}, language = {en} } @misc{HillerKochScheweetal., author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, title = {A System to Evaluate Gas Network Capacities: Concepts and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67438}, abstract = {In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.}, language = {en} } @article{HillerKochScheweetal., author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, title = {A System to Evaluate Gas Network Capacities: Concepts and Implementation}, series = {European Journal of Operational Research}, volume = {270}, journal = {European Journal of Operational Research}, number = {3}, pages = {797 -- 808}, abstract = {In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now trans- ported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.}, language = {en} } @article{HillerSaitenmacherWalther, author = {Hiller, Benjamin and Saitenmacher, Ren{\´e} and Walther, Tom}, title = {Improved models for operation modes of complex compressor stations}, series = {Mathematical Methods of Operations Research}, volume = {94}, journal = {Mathematical Methods of Operations Research}, doi = {https://doi.org/10.1007/s00186-021-00745-x}, pages = {171 -- 195}, abstract = {We study combinatorial structures in large-scale mixed-integer (nonlinear) programming problems arising in gas network optimization. We propose a preprocessing strategy exploiting the observation that a large part of the combinatorial complexity arises in certain subnetworks. Our approach analyzes these subnetworks and the combinatorial structure of the flows within these subnetworks in order to provide alternative models with a stronger combinatorial structure that can be exploited by off-the-shelve solvers. In particular, we consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. We propose a refined model that allows to precompute tighter bounds for each operation mode and a number of model variants based on the refined model exploiting these tighter bounds. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode. We evaluate our model variants on reference benchmark data, showing that they reduce the average running time between 10\% for easy instances and 46\% for hard instances. Moreover, for three of four considered networks, the average number of search tree nodes is at least halved, showing the effectivity of our model variants to guide the solver's search.}, language = {en} } @misc{HillerBecker, author = {Hiller, Benjamin and Becker, Kai-Helge}, title = {Improving relaxations for potential-driven network flow problems via acyclic flow orientations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69622}, abstract = {The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the usually employed relaxations are rather weak due to cycles in the network. We propose acyclic flow orientations as a combinatorial relaxation of feasible solutions of potential-driven flow problems and show how they can be used to strengthen existing relaxations. First computational results indicate that the strengthend model is much tighter than the original relaxation, thus promising a computational advantage.}, language = {en} } @misc{HillerWalther, author = {Hiller, Benjamin and Walther, Tom}, title = {Improving branching for disjunctive polyhedral models using approximate convex decompositions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67462}, abstract = {Disjunctive sets arise in a variety of optimization models and much esearch has been devoted to obtain strong relaxations for them. This paper focuses on the evaluation of the relaxation during the branch-and-bound search process. We argue that the branching possibilities (\ie binary variables) of the usual formulations are unsuitable to obtain strong bounds early in the search process as they do not capture the overall shape of the the entire disjunctive set. To analyze and exploit the shape of the disjunctive set we propose to compute a hierarchy of approximate convex decompositions and show how to extend the known formulations to obtain improved branching behavior.}, language = {en} } @misc{HillerSaitenmacherWalther, author = {Hiller, Benjamin and Saitenmacher, Ren{\´e} and Walther, Tom}, title = {Analysis of operating modes of complex compressor stations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68179}, abstract = {We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode.}, language = {en} } @misc{BeckerHiller, author = {Becker, Kai-Helge and Hiller, Benjamin}, title = {Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77684}, abstract = {In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested.}, language = {en} } @misc{HillerTuchscherer, author = {Hiller, Benjamin and Tuchscherer, Andreas}, title = {Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10108}, number = {07-26}, abstract = {Algorithmic control of elevator systems has been studied for a long time. More recently, a new paradigm for elevator control has emerged. In destination call systems, the passenger specifies not only the direction of his ride, but the destination floor. Such a destination call system is very interesting from an optimization point of view, since more information is available earlier, which should allow improved planning. However, the real-world destination call system envisioned by our industry partner requires that each destination call (i.e. passenger) is assigned to a serving elevator immediately. This early assignment restricts the potential gained from the destination information. Another aspect is that there is no way to specify the destination floor in the cabin. Therefore, the elevator has to stop on every destination floor of an assigned call, although the passenger may not have boarded the cabin, e.g. due to insufficient capacity. In this paper we introduce a new destination call control algorithm suited to this setting. Since the control algorithm for an entire elevator group has to run on embedded microprocessors, computing resources are very scarce. Since exact optimization is not feasible on such hardware, the algorithm is an insertion heuristic using a non-trivial data structure to maintain a set of tours. To assess the performance of our algorithm, we compare it to similar and more powerful algorithms by simulation. We also compare to algorithms for a conventional system and with a more idealized destination call system. This gives an indication of the relative potentials of these systems. In particular, we assess how the above real-world restrictions influence performance. The algorithm introduced has been implemented by our industry partner for real-world use.}, language = {en} } @misc{HillerKlugTuchscherer, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {Improving the performance of elevator systems using exact reoptimization algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11155}, number = {09-05}, abstract = {This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems.}, 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} } @misc{WaltherHillerSaitenmacher, author = {Walther, Tom and Hiller, Benjamin and Saitenmacher, Ren{\´e}}, title = {Polyhedral 3D Models for compressors in gas networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65864}, abstract = {Compressor machines are crucial elements in a gas transmission network, required to compensate for the pressure loss caused by friction in the pipes. Modelling all physical and technical details of a compressor machine involves a large amount of nonlinearity, which makes it hard to use such models in the optimization of large-scale gas networks. In this paper, we are going to describe a modelling approach for the operating range of a compressor machine, starting from a physical reference model and resulting in a polyhedral representation in the 3D space of mass flow throughput as well as in- and outlet pressure.}, language = {en} } @misc{HillerKochScheweetal., author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, title = {A System to Evaluate Gas Network Capacities: Concepts and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61931}, abstract = {Since 2005, the gas market in the European Union is liberalized and the trading of natural gas is decoupled from its transport. The transport is done by so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer maximum independent capacities at each entry and exit such that the resulting gas flows can be realized by the network without compromising security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This paper gives an overview of the toolset for evaluating gas network capacities that has been developed within the ForNe project, a joint research project of seven research partners initiated by Open Grid Europe, Germany's biggest TSO. While most of the relevant mathematics is described in the book "Evaluating Gas Network Capacities", this article sketches the system as a whole, describes some developments that have taken place recently, and gives some details about the current implementation.}, language = {en} } @misc{MartinGeisslerHaynetal., author = {Martin, Alexander and Geißler, Bj{\"o}rn and Hayn, Christine and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Steinbach, Marc and Willert, Bernhard}, title = {Optimierung Technischer Kapazit{\"a}ten in Gasnetzen}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15121}, abstract = {Die mittel- und l{\"a}ngerfristige Planung f{\"u}r den Gastransport hat sich durch {\"A}nderungen in den regulatorischen Rahmenbedingungen stark verkompliziert. Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel diskutiert die hieraus resultierenden mathematischen Planungsprobleme, welche als Validierung von Nominierungen und Buchungen, Bestimmung der technischen Kapazit{\"a}t und Topologieplanung bezeichnet werden. Diese mathematischen Optimierungsprobleme werden vorgestellt und L{\"o}sungsans{\"a}tze skizziert.}, language = {de} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Probabilistic alternatives for competitive analysis}, issn = {1438-0064}, doi = {10.1007/s00450-011-0149-1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15131}, abstract = {In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.}, language = {en} } @misc{HillerWalther, author = {Hiller, Benjamin and Walther, Tom}, title = {Modelling compressor stations in gas networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67443}, abstract = {Gas networks are an important application area for optimization. When considering long-range transmission, compressor stations play a crucial role in these applications. The purpose of this report is to collect and systematize the models used for compressor stations in the literature. The emphasis is on recent work on simple yet accurate polyhedral models that may replace more simplified traditional models without increasing model complexity. The report also describes an extension of the compressor station data available in GasLib (http://gaslib.zib.de/) with the parameters of these models.}, language = {en} } @misc{BeckerHiller, author = {Becker, Kai-Helge and Hiller, Benjamin}, title = {Improved optimization models for potential-driven network flow problems via ASTS orientations}, issn = {1438-0064}, doi = {10.12752/7534}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75347}, abstract = {The class of potential-driven network flow problems provides important models for a range of infrastructure networks that lead to hard-to-solve MINLPs in real-world applications. On large-scale meshed networks the relaxations usually employed are rather weak due to cycles in the network. To address this situation, we introduce the concept of ASTS orientations, a generalization of bipolar orientations, as a combinatorial relaxation of feasible solutions of potential-driven flow problems, study their structure, and show how they can be used to strengthen existing relaxations and thus provide improved optimization models. Our computational results indicate that ASTS orientations can be used to derive much stronger bounds on the flow variables than existing bound tightening methods and to yield significant performance improvements for an existing state-of-the-art MILP model for large-scale gas networks.}, language = {en} } @misc{Hiller, type = {Master Thesis}, author = {Hiller, Benjamin}, title = {Bad Guys are Rare: Probabilistic Analysis of an Elementary Dial-a-Ride Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10114}, school = {Zuse Institute Berlin (ZIB)}, abstract = {This thesis deals with a Dial-a-Ride problem on trees and considers both offline and online versions of this problem. We study the behavior of certain algorithms on random instances, i.e. we do probabilistic analysis. The focus is on results describing the typical behavior of the algorithms, i.e. results holding with (asymptotically) high probability. For the offline version, we present a simplified proof of a result of Coja-Oghlan, Krumke und Nierhoff. The results states that some heuristic using a minimum spanning tree to approximate a Steiner tree gives optimal results with high probability. This explains why this heuristic produces optimal solutions quite often. In the second part, probabilistic online versions of the problem are introduced. We study the online strategies REPLAN and IGNORE. Regarding the IGNORE strategy we can show that it works almost optimal under high load with high probability.}, language = {en} } @misc{Hiller, author = {Hiller, Benjamin}, title = {Probabilistic Competitive Analysis of a Dial-a-Ride Problem on Trees Under High Load}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8896}, number = {05-56}, abstract = {In this paper we consider a simple variant of the Online Dial-a-Ride Problem from a probabilistic point of view. To this end, we look at a probabilistic version of this online Dial-a-Ride problem and introduce a probabilistic notion of the competitive ratio which states that an algorithm performs well on the vast majority of the instances. Our main result is that under the assumption of high load a certain online algorithm is probabilistically \$(1+o(1))\$-competitive if the underlying graph is a tree. This result can be extended to general graphs by using well-known approximation techniques at the expense of a distortion factor~\$O(\log\|V\|)\$.}, language = {en} } @article{KochSchmidtHilleretal., author = {Koch, Thorsten and Schmidt, Martin and Hiller, Benjamin and Pfetsch, Marc and Geißler, Bj{\"o}rn and Henrion, Ren{\´e} and Joormann, Imke and Martin, Alexander and Morsi, Antonio and R{\"o}misch, Werner and Schewe, Lars and Schultz, R{\"u}diger}, title = {Capacity Evaluation for Large-Scale Gas Networks}, series = {German Success Stories in Industrial Mathematics}, volume = {35}, journal = {German Success Stories in Industrial Mathematics}, isbn = {978-3-030-81454-0}, doi = {10.1007/978-3-030-81455-7}, pages = {23 -- 28}, language = {en} } @misc{WitzigGamrathHiller, author = {Witzig, Jakob and Gamrath, Gerald and Hiller, Benjamin}, title = {Reoptimization Techniques in MIP Solvers}, issn = {1438-0064}, doi = {10.1007/978-3-319-20086-6_14}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54375}, abstract = {Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to ``warmstart'' using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.}, language = {en} } @inproceedings{GamrathHillerWitzig, author = {Gamrath, Gerald and Hiller, Benjamin and Witzig, Jakob}, title = {Reoptimization Techniques in MIP Solvers}, volume = {9125}, edition = {Experimental Algorithms, Lecture Notes in Computer Science}, publisher = {Springer}, isbn = {978-3-319-20086-6}, doi = {10.1007/978-3-319-20086-6_14}, pages = {181 -- 192}, abstract = {Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to ``warmstart'' using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.}, language = {en} } @inproceedings{HillerKlugWitzig, author = {Hiller, Benjamin and Klug, Torsten and Witzig, Jakob}, title = {Reoptimization in branch-and-bound algorithms with an application to elevator control}, series = {Proceedings of the 12th International Symposium on Experimental Algorithms}, volume = {7933}, booktitle = {Proceedings of the 12th International Symposium on Experimental Algorithms}, doi = {10.1007/978-3-642-38527-8_33}, pages = {378 -- 389}, language = {en} } @misc{HillerKlugWitzig, author = {Hiller, Benjamin and Klug, Torsten and Witzig, Jakob}, title = {Reoptimization in branch-and-bound algorithms with an application to elevator control}, issn = {1438-0064}, doi = {10.1007/978-3-642-38527-8_33}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17876}, abstract = {We consider reoptimization (i.e. the solution of a problem based on information available from solving a similar problem) for branch-and-bound algorithms and propose a generic framework to construct a reoptimizing branch-and-bound algorithm. We apply this to an elevator scheduling algorithm solving similar subproblems to generate columns using branch-and-bound. Our results indicate that reoptimization techniques can substantially reduce the running times of the overall algorithm.}, language = {en} } @misc{AndersonHiller, author = {Anderson, Lovis and Hiller, Benjamin}, title = {A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69489}, abstract = {Optimization models often feature disjunctions of polytopes as submodels. Such a disjunctive set is initially (at best) relaxed to its convex hull, which is then refined by branching. To measure the error of the convex relaxation, the (relative) difference between the volume of the convex hull and the volume of the disjunctive set may be used. This requires a method to compute the volume of the disjunctive set. Naively, this can be done via inclusion/exclusion and leveraging the existing code for the volume of polytopes. However, this is often inefficient. We propose a revised variant of an old algorithm by Bieri and Nef (1983) for this purpose. The algorithm uses a sweep-plane to incrementally calculate the volume of the disjunctive set as a function of the offset parameter of the sweep-plane.}, language = {en} } @inproceedings{AndersonHiller, author = {Anderson, Lovis and Hiller, Benjamin}, title = {A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes}, series = {Operations Research Proceedings 2018}, volume = {Operations Research Proceedings}, booktitle = {Operations Research Proceedings 2018}, doi = {10.1007/978-3-030-18500-8_12}, abstract = {Optimization models often feature disjunctions of polytopes as submodels. Such a disjunctive set is initially at best) relaxed to its convex hull, which is then refined by branching. To measure the error of the convex relaxation, the (relative) difference between the volume of the convex hull and the volume of the disjunctive set may be used. This requires a method to compute the volume of the disjunctive set. We propose a revised variant of an old algorithm by Bieri and Nef (1983) for this purpose. The algorithm uses a sweep-plane to incrementally calculate the volume of the disjunctive set as a function of the offset parameter of the sweep-plane.}, language = {en} }