@misc{RenkenAhmadiBorndoerferetal.2017, author = {Renken, Malte and Ahmadi, Amin and Bornd{\"o}rfer, Ralf and Sahin, Guvenc and Schlechte, Thomas}, title = {Demand-Driven Line Planning with Selfish Routing}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_91}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64547}, year = {2017}, abstract = {Bus rapid transit systems in developing and newly industrialized countries are often operated at the limits of passenger capacity. In particular, demand during morning and afternoon peaks is hardly or even not covered with available line plans. In order to develop demand-driven line plans, we use two mathematical models in the form of integer programming problem formulations. While the actual demand data is specified with origin-destination pairs, the arc-based model considers the demand over the arcs derived from the origin-destination demand. In order to test the accuracy of the models in terms of demand satisfaction, we simulate the optimal solutions and compare number of transfers and travel times. We also question the effect of a selfish route choice behavior which in theory results in a Braess-like paradox by increasing the number of transfers when system capacity is increased with additional lines.}, language = {en} } @misc{Humpola2015, author = {Humpola, Jesco}, title = {Sufficient Pruning Conditions for MINLP in Gas Network Design}, doi = {10.1007/s13675-016-0077-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53489}, year = {2015}, abstract = {One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology extension problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. In this article we offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex NLP can be certified by solving an MILP. These results provide an efficient bounding procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speed-up for the necessary computations.}, language = {en} } @misc{BrettHobergPachecoetal.2015, author = {Brett, Charles and Hoberg, Rebecca and Pacheco, Meritxell and Smith, Kyle and Bornd{\"o}rfer, Ralf and Euler, Ricardo and Gamrath, Gerwin and Grimm, Boris and Heismann, Olga and Reuther, Markus and Schlechte, Thomas and Tesch, Alexander}, title = {G-RIPS 2014 RailLab - Towards robust rolling stock rotations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53475}, year = {2015}, abstract = {The Graduate-Level Research in Industrial Projects (G-RIPS) Program provides an opportunity for high-achieving graduate-level students to work in teams on a real-world research project proposed by a sponsor from industry or the public sector. Each G-RIPS team consists of four international students (two from the US and two from European universities), an academic mentor, and an industrial sponsor. This is the report of the Rail-Lab project on the definition and integration of robustness aspects into optimizing rolling stock schedules. In general, there is a trade-off for complex systems between robustness and efficiency. The ambitious goal was to explore this trade-off by implementing numerical simulations and developing analytic models. In rolling stock planning a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects, have to be considered in an integrated model. General hypergraphs provide the modeling power to tackle those requirements. Furthermore, integer programming approaches are able to produce high quality solutions for the deterministic problem. When stochastic time delays are considered, the mathematical programming problem is much more complex and presents additional challenges. Thus, we started with a basic variant of the deterministic case, i.e., we are only considering hypergraphs representing vehicle composition and regularity. We transfered solution approaches for robust optimization from the airline industry to the setting of railways and attained a reasonable measure of robustness. Finally, we present and discuss different methods to optimize this robustness measure.}, language = {en} } @misc{Witzig2017, author = {Witzig, Jakob}, title = {Conflict Driven Diving for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66116}, year = {2017}, abstract = {The analysis of infeasibility plays an important role in solving satisfiability problems (SAT) and mixed integer programs (MIPs). In mixed integer programming, this procedure is called conflict analysis. So far, modern MIP solvers use conflict analysis only for propagation and improving the dual bound, i.e., fathoming nodes that cannot contain feasible solutions. In this short paper, we present a new approach which uses conflict information to improve the primal bound during a MIP solve. To derive new improving primal solutions we use a conflict driven diving heuristic called conflict diving that uses the information obtained by conflict analysis. Conflict diving pursues a twofold strategy. By using conflict information the new diving approach is guided into parts of the search space that are usually not explored by other diving heuristics. At the same time, conflict diving has a fail-fast-strategy to reduce the time spent if it cannot find a new primal solution. As a byproduct, additional valid conflict constraints can be derived, from which a MIP solver can gain benefit to improve the dual bound as well. To show the added-value of conflict diving within a MIP solver, conflict diving has been implemented within the non-commercial MIP solver SCIP. Experiments are carried out on general MIP instances from standard public test sets, like MIPLIB2010 or Cor@l.}, language = {en} } @misc{RehfeldtKochMaher2016, author = {Rehfeldt, Daniel and Koch, Thorsten and Maher, Stephen J.}, title = {Reduction Techniques for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem}, issn = {1438-0064}, doi = {10.1002/net.21857}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60420}, year = {2016}, abstract = {The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this paper we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90 percent of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-Jack.}, language = {en} } @misc{WitzigBeckenbachEifleretal.2016, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, issn = {1438-0064}, doi = {10.1137/16M1091162}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60353}, year = {2016}, abstract = {In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.}, language = {en} } @misc{FischerGrimmKlugetal.2016, author = {Fischer, Frank and Grimm, Boris and Klug, Torsten and Schlechte, Thomas}, title = {A Re-optimization Approach for Train Dispatching}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60493}, year = {2016}, abstract = {The Train Dispatching Problem (TDP) is to schedule trains through a network in a cost optimal way. Due to disturbances during operation existing track allocations often have to be re-scheduled and integrated into the timetable. This has to be done in seconds and with minimal timetable changes to guarantee smooth and conflict free operation. We present an integrated modeling approach for the re-optimization task using Mixed Integer Programming. Finally, we provide computational results for scenarios provided by the INFORMS RAS Problem Soling Competition 2012.}, language = {en} } @article{WitzigBeckenbachEifleretal.2018, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, volume = {16}, journal = {Multiscale Modeling and Simulation}, number = {1}, issn = {1438-0064}, doi = {10.1137/16M1091162}, pages = {248 -- 265}, year = {2018}, abstract = {In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.}, language = {en} } @misc{BorndoerferKlugLamorgeseetal.2015, author = {Bornd{\"o}rfer, Ralf and Klug, Torsten and Lamorgese, Leonardo and Mannino, Carlo and Reuther, Markus and Schlechte, Thomas}, title = {Recent Success Stories on Optimization of Railway Systems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53726}, year = {2015}, abstract = {Planning and operating railway transportation systems is an extremely hard task due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. Because of that, however, mathematical models and optimization techniques can result in large gains for both railway cus- tomers and operators, e.g., in terms of cost reductions or service quality improvements. In the last years a large and growing group of researchers in the OR community have devoted their attention to this domain devel- oping mathematical models and optimization approaches to tackle many of the relevant problems in the railway planning process. However, there is still a gap to bridge between theory and practice, with a few notable exceptions. In this paper we address three success stories, namely, long-term freight train routing (part I), mid-term rolling stock rotation planning (part II), and real-time train dispatching (part III). In each case, we describe real-life, successful implementations. We will dis- cuss the individual problem setting, survey the optimization literature, and focus on particular aspects addressed by the mathematical models. We demonstrate on concrete applications how mathematical optimization can support railway planning and operations. This gives proof that math- ematical optimization can support the planning of rolling stock resources. Thus, mathematical models and optimization can lead to a greater effi- ciency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry.}, language = {en} } @misc{DraegertEisenblaetterGamrathetal.2015, author = {Draegert, Andreas and Eisenbl{\"a}tter, Andreas and Gamrath, Inken and Werner, Axel}, title = {Optimal Battery Controlling for Smart Grid Nodes}, issn = {1438-0064}, doi = {10.1007/978-4-431-55420-2_6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53550}, year = {2015}, abstract = {Energy storages can be of great value when added to power grids. They introduce the possibility to store and release energy whenever this is favorable. This is particularly relevant, for example, if power supply is volatile (as is the case with renewable energy) and the network is small (so that there are few other nodes that might balance fluctuations in consumption or production). We present models and methods from mathematical optimization for computing an optimized storage schedule for this purpose. We look at alternative optimization objectives, such as smallest possible peak load, low energy costs, or the close approximation of a prescribed load curve. The optimization needs to respect general operational and economic constraints as well as limitations in the use of storage, which are imposed by the chosen storage technology. We therefore introduce alternative approaches for modeling the non-linear properties of energy storages and study their impact on the efficiency of the optimization process. Finally, we present a computational study with batteries as storage devices. We use this to highlight the trade-off between solution quality and computational tractability. A version of the model for the purpose of leveling peaks and instabilities has been implemented into a control system for an office-building smart grid scenario.}, language = {en} } @misc{HarmanSagnol2015, author = {Harman, Radoslav and Sagnol, Guillaume}, title = {Computing D-optimal experimental designs for estimating treatment contrasts under the presence of a nuisance time trend}, issn = {1438-0064}, doi = {10.1007/978-3-319-13881-7_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53640}, year = {2015}, abstract = {We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.}, language = {en} } @misc{OrlowskiWernerWessaely2012, author = {Orlowski, Sebastian and Werner, Axel and Wess{\"a}ly, Roland}, title = {Estimating trenching costs in FTTx network planning}, issn = {1438-0064}, doi = {10.1007/978-3-642-29210-1_15}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14884}, year = {2012}, abstract = {In this paper we assess to which extent trenching costs of an FTTx network are unavoidable, even if technical side constraints are neglected. For that purpose we present an extended Steiner tree model. Using a variety of realistic problem instances we demonstrate that the total trenching cost can only be reduced by about 5 percent in realistic scenarios. This work has been funded by BMBF (German Federal Ministry of Education and Research) within the program "KMU-innovativ".}, language = {en} } @masterthesis{Hendel2011, type = {Bachelor Thesis}, author = {Hendel, Gregor}, title = {New Rounding and Propagation Heuristics for Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13322}, school = {Zuse Institute Berlin (ZIB)}, pages = {95}, year = {2011}, abstract = {Die vorliegende Arbeit befasst sich mit Primalheuristiken f{\"u}r gemischt-ganzzahlige, lineare Optimierungsprobleme (engl.: mixed integer program MIP). Zahlreiche Optimierungsprobleme aus der Praxis lassen sich als MIP modellieren, Beispiele hierf{\"u}r sind u. a. Optimierungsprobleme im {\"o}ffentlichen Nah- und Fernverkehr, bei logistischen Fragestellungen oder im Bereich der Chip-Verifikation. Das L{\"o}sen von MIP ist NP-schwer und wird heutzutage meistens mit Hilfe von Branch-and-Bound-basierenden Algorithmen versucht. Das Branch-and-Bound-Ver\-fah\-ren profitiert unter Umst{\"a}nden von bereits fr{\"u}hzeitig zur Verf{\"u}gung stehenden L{\"o}sungen, daher sind wir sehr an heuristischen Verfahren interessiert, die in der Praxis schnell eine gute L{\"o}sung f{\"u}r eine große Zahl an MIPs liefern und somit die L{\"o}sezeit des Branch-and-Bound-Verfahrens erheblich beschleunigen k{\"o}nnen. Primalheuristiken sind Suchverfahren zum Auffinden zul{\"a}ssiger L{\"o}sungen eines MIP. Verschiedene Typen von Primalheuristiken sollen dabei den jeweiligen Bedarf des Anwenders zu unterschiedlichen Zeiten w{\"a}hrend der Branch-and-Bound-Suche decken. W{\"a}hrend Start- und Rundeheuristiken zu Beginn des L{\"o}seprozesses eine große Rolle bei der Suche nach der ersten zul{\"a}ssigen L{\"o}sung haben, arbeiten Verbesserungs-heuristiken auf schon bekannten L{\"o}sungen, um neue, bessere L{\"o}sungen zu produzieren. Diese Arbeit besch{\"a}ftigt sich mit Primalheuristiken, welche Teil des MIP-L{\"o}sers SCIP sind. Im ersten Kapitel werden nach der Erarbeitung grundlegender Definitionen viele der durch Tobias Achterberg und Timo Berthold in SCIP integrierten heuristischen Verfahren vorgestellt und kategorisiert. Auf dieser Grundlage bauen dann die Kapitel 2-4 der Arbeit auf. In diesen werden drei zus{\"a}tzliche Heuristiken vorgestellt, im Einzelnen sind dies ZI Round, eine Rundeheuristik, welche zuerst von Wallace beschrieben wurde, außerdem eine 2-Opt-Heuristik f{\"u}r MIP und eine neue Startheuristik, Shift-And-Propagate. Großer Wert wird in jedem Kapitel auf die algorithmische Beschreibung der Heuristiken gelegt, die stets anhand von motivierenden Beispielen eingef{\"u}hrt und anhand von Pseudocode-Algorithmen begleitet werden. Zus{\"a}tzlich enth{\"a}lt jedes Kapitel Auswertungen der mit den neuen Heuristiken gemessenen Ergebnisse von SCIP. Eine kurze Zusammenfassung in Kapitel 5 schließt diese Arbeit ab.}, language = {en} } @misc{BertholdHeinzPfetschetal.2011, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc and Vigerske, Stefan}, title = {Large Neighborhood Search beyond MIP}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12989}, number = {11-21}, year = {2011}, abstract = {Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics.}, language = {en} } @misc{FuegenschuhHumpola2013, author = {F{\"u}genschuh, Armin and Humpola, Jesco}, title = {A Unified View on Relaxations for a Nonlinear Network Flow Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18857}, year = {2013}, abstract = {We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is how to numerically compute this flow and pressures. We review an existing approach of Maugis (1977) and extend it to the case of networks with active elements (for example, compressors). We further examine different ways of relaxations for the nonlinear network flow model. We compare different approaches based on nonlinear optimization numerically on a set of test instances.}, language = {en} } @misc{FuegenschuhVierhaus2013, author = {F{\"u}genschuh, Armin and Vierhaus, Ingmar}, title = {A Global Approach to the Optimal Control of System Dynamics Models}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18600}, year = {2013}, abstract = {The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually ordinary differential equations and nonlinear algebraic constraints. Therefore 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. We apply our new method to a predator-prey model with additional hunting activity as control, and to a mini-world model with the consumption level as control. Numerical results for these test cases are presented.}, language = {en} } @misc{LindnerLiebchen2021, author = {Lindner, Niels and Liebchen, Christian}, title = {Timetable Merging for the Periodic Event Scheduling Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81587}, year = {2021}, abstract = {We propose a new mixed integer programming based heuristic for computing new benchmark primal solutions for instances of the PESPlib. The PESPlib is a collection of instances for the Periodic Event Scheduling Problem (PESP), comprising periodic timetabling problems inspired by real-world railway timetabling settings, and attracting several international research teams during the last years. We describe two strategies to merge a set of good periodic timetables. These make use of the instance structure and minimum weight cycle bases, finally leading to restricted mixed integer programming formulations with tighter variable bounds. Implementing this timetable merging approach in a concurrent solver, we improve the objective values of the best known solutions for the smallest and largest PESPlib instances by 1.7 and 4.3 percent, respectively.}, language = {en} } @misc{LeitnerLjubicSinnletal.2013, author = {Leitner, Markus and Ljubic, Ivana and Sinnl, Markus and Werner, Axel}, title = {On the Two-Architecture Connected Facility Location Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18610}, year = {2013}, abstract = {We introduce a new variant of the connected facility location problem that allows for modeling mixed deployment strategies (FTTC/FTTB/FTTH) in the design of local access telecommunication networks. Several mixed integer programming models and valid inequalities are presented. Computational studies on realistic instances from three towns in Germany are provided.}, language = {en} } @misc{HumpolaFuegenschuh2013, author = {Humpola, Jesco and F{\"u}genschuh, Armin}, title = {A New Class of Valid Inequalities for Nonlinear Network Design Problems}, issn = {1438-0064}, doi = {10.1007/s00291-015-0390-2}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17771}, year = {2013}, abstract = {We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. Assume that there does not exist a feasible flow that fulfills all physical constraints and meets the desired entry and exit amounts. Then a natural question is where to extend the network by adding pipes in the most economic way such that this flow becomes feasible. Answering this question is computationally demanding because of the difficult problem structure. We use mixed-integer nonlinear programming techniques that rely on an outer approximation of the overall problem, and a branching on decision variables. We formulate a new class of valid inequalities (or cutting planes) which reduce the overall solution time when added to the formulation. We demonstrate the computational merits of our approach on test instances.}, language = {en} } @misc{LindnerLiebchenMasing2021, author = {Lindner, Niels and Liebchen, Christian and Masing, Berenike}, title = {Forward Cycle Bases and Periodic Timetabling}, issn = {1438-0064}, doi = {10.4230/OASIcs.ATMOS.2021.2}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82756}, year = {2021}, abstract = {Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance \texttt{R1L1} of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds.}, language = {en} } @misc{LindnerMaristanydelasCasasSchiewe2021, author = {Lindner, Niels and Maristany de las Casas, Pedro and Schiewe, Philine}, title = {Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data}, issn = {1438-0064}, doi = {10.4230/OASIcs.ATMOS.2021.7}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82716}, year = {2021}, abstract = {We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport.}, language = {en} } @misc{LindnervanLieshout2021, author = {Lindner, Niels and van Lieshout, Rolf}, title = {Benders Decomposition for the Periodic Event Scheduling Problem}, issn = {1438-0064}, doi = {10.1007/978-3-031-08623-6_43}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-83338}, year = {2021}, abstract = {The Periodic Event Scheduling Problem (PESP) is the central mathematical model behind the optimization of periodic timetables in public transport. We apply Benders decomposition to the incidence-based MIP formulation of PESP. The resulting formulation exhibits particularly nice features: The subproblem is a minimum cost network flow problem, and feasibility cuts are equivalent to the well-known cycle inequalities by Odijk. We integrate the Benders approach into a branch-and-cut framework, and assess the performance of this method on instances derived from the benchmarking library PESPlib.}, language = {en} } @misc{FuegenschuhVierhaus2013, 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}, year = {2013}, abstract = {The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually nonlinear. Therefore seemingly simple systems can show a nonintuitive, nonpredictable behavior over time. Controlling a dynamical system means to define a desired final state in which the system should be, and to specify potential interventions from outside that should keep the system on the right track. The central question is how to compute such globally optimal control for a given SD model. We propose a branch-and-bound approach that is based on a bound propagation method, primal heuristics, and spatial branching. We apply our new SD-control method to a small System Dynamics model, that describes the evolution of a social-economic system over time. We examine the problem of steering this system on a sustainable consumption path.}, language = {en} }