@masterthesis{Roessig2016, type = {Bachelor Thesis}, author = {Roessig, Ansgar}, title = {Formulations and algorithms for the USCCSP}, year = {2016}, language = {en} } @misc{Teuchert2017, type = {Master Thesis}, author = {Teuchert, Andreas}, title = {Degeneriertheit im Simplexverfahren}, year = {2017}, language = {de} } @misc{Hendel2015, author = {Hendel, Gregor}, title = {Exploiting Solving Phases for Mixed-Integer Programs}, issn = {1438-0064}, doi = {10.1007/978-3-319-42902-1_1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57098}, year = {2015}, abstract = {Modern MIP solving software incorporates dozens of auxiliary algorithmic components for supporting the branch-and-bound search in finding and improving solutions and in strengthening the relaxation. Intuitively, a dynamic solving strategy with an appropriate emphasis on different solving components and strategies is desirable during the search process. We propose an adaptive solver behavior that dynamically reacts on transitions between the three typical phases of a MIP solving process: The first phase objective is to find a feasible solution. During the second phase, a sequence of incumbent solutions gets constructed until the incumbent is eventually optimal. Proving optimality is the central objective of the remaining third phase. Based on the MIP-solver SCIP, we demonstrate the usefulness of the phase concept both with an exact recognition of the optimality of a solution, and provide heuristic alternatives to make use of the concept in practice.}, language = {en} } @article{BorndoerferReutherSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Waas, Kerstin and Weider, Steffen}, title = {Integrated Optimization of Rolling Stock Rotations for Intercity Railways}, volume = {50}, journal = {Transportation Science}, number = {3}, doi = {10.1287/trsc.2015.0633}, pages = {863 -- 877}, year = {2016}, abstract = {This paper proposes a highly integrated solution approach for rolling stock planning problems in the context of long distance passenger traffic between cities. The main contributions are a generic hypergraph-based mixed-integer programming model for the considered rolling stock rotation problem and an integrated algorithm for its solution. The newly developed algorithm is able to handle a large spectrum of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacities, and regularity aspects. We show that our approach has the power to produce rolling stock rotations that can be implemented in practice. In this way, the rolling stock rotations at the largest German long distance operator Deutsche Bahn Fernverkehr AG could be optimized by an automated system utilizing advanced mathematical programming techniques.}, language = {en} } @misc{YokoyamaShinanoTaniguchietal.2014, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation}, issn = {1438-0064}, doi = {10.1016/j.enconman.2014.12.020}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49413}, year = {2014}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. In the combinatorial optimization method based on the mixed-integer linear programming (MILP), integer variables are used to express the selection, numbers, and on/off status of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. In this paper, a MILP method utilizing the hierarchical relationship between design and operation variables is proposed to solve the optimal design problem of energy supply systems efficiently: At the upper level, the optimal values of design variables are searched by the branch and bound method; At the lower level, the values of operation variables are optimized independently at each period by the branch and bound method under the values of design variables given tentatively during the search at the upper level; Lower bounds for the optimal value of the objective function are evaluated, and are utilized for the bounding operations at both the levels. This method is implemented into open and commercial MILP solvers. Illustrative and practical case studies on the optimal design of cogeneration systems are conducted, and the validity and effectiveness of the proposed method are clarified.}, language = {en} } @misc{GleixnerSteffyWolter2015, author = {Gleixner, Ambros and Steffy, Daniel and Wolter, Kati}, title = {Iterative Refinement for Linear Programming}, issn = {1438-0064}, doi = {10.1287/ijoc.2016.0692}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55118}, year = {2015}, abstract = {We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, while numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description. We show that this algorithm is effective in practice for computing extended precision solutions and that it leads to a direct improvement of the best known methods for solving LPs exactly over the rational numbers. Our implementation is publically available as an extension of the academic LP solver SoPlex.}, language = {en} } @misc{GamrathBertholdHeinzetal.2015, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-based primal heuristics for mixed integer programming}, issn = {1438-0064}, doi = {http://dx.doi.org/10.1007/978-4-431-55420-2_3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55518}, year = {2015}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time.}, language = {en} } @article{MaherMurray2016, author = {Maher, Stephen J. and Murray, John M.}, title = {The unrooted set covering connected subgraph problem differentiating between HIV envelope sequences}, volume = {248}, journal = {European Journal of Operational Research}, number = {2}, doi = {doi:10.1016/j.ejor.2015.07.011}, pages = {668 -- 680}, year = {2016}, abstract = {This paper presents a novel application of operations research techniques to the analysis of HIV Env gene sequences, aiming to identify key features that are possible vaccine targets. These targets are identified as being critical to the transmission of HIV by being present in early transmitted (founder) sequences and absent in later chronic sequences. Identifying the key features of Env involves two steps: first, calculating the covariance of amino acid combinations and positions to form a network of related and compensatory mutations; and second, developing an integer program to identify the smallest connected subgraph of the constructed covariance network that exhibits a set covering property. The integer program developed for this analysis, labelled the unrooted set covering connected subgraph problem (USCCSP), integrates a set covering problem and connectivity evaluation, the latter formulated as a network flow problem. The resulting integer program is very large and complex, requiring the use of Benders' decomposition to develop an efficient solution approach. The results will demonstrate the necessity of applying acceleration techniques to the Benders' decomposition solution approach and the effectiveness of these techniques and heuristic approaches for solving the USCCSP.}, language = {en} } @inproceedings{GamrathHillerWitzig2015, 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}, year = {2015}, 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} } @incollection{HillerHaynHeitschetal.2015, 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}, booktitle = {Evaluating gas network capacities}, publisher = {Society for Industrial and Applied Mathematics}, pages = {291 -- 315}, year = {2015}, language = {en} } @misc{GamrathBertholdHeinzetal.2017, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-driven fix-and-propagate heuristics for mixed integer programming}, issn = {1438-0064}, doi = {10.1007/s12532-019-00159-1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65387}, year = {2017}, abstract = {Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early in the solving process and help to solve instances to optimality faster. In this paper, we present a scheme for primal start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved as an LP and the solution is rounded. If the rounded solution did not provide a feasible solution already, a sub-MIP is solved for the neighborhood defined by the variable fixings performed in the first phase. The global structures help to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about three out of five instances and therewith help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.}, language = {en} } @misc{BertholdHendelKoch2016, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {The Three Phases of MIP Solving}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1392519}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61607}, year = {2016}, abstract = {Modern MIP solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three different phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behavior of the MIP solver SCIP at the predicted phase transition points.}, language = {en} } @misc{HillerKochScheweetal.2017, 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}, year = {2017}, 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{GriewankStreubelLehmannetal.2016, author = {Griewank, Andreas and Streubel, Tom and Lehmann, Lutz and Hasenfelder, Richard and Radons, Manuel}, title = {Piecewise linear secant approximation via Algorithmic Piecewise Differentiation}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1387256}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61642}, year = {2016}, abstract = {It is shown how piecewise differentiable functions \(F: R^n → R^m\) that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points x̌ and x̂. We show that the discrepancy between function and model at any point x is of the bilinear order O(||x - x̌|| ||x - x̂||). This is a little surprising since x ∈ R^n may vary over the whole Euclidean space, and we utilize only two function samples F̌ = F(x̌) and F̂ = F(x̂), as well as the intermediates computed during their evaluation. As an application of the piecewise linearization procedure we devise a generalized Newton's method based on successive piecewise linearization and prove for it sufficient conditions for convergence and convergence rates equaling those of semismooth Newton. We conclude with the derivation of formulas for the numerically stable implementation of the aforedeveloped piecewise linearization methods.}, language = {en} } @article{KickhoeferKern2015, author = {Kickh{\"o}fer, Benjamin and Kern, Julia}, title = {Pricing local emission exposure of road traffic: An agent-based approach}, volume = {37}, journal = {Transportation Research Part D: Transport and Environment}, doi = {10.1016/j.trd.2015.04.019}, pages = {14 -- 28}, year = {2015}, abstract = {This paper proposes a new approach to iteratively calculate local air pollution exposure tolls in large-scale urban settings by taking the exposure times and locations of individuals into consideration. It explicitly avoids detailed air pollution concentration calculations and is therefore characterized by little data requirements, reasonable computation times for iterative calculations, and open-source compatibility. In a first step, the paper shows how to derive time-dependent vehicle-specific exposure tolls in an agent-based model. It closes the circle from the polluting entity, to the receiving entity, to damage costs, to tolls, and back to the behavioral change of the polluting entity. In a second step, the approach is applied to a large-scale real-world scenario of the Munich metropolitan area in Germany. Changes in emission levels, exposure costs, and user benefits are calculated. These figures are compared to a flat emission toll, and to a regulatory measure (a speed reduction in the inner city), respectively. The results indicate that the flat emission toll reduces overall emissions more significantly than the exposure toll, but its exposure cost reductions are rather small. For the exposure toll, overall emissions increase for freight traffic which implies a potential conflict between pricing schemes to optimize local emission exposure and others to abate climate change. Regarding the mitigation of exposure costs caused by urban travelers, the regulatory measure is found to be an effective strategy, but it implies losses in user benefits.}, language = {en} } @article{BorndoerferGrimmReutheretal.2017, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Template-based Re-optimization of Rolling Stock Rotations}, journal = {Public Transport}, publisher = {Springer}, doi = {10.1007/s12469-017-0152-4}, pages = {1 -- 19}, year = {2017}, abstract = {Rolling stock, i.e., the set of railway vehicles, is among the most expensive and limited assets of a railway company and must be used efficiently. We consider in this paper the re-optimization problem to recover from unforeseen disruptions. We propose a template concept that allows to recover cost minimal rolling stock rotations from reference rotations under a large variety of operational requirements. To this end, connection templates as well as rotation templates are introduced and their application within a rolling stock rotation planning model is discussed. We present an implementation within the rolling stock rotation optimization framework rotor and computational results for scenarios provided by DB Fernverkehr AG, one of the leading railway operators in Europe.}, language = {en} } @incollection{SchenkerVierhausBorndoerferetal.2017, author = {Schenker, Sebastian and Vierhaus, Ingmar and Bornd{\"o}rfer, Ralf and F{\"u}genschuh, Armin and Skutella, Martin}, title = {Optimisation Methods in Sustainable Manufacturing}, booktitle = {Sustainable Manufacturing}, editor = {Stark, Rainer and Seliger, G{\"u}nther and Bonvoisin, J{\´e}r{\´e}my}, publisher = {Springer International Publishing}, isbn = {978-3-319-48514-0}, doi = {10.1007/978-3-319-48514-0_15}, pages = {239 -- 253}, year = {2017}, abstract = {Sustainable manufacturing is driven by the insight that the focus on the economic dimension in current businesses and lifestyles has to be broadened to cover all three pillars of sustainability: economic development, social development, and environmental protection.}, language = {en} } @misc{MaherDesaulniersSoumis2015, author = {Maher, Stephen J. and Desaulniers, Guy and Soumis, Francois}, title = {The tail assignment problem with look-ahead maintenance constraints}, issn = {1438-0064}, doi = {10.1016/j.ejor.2017.06.041}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56717}, year = {2015}, abstract = {The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to be operated the next day. The aim of this paper is to develop an operationally flexible tail assignment that satisfies short-range---within the next three days---aircraft maintenance requirements and performs the aircraft/flight gate assignment for each input line-of-flight. While maintenance plans commonly span multiple days, the related tail assignment problems can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by extending the one-day routes aircraft maintenance routing approach to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A mathematical model is presented that integrates the gate assignment and maintenance planning problems. To increase the satisfaction of maintenance requirements, an iterative algorithm is developed that modifies the fixed lines-of-flight provided as input to the tail assignment problem. The tail assignment problem and iterative algorithm are demonstrated to effectively satisfy maintenance requirements within appropriate run times using input data collected from three different airlines.}, language = {en} } @misc{AhmadiGritzbachLundNguyenetal.2015, author = {Ahmadi, Sepideh and Gritzbach, Sascha F. and Lund-Nguyen, Kathryn and McCullough-Amal, Devita}, title = {Rolling Stock Rotation Optimization in Days of Strike: An Automated Approach for Creating an Alternative Timetable}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56425}, year = {2015}, abstract = {The operation of a railway network as large as Deutsche Bahn's Intercity Express (ICE) hinges on a number of factors, such as the availability of personnel and the assignment of physical vehicles to a timetable schedule, a problem known as the rolling stock rotation problem (RSRP). In this paper, we consider the problem of creating an alternative timetable in the case that there is a long-term disruption, such as a strike, and the effects that this alternative timetable has on the resulting vehicle rotation plan. We define a priority measure via the Analytic Hierarchy Process (AHP) to determine the importance of each trip in the timetable and therefore which trips to cancel or retain. We then compare our results with those of a limited timetable manually designed by Deutsche Bahn (DB). We find that while our timetable results in a more expensive rotation plan, its flexibility lends itself to a number of simple improvements. Furthermore, our priority measure has the potential to be integrated into the rolling stock rotation optimization process, in particular, the Rotation Optimizer for Railways (ROTOR) software, via the cost function. Ultimately, our method provides the foundation for an automated way of creating a new timetable quickly, and potentially in conjunction with a new rotation plan, in the case of a limited scenario.}, language = {en} } @misc{BorndoerferSchulzSeidletal.2015, author = {Bornd{\"o}rfer, Ralf and Schulz, Christof and Seidl, Stephan and Weider, Steffen}, title = {Integration of Duty Scheduling and Rostering to Increase Driver Satisfaction}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56299}, year = {2015}, abstract = {Integrated treatment of hitherto individual steps in the planning process of public transit companies discloses opportunities to reduce costs and to improve the quality of service. The arising integrated planning problems are complex and their solution requires the development of novel mathematical methods. This article proposes a mathematical optimization approach to integrate duty scheduling and rostering in public transit, which allows to significantly increase driver satisfaction at almost zero cost. This is important in order to to increase the attractiveness of the driver profession. The integration is based on coupling the subproblems by duty templates, which, compared to a coupling by duties, drastically reduces the problem complexity.}, language = {en} } @misc{BeckenbachBorndoerfer2015, author = {Beckenbach, Isabel and Bornd{\"o}rfer, Ralf}, title = {A Hall Condition for Normal Hypergraphs}, issn = {1438-0064}, doi = {10.1016/j.disc.2018.06.013}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56175}, year = {2015}, abstract = {Conforti, Cornu{\´e}jols, Kapoor, and Vusković gave a Hall-type condition for the non-existence of a perfect matching in a balanced hypergraph. We generalize this result to the class of normal hypergraphs.}, language = {en} } @article{GamrathKochMartinetal.2015, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in presolving for mixed integer programming}, volume = {7}, journal = {Mathematical Programming Computation}, number = {4}, doi = {10.1007/s12532-015-0083-5}, pages = {367 -- 398}, year = {2015}, abstract = {This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 \% on affected instances while not degrading the performance on the remaining problems.}, language = {en} } @inproceedings{BorndoerferReutherSchlechte2014, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas}, title = {A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem}, volume = {42}, booktitle = {14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, doi = {10.4230/OASIcs.ATMOS.2014.79}, pages = {79 -- 91}, year = {2014}, abstract = {We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.}, language = {en} } @misc{BorndoerferReutherSchlechteetal.2012, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Vehicle Rotation Planning for Intercity Railways}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14731}, number = {12-11}, year = {2012}, abstract = {This paper provides a generic formulation for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a graph theoretical model and a Mixed-Integer-Programming formulation that integrate all main requirements of the considered Vehicle-Rotation-Planning problem (VRPP). We show that it is possible to solve this model for real-world instances provided by our industrial partner DB Fernverkehr AG using modern algorithms and computers.}, language = {en} } @inproceedings{EulerBorndoerferPuchertetal.2024, author = {Euler, Ricardo and Bornd{\"o}rfer, Ralf and Puchert, Christian and Takkula, Tuomo}, title = {ULD Build-Up Scheduling with Logic-Based Benders Decomposition}, volume = {14742}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, doi = {10.1007/978-3-031-60597-0_17}, pages = {259 -- 276}, year = {2024}, abstract = {We study a complex planning and scheduling problem arising from the build-up process of air cargo pallets and containers, collectively referred to as unit load devices (ULD), in which ULDs must be assigned to workstations for loading. Since air freight usually becomes available gradually along the planning horizon, ULD build-ups must be scheduled neither too early to avoid underutilizing ULD capacity, nor too late to avoid resource conflicts with other flights. Whenever possible, ULDs should be built up in batches, thereby giving ground handlers more freedom to rearrange cargo and utilize the ULD's capacity efficiently. The resulting scheduling problem has an intricate cost function and produces large time-expanded models, especially for longer planning horizons. We propose a logic-based Benders decomposition approach that assigns batches to time intervals and workstations in the master problem, while the actual schedule is decided in a subproblem. By choosing appropriate intervals, the subproblem becomes a feasibility problem that decomposes over the workstations. Additionally, the similarity of many batches is exploited by a strengthening procedure for no-good cuts. We benchmark our approach against a time-expanded MIP formulation from the literature on a publicly available data set. It solves 15\% more instances to optimality and decreases run times by more than 50\% in the geometric mean. This improvement is especially pronounced for longer planning horizons of up to one week, where the Benders approach solves over 50\% instances more than the baseline}, language = {en} } @article{EulerMaristanydelasCasas2024, author = {Euler, Ricardo and Maristany de las Casas, Pedro}, title = {Labeling methods for partially ordered paths}, volume = {318}, journal = {European Journal of Operational Research}, number = {1}, edition = {1}, publisher = {Elsevier BV}, arxiv = {http://arxiv.org/abs/2307.10332}, doi = {10.1016/j.ejor.2024.05.002}, pages = {19 -- 30}, year = {2024}, abstract = {The landscape of applications and subroutines relying on shortest path computations continues to grow steadily. This growth is driven by the undeniable success of shortest path algorithms in theory and practice. It also introduces new challenges as the models and assessing the optimality of paths become more complicated. Hence, multiple recent publications in the field adapt existing labeling methods in an ad hoc fashion to their specific problem variant without considering the underlying general structure: they always deal with multi-criteria scenarios, and those criteria define different partial orders on the paths. In this paper, we introduce the partial order shortest path problem (POSP), a generalization of the multi-objective shortest path problem (MOSP) and in turn also of the classical shortest path problem. POSP captures the particular structure of many shortest path applications as special cases. In this generality, we study optimality conditions or the lack of them, depending on the objective functions' properties. Our final contribution is a big lookup table summarizing our findings and providing the reader with an easy way to choose among the most recent multi-criteria shortest path algorithms depending on their problems' weight structure. Examples range from time-dependent shortest path and bottleneck path problems to the electric vehicle shortest path problem with recharging and complex financial weight functions studied in the public transportation community. Our results hold for general digraphs and, therefore, surpass previous generalizations that were limited to acyclic graphs.}, language = {en} } @misc{Henning2020, type = {Master Thesis}, author = {Henning, Erin}, title = {Tropical Geometry Approach to Shortest Paths with Parameterized Arc Weights - A Case Study in Public Transportation Networks}, year = {2020}, abstract = {In graphical representations of public transportation networks, there is often some degree of uncertainty in the arc values, due to delays or transfer times. This uncertainty can be expressed as a parameterized weight on the transfer arcs. Classical shortest path algorithms often have difficulty handling parameterized arc weights and a tropical geometry approach has been shown as a possible solution. The connection between the classical shortest path problem and tropical geometry is well establish: Tropically multiplying the n × n adjacency matrix of a graph with itself n - 1 times results in the so-called Kleene star, and is a matrix-form solution to the all-pairs shortest path problem. Michael Joswig and Benjamin Schr{\"o}ter showed in their paper The Tropical Geometry of Shortest Paths that the same method can be used to find the solution to the all-pairs shortest path problem even in the case of variable arc weights and they proposed an algorithm to solve the single-target shortest path problem in such a case. The solution takes the form of a polyhedral subdivision of the parameter space. As the number of variable arc weights grows, the time needed to execute an implementation of this algorithm grows exponentially. As the size of a public transportation network grows, the number of variable arc weights grows exponentially as well. However, it has been observed that in public transportation networks, there are usually only a few possible shortest routes. Geometrically, this means that there should be few polyhedra in the polyhedral subdivision. This algorithm is used on an example of a real-world public transportation network and an analysis of the polyhedral subdivision is made. Then a geometrical approach is used to analyze the impact of limiting the number of transfers, and thereby limiting the number of parameterized arcs used, as an estimation of the solution to the all-pairs shortest path problem}, language = {en} } @misc{Masing2020, type = {Master Thesis}, author = {Masing, Berenike}, title = {Optimal Line Planning in the Parametric City}, year = {2020}, abstract = {One of the fundamental steps in the optimization of public transport is line planning. It involves determining lines and assigning frequencies of service such that costs are minimized while also maximizing passenger comfort and satisfying travel demands. We formulate the problem as a mixed integer linear program that considers all circuit-like lines in a graph and allows free passenger routing. Traveler and operator costs are included in a linear scalarization in the objective. We apply said programming problem to the Parametric City, which is a graph model introduced by Fielbaum, Jara-D{\´i}az and Gschwender that exibly represents different cities. In his dissertation, Fielbaum solved the line planning problem for various parameter choices in the Parametric City. In a first step, we therefore review his results and make comparative computations. Unlike Fielbaum we arrive at the conclusion that the optimal line plan for this model indeed depends on the demand. Consequently, we analyze the line planning problem in-depth: We find equivalent, but easier to compute formulations and provide a lower bound by LP-relaxation, which we show to be equivalent to a multi-commodity flow problem. Further, we examine what impact symmetry has on the solutions. Supported both by computational results as well as by theoretical analysis, we reach the conclusion that symmetric line plans are optimal or near-optimal in the Parametric City. Restricting the model to symmetric line plans allows for a \kappa-factor approximation algorithm for the line planning problem in the Parametric City.}, language = {en} } @masterthesis{Lange2021, type = {Bachelor Thesis}, author = {Lange, Johanna}, title = {A Decomposition and Dualization Approach to the Periodic Event Scheduling Problem}, year = {2021}, abstract = {Scheduling ist ein wichtiger Forschungsgegenstand im Bereich der diskreten Optimierung. Es geht darum, einen Schedule, d.h. einen Ablaufplan, f{\"u}r gegebene Ereignisse zu finden. Dieser soll optimal hinsichtlich einer Zielfunktion wie zum Beispiel minimaler Dauer oder Kosten sein. Dabei gibt es in der Regel Nebenbedingungen wie Vorrangbeziehungen zwischen den Ereignissen oder zeitliche Einschr{\"a}nkungen, die zu erf{\"u}llen sind. Falls die Ereignisse periodisch wiederkehren, spricht man von periodischem Scheduling. Beispiele sind das Erstellen von Zugfahrpl{\"a}nen, die Schaltungvon Ampelsignalen oder die Planung von Produktionsabl{\"a}ufen. Mathematisch k{\"o}nnen diese Probleme mit dem Periodic Event Scheduling Problem (PESP) modelliert werden, das als gemischt-ganzzahliges Programm formuliert werden kann. In dieser Bachelorarbeit wird ein Ansatz zur L{\"o}sung des PESP mittels Zerlegung und Dualisierung entwickelt. In den Kapiteln 2 und 3 werden zun{\"a}chst die notwendigen graphentheoretischen Grundlagen und das PESP eingef{\"u}hrt. In Kapitel 4 wird das PESP durch Fixierung der ganzzahligen Variablen in lineare Programme zerlegt. Dieses Unterproblem wird dualisiert und wieder in das PESP eingesetzt. Daf{\"u}r ist eine weitere Nebenbedingung n{\"o}tig. Im f{\"u}nften Kapitel behandeln wir die L{\"o}sung des teildualisierten PESP. Eine M{\"o}glichkeit ist es, sich auf eine Teilmenge der Nebenbedingungen zu beschr{\"a}nken. Eine weitere M{\"o}glichkeit ist ein Algorithmus, der{\"a}hnlich wie BendersZerlegung die Nebenbedingungen dynamisch erzeugt. Dieser Algorithmus wird in Kapitel 6 implementiert und an vier Beispielen getestet.}, language = {en} } @misc{Kuehner2021, type = {Master Thesis}, author = {K{\"u}hner, Arno}, title = {Shortest Paths with Boolean Constraints}, year = {2021}, abstract = {For this thesis we study the Constrained Horizontal Flightplanning Problem (CHFPP) for which one has to find the path of minimum cost between airports s and t in a directed graph that respects a set of boolean constraints. To this end we give a survey of three different multilabel algorithms that all use a domination subroutine. We summarize an approach by Knudsen, Chiarandini and Larsen to define this domination and afterwards present our own method which builds on that approach. We suggest different implementation techniques to speed up the computation time, most notably a Reoptimization for an iterative method to solve the problem. Furthermore we implemented the different versions of the algorithm and present statistics on their computation as well as an overview of statistics on the set of real-world constraints that we were given. Finally we present two alternative approaches that tackle the problem, a heuristic with similarities to a Lagrangian relaxation and an approach that makes use of an algorithm which finds the k shortest path of a graph such as the ones of Epstein or Yen.}, language = {en} } @misc{MaristanydelasCasasSedenoNodaBorndoerfer2021, author = {Maristany de las Casas, Pedro and Sedeno-Noda, Antonio and Bornd{\"o}rfer, Ralf}, title = {An Improved Multiobjective Shortest Path Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79712}, year = {2021}, abstract = {We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes the minimal complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra's algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm \emph{Multiobjective Dijkstra Algorithm} (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins', which we improved using new data structures and pruning techniques. On average, the MDA is \$\times2\$ to \$\times9\$ times faster on all used graph types. On some instances the speedup reaches an order of magnitude.}, language = {en} } @misc{PrauseBorndoerferGrimmetal.2023, author = {Prause, Felix and Bornd{\"o}rfer, Ralf and Grimm, Boris and Tesch, Alexander}, title = {Approximating the RSRP with Predictive Maintenance}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89531}, year = {2023}, abstract = {We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.}, language = {en} } @misc{Prause2023, author = {Prause, Felix}, title = {A Multi-Swap Heuristic for Rolling Stock Rotation Planning with Predictive Maintenance}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93133}, year = {2023}, abstract = {We present a heuristic solution approach for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). The task of this problem is to assign a sequence of trips to each of the vehicles and to schedule their maintenance such that all trips can be operated. Here, the health states of the vehicles are considered to be random variables distributed by a family of probability distribution functions, and the maintenance services should be scheduled based on the failure probability of the vehicles. The proposed algorithm first generates a solution by solving an integer linear program and then heuristically improves this solution by applying a local search procedure. For this purpose, the trips assigned to the vehicles are split up and recombined, whereby additional deadhead trips can be inserted between the partial assignments. Subse- quently, the maintenance is scheduled by solving a shortest path problem in a state-expanded version of a space-time graph restricted to the trips of the individual vehicles. The solution approach is tested and evaluated on a set of test instances based on real-world timetables.}, language = {en} } @misc{LoebelBorndoerferWeider2024, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates}, arxiv = {http://arxiv.org/abs/2407.14446}, year = {2024}, abstract = {Public transport operators are gradually electrifying their bus fleets, predominantly with battery-powered drive trains. These buses commonly have to be scheduled to recharge in-service, which gives rise to a number of challenges. A major problem is that the relationship between charging time and replenished driving range is non-linear, which is often approximately modeled. We examine the associated approximation error and show how it can result in a gross over- or underestimation of the fleet size. Moreover, we demonstrate that commonly used piecewise linear underestimations of the charge curve do not result in an underestimation of the predicted charge states in electric vehicle scheduling and routing models. Furthermore, since power grid upgrades are currently not keeping up with an ever growing electricity demand, operators are introducing active charge management tools to dynamically adjust the charging speed depending on the amount of available energy. It is therefore imperative to extend electric bus scheduling models to account for these developments. We propose a novel mixed-integer programming formulation for the electric bus scheduling problem featuring an improved approximation of the non-linear battery charging behavior as well as dynamic recharge speeds to accommodate grid load limits. The idea is to linearly interpolate what we call the charge increment function, which is closely related to the derivative of the commonly used charge curve. This provides very good error control and integrates easily into integer programming models. We demonstrate the practical usefulness of our model on a diverse library of real-life instances.}, language = {en} } @inproceedings{BorndoerferLoebelLoebeletal.2024, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and L{\"o}bel, Fabian and Weider, Steffen}, title = {Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach}, volume = {123}, booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, doi = {10.4230/OASIcs.ATMOS.2024.11}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-211992}, pages = {11:1 -- 11:16}, year = {2024}, abstract = {Attractive and cost-efficient public transport requires solving computationally difficult optimization problems from network design to crew rostering. While great progress has been made in many areas, new requirements to handle increasingly complex constraints are constantly coming up. One such challenge is a new type of resource constraints that are used to deal with the state-of-charge of battery-electric vehicles, which have limited driving ranges and need to be recharged in-service. Resource constrained vehicle scheduling problems can classically be modelled in terms of either a resource constrained (multi-commodity) flow problem or in terms of a path-based set partition problem. We demonstrate how a novel integrated version of both formulations can be leveraged to solve resource constrained vehicle scheduling with replenishment in general and the electric bus scheduling problem in particular by Lagrangian relaxation and the proximal bundle method.}, language = {en} } @article{PrauseBorndoerfer2024, author = {Prause, Felix and Bornd{\"o}rfer, Ralf}, title = {An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance}, arxiv = {http://arxiv.org/abs/2404.08367}, year = {2024}, abstract = {The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These probabilities are determined by the health states of the vehicles, which are considered to be random variables distributed by a parameterized family of probability distribution functions. During the operation of the trips, the corresponding parameters get updated. In this article, we present a dual solution approach for RSRP-PdM and generalize a linear programming based lower bound for this problem to families of probability distribution functions with more than one parameter. For this purpose, we define a rounding function that allows for a consistent underestimation of the parameters and model the problem by a state-expanded event-graph in which the possible states are restricted to a discrete set. This induces a flow problem that is solved by an integer linear program. We show that the iterative refinement of the underlying discretization leads to solutions that converge from below to an optimal solution of the original instance. Thus, the linear relaxation of the considered integer linear program results in a lower bound for RSRP-PdM. Finally, we report on the results of computational experiments conducted on a library of test instances.}, language = {en} } @inproceedings{Prause2024, author = {Prause, Felix}, title = {A Multi-Swap Heuristic for Rolling Stock Rotation Planning with Predictive Maintenance}, booktitle = {Proceedings of the 11th International Network Optimization Conference (INOC), Dublin, Ireland, March 11-23, 2024}, doi = {10.48786/inoc.2024.11}, pages = {58 -- 63}, year = {2024}, abstract = {We present a heuristic solution approach for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). The task of this problem is to assign a sequence of trips to each of the vehicles and to schedule their maintenance such that all trips can be operated. Here, the health states of the vehicles are considered to be random variables distributed by a family of probability distribution functions, and the maintenance services should be scheduled based on the failure probability of the vehicles. The proposed algorithm first generates a solution by solving an integer linear program and then heuristically improves this solution by applying a local search procedure. For this purpose, the trips assigned to the vehicles are split up and recombined, whereby additional deadhead trips can be inserted between the partial assignments. Subsequently, the maintenance is scheduled by solving a shortest path problem in a state-expanded version of a space-time graph restricted to the trips of the individual vehicles. The solution approach is tested and evaluated on a set of test instances based on real-world timetables.}, language = {en} } @article{PrauseBorndoerferGrimmetal.2024, author = {Prause, Felix and Bornd{\"o}rfer, Ralf and Grimm, Boris and Tesch, Alexander}, title = {Approximating rolling stock rotations with integrated predictive maintenance}, volume = {30}, journal = {Journal of Rail Transport Planning \& Management}, doi = {10.1016/j.jrtpm.2024.100434}, pages = {100434}, year = {2024}, abstract = {We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PdM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for six instances derived from real-world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.}, language = {en} } @misc{Bortoletto2021, type = {Master Thesis}, author = {Bortoletto, Enrico}, title = {The tropical tiling of periodic timetable space and a dual modulo network simplex algorithm}, year = {2021}, abstract = {We propose a tropical interpretation of the solution space of the Periodic Event Scheduling Problem as a collection of polytropes, making use of the characterization of tropical cones as weighted digraph polyhedra. General and geometric properties of the polytropal collection are inspected and understood in connection with the combinatorial properties of the underlying periodic event scheduling instance. Novel algorithmic ideas are presented and tested, making use of the aforementioned theoretical results to solve and optimize the problem.}, language = {en} } @masterthesis{Kraus2021, type = {Bachelor Thesis}, author = {Kraus, Luitgard}, title = {A Label Setting Multiobjective Shortest Path FPTAS}, year = {2021}, abstract = {Algorithms that solve the shortest path problem can largely be split into the two categories of label setting and label correcting. The Multiobjective Shortest Path (MOSP) problem is a generalization of the classical shortest path problem in terms of the dimension of the cost function. We explore the differences of two similar MOSP label setting algorithms. Furthermore, we present and prove a general method of how to derive Fully Polynomial Time Approximation Schemes (FPTAS) for MOSP label setting algorithms. Finally, we explore two pruning techniques for the one to one variants of exact label setting MOSP algorithms and adapt them to their FPTAS variants.}, language = {en} } @misc{Rahmati2021, type = {Master Thesis}, author = {Rahmati, Niloofar}, title = {Resource Constrained APSP-Algorithm with Possible Reloading Stops}, year = {2021}, language = {en} } @misc{PrauseBorndoerfer2023, author = {Prause, Felix and Bornd{\"o}rfer, Ralf}, title = {Construction of a Test Library for the Rolling Stock Rotation Problem with Predictive Maintenance}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91734}, year = {2023}, abstract = {We describe the development of a test library for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). Our approach involves the utilization of genuine timetables from a private German railroad company. The generated instances incorporate probability distribution functions for modeling the health states of the vehicles and the considered trips possess varying degradation functions. RSRP-PdM involves assigning trips to a fleet of vehicles and scheduling their maintenance based on their individual health states. The goal is to minimize the total costs consisting of operational costs and the expected costs associated with vehicle failures. The failure probability is dependent on the health states of the vehicles, which are assumed to be random variables distributed by a family of probability distributions. Each distribution is represented by the parameters characterizing it and during the operation of the trips, these parameters get altered. Our approach incorporates non-linear degradation functions to describe the inference of the parameters but also linear ones could be applied. The resulting instances consist of the timetables of the individual lines that use the same vehicle type. Overall, we employ these assumptions and utilize open-source data to create a library of instances with varying difficulty. Our approach is vital for evaluating and comparing algorithms designed to solve the RSRP-PdM.}, language = {en} } @misc{LoebelBorndoerferWeider2023, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Non-Linear Battery Behavior in Electric Vehicle Scheduling Problems}, issn = {1438-0064}, doi = {10.1007/978-3-031-58405-3_53}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-92441}, year = {2023}, abstract = {The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve.}, language = {en} } @article{BorndoerferEsserFrankenbergeretal.2021, author = {Bornd{\"o}rfer, Ralf and Eßer, Thomas and Frankenberger, Patrick and Huck, Andreas and Jobmann, Christoph and Krostitz, Boris and Kuchenbecker, Karsten and Moorhagen, Kai and Nagl, Philipp and Peterson, Michael and Reuther, Markus and Schang, Thilo and Schoch, Michael and Sch{\"u}lldorf, Hanno and Sch{\"u}tz, Peter and Therolf, Tobias and Waas, Kerstin and Weider, Steffen}, title = {Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization}, volume = {51}, journal = {Informs Journal on Applied Analytics}, number = {1}, doi = {10.1287/inte.2020.1069}, pages = {42 -- 62}, year = {2021}, abstract = {Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. DB models train compositions using hyperarcs. The resulting hypergraph models are ad-dressed using a novel coarse-to-fine method that implements a hierarchical column genera-tion over three levels of detail. This algorithm is the mathematical core of DB's fleet em-ployment optimization (FEO) system for rolling stock rotation planning. FEO's impact within DB's planning departments has been revolutionary. DB has used it to support the company's procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for cross-border operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB's plan-ning departments appreciate FEO's high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in cross-border operations to the implementation of FEO.}, language = {en} } @article{SahinAhmadiBorndoerferetal.2020, author = {Sahin, Guvenc and Ahmadi, Amin and Bornd{\"o}rfer, Ralf and Schlechte, Thomas}, title = {Multi-period line planning with resource transfers}, volume = {119}, journal = {Transportation Research Part C: Emerging Technologies}, doi = {10.1016/j.trc.2020.102726}, pages = {102726}, year = {2020}, abstract = {Urban transportation systems are subject to a high level of variation and fluctuation in demand over the day. When this variation and fluctuation are observed in both time and space, it is crucial to develop line plans that are responsive to demand. A multi-period line planning approach that considers a changing demand during the planning horizon is proposed. If such systems are also subject to limitations of resources, a dynamic transfer of resources from one line to another throughout the planning horizon should also be considered. A mathematical modelling framework is developed to solve the line planning problem with a cost-oriented approach considering transfer of resources during a finite length planning horizon of multiple periods. We use real-life public transportation network data for our computational results. We analyze whether or not multi-period solutions outperform single period solutions in terms of feasibility and relevant costs. The importance of demand variation on multi-period solutions is investigated. We evaluate the impact of resource transfer constraints on the effectiveness of solutions. We also study the effect of period lengths along with the problem parameters that are significant for and sensitive to the optimality of solutions.}, language = {en} } @inproceedings{LoebelBorndoerferWeider2023, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.15}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-187765}, pages = {15:1 -- 15:6}, year = {2023}, abstract = {The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems. Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear. In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized. Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic. We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.}, language = {en} } @misc{Loebel2020, type = {Master Thesis}, author = {L{\"o}bel, Fabian}, title = {Implementing the Network Simplex for Hypergraphs}, year = {2020}, abstract = {The well-known network simplex algorithm is a powerful tool to solve flow problems on graphs. Based on a recent dissertation by Isabel Beckenbach, we develop the necessary theory to extend the network simplex to capacitated flow problems on hypergraphs and implement this new variant. We then attempt to solve instances arising from real-life vehicle rotation planning problems.}, language = {en} } @article{EulerLindnerBorndoerfer2024, author = {Euler, Ricardo and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {Price optimal routing in public transportation}, volume = {13}, journal = {EURO Journal on Transportation and Logistics}, publisher = {Elsevier BV}, issn = {2192-4376}, doi = {10.1016/j.ejtl.2024.100128}, pages = {1 -- 15}, year = {2024}, language = {en} } @article{EulerMaristanydelasCasasBorndoerfer2024, author = {Euler, Ricardo and Maristany de las Casas, Pedro and Bornd{\"o}rfer, Ralf}, title = {Logic-Constrained Shortest Paths for Flight Planning}, arxiv = {http://arxiv.org/abs/2412.13235}, year = {2024}, abstract = {The Logic-Constrained Shortest Path Problem (LCSP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC) authorities are enforcing a set of traffic flow restrictions (TFRs) on aircraft routes in order to increase safety and throughput. We propose a new branch and bound-based algorithm for the LCSP. The resulting algorithm has three main degrees of freedom: the node selection rule, the branching rule and the conflict. While node selection and branching rules have been long studied in the MIP and SAT communities, most of them cannot be applied out of the box for the LCSP. We review the existing literature and develop tailored variants of the most prominent rules. The conflict, the set of variables to which the branching rule is applied, is unique to the LCSP. We analyze its theoretical impact on the B\&B algorithm. In the second part of the paper, we show how to model the Flight Planning Problem with TFRs as an LCSP and solve it using the branch and bound algorithm. We demonstrate the algorithm's efficiency on a dataset consisting of a global flight graph and a set of around 20000 real TFRs obtained from our industry partner Lufthansa Systems GmbH. We make this dataset publicly available. Finally, we conduct an empirical in-depth analysis of node selection rules, branching rules and conflicts. Carefully choosing an appropriate combination yields an improvement of an order of magnitude compared to an uninformed choice.}, language = {en} } @article{MasingLindnerEbert2023, author = {Masing, Berenike and Lindner, Niels and Ebert, Patricia}, title = {Forward and Line-Based Cycle Bases for Periodic Timetabling}, volume = {4}, journal = {Operations Research Forum}, number = {3}, doi = {10.1007/s43069-023-00229-0}, pages = {53}, year = {2023}, abstract = {The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak, and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure, and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances.}, language = {en} } @inproceedings{KlugReutherSchlechte2022, author = {Klug, Torsten and Reuther, Markus and Schlechte, Thomas}, title = {Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/OASIcs.ATMOS.2022.11}, pages = {11:1 -- 11:8}, year = {2022}, abstract = {Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [8 ], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [3]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches.}, language = {en} } @article{MaristanydelasCasasSedenoNodaBorndoerfer2021, author = {Maristany de las Casas, Pedro and Sedeno-Noda, Antonio and Bornd{\"o}rfer, Ralf}, title = {An Improved Multiobjective Shortest Path Algorithm}, volume = {135}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2021.105424}, year = {2021}, abstract = {We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes a minimum complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra's algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm Multiobjective Dijkstra Algorithm (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins, which we improved using new data structures and pruning techniques. On average, the MDA is 2 to 9 times faster on all used graph types. On some instances the speedup reaches an order of magnitude.}, language = {en} } @article{SchlechteBorndoerferDenissenetal.2022, author = {Schlechte, Thomas and Bornd{\"o}rfer, Ralf and Denißen, Jonas and Heller, Simon and Klug, Torsten and K{\"u}pper, Michael and Lindner, Niels and Reuther, Markus and S{\"o}hlke, Andreas and Steadman, William}, title = {Timetable Optimization for a Moving Block System}, volume = {22}, journal = {Journal of Rail Transport Planning \& Management}, issn = {2210-9706}, doi = {10.1016/j.jrtpm.2022.100315}, pages = {100315}, year = {2022}, abstract = {We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality.}, language = {en} } @article{Roth2021, author = {Roth, Sarah}, title = {SAT-Heuristiken f{\"u}r das Periodic Event Scheduling-Problem}, journal = {OR News}, number = {71}, issn = {1437-2045}, year = {2021}, language = {en} } @misc{BortolettoLindnerMasing2022, author = {Bortoletto, Enrico and Lindner, Niels and Masing, Berenike}, title = {The Tropical and Zonotopal Geometry of Periodic Timetables}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/2204.13501}, doi = {https://doi.org/10.1007/s00454-024-00686-2}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86708}, year = {2022}, abstract = {The Periodic Event Scheduling Problem (PESP) is the standard mathematical tool for optimizing periodic timetabling problems in public transport. A solution to PESP consists of three parts: a periodic timetable, a periodic tension, and integer periodic offset values. While the space of periodic tension has received much attention in the past, we explore geometric properties of the other two components, establishing novel connections between periodic timetabling and discrete geometry. Firstly, we study the space of feasible periodic timetables, and decompose it into polytropes, i.e., polytopes that are convex both classically and in the sense of tropical geometry. We then study this decomposition and use it to outline a new heuristic for PESP, based on the tropical neighbourhood of the polytropes. Secondly, we recognize that the space of fractional cycle offsets is in fact a zonotope. We relate its zonotopal tilings back to the hyperrectangle of fractional periodic tensions and to the tropical neighbourhood of the periodic timetable space. To conclude we also use this new understanding to give tight lower bounds on the minimum width of an integral cycle basis.}, language = {en} } @misc{BortolettoLindnerMasing2022, author = {Bortoletto, Enrico and Lindner, Niels and Masing, Berenike}, title = {Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling}, issn = {1438-0064}, doi = {10.4230/OASIcs.ATMOS.2022.3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-87385}, year = {2022}, abstract = {Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [3]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [4]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances.}, language = {en} } @misc{MasingLindnerLiebchen2022, author = {Masing, Berenike and Lindner, Niels and Liebchen, Christian}, title = {Periodic Timetabling with Integrated Track Choice for Railway Construction Sites}, issn = {1438-0064}, doi = {10.1016/j.jrtpm.2023.100416}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88626}, year = {2022}, abstract = {We propose a mixed-integer linear programming model to generate and optimize periodic timetables with integrated track choice in the context of railway construction sites. When a section of a railway network becomes unavailable, the nearby areas are typically operated close to their capacity limits, and hence carefully modeling headways and allowing flexible routings becomes vital. We therefore discuss first how to integrate headway constraints into the Periodic Event Scheduling Problem (PESP) that do not only prevent overtaking, but also guarantee conflict-free timetables in general and particularly inside stations. Secondly, we introduce a turn-sensitive event-activity network, which is able to integrate routing alternatives for turnarounds at stations, e.g., turning at a platform vs. at a pocket track for metro-like systems. We propose several model formulations to include track choice, and finally evaluate them on six real construction site scenarios on the S-Bahn Berlin network.}, language = {en} } @article{EulerLindnerBorndoerfer2022, author = {Euler, Ricardo and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {Price Optimal Routing in Public Transportation}, arxiv = {http://arxiv.org/abs/2204.01326}, doi = {https://doi.org/10.48550/arXiv.2204.01326}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86414}, year = {2022}, abstract = {We consider the price-optimal earliest arrival problem in public transit (POEAP) in which we aim to calculate the Pareto-front of journeys with respect to ticket price and arrival time in a public transportation network. Public transit fare structures are often a combination of various fare strategies such as, e.g., distance-based fares, zone-based fares or flat fares. The rules that determine the actual ticket price are often very complex. Accordingly, fare structures are notoriously difficult to model as it is in general not sufficient to simply assign costs to arcs in a routing graph. Research into POEAP is scarce and usually either relies on heuristics or only considers restrictive fare models that are too limited to cover the full scope of most real-world applications. We therefore introduce conditional fare networks (CFNs), the first framework for representing a large number of real-world fare structures. We show that by relaxing label domination criteria, CFNs can be used as a building block in label-setting multi-objective shortest path algorithms. By the nature of their extensive modeling capabilities, optimizing over CFNs is NP-hard. However, we demonstrate that adapting the multi-criteria RAPTOR (MCRAP) algorithm for CFNs yields an algorithm capable of solving POEAP to optimality in less than 400 ms on average on a real-world data set. By restricting the size of the Pareto-set, running times are further reduced to below 10 ms.}, language = {en} } @article{LindnerReisch2022, author = {Lindner, Niels and Reisch, Julian}, title = {An analysis of the parameterized complexity of periodic timetabling}, volume = {25}, journal = {Journal of Scheduling}, doi = {10.1007/s10951-021-00719-1}, pages = {157 -- 176}, year = {2022}, abstract = {Public transportation networks are typically operated with a periodic timetable. The periodic event scheduling problem (PESP) is the standard mathematical modeling tool for periodic timetabling. PESP is a computationally very challenging problem: For example, solving the instances of the benchmarking library PESPlib to optimality seems out of reach. Since PESP can be solved in linear time on trees, and the treewidth is a rather small graph parameter in the networks of the PESPlib, it is a natural question to ask whether there are polynomial-time algorithms for input networks of bounded treewidth, or even better, fixed-parameter tractable algorithms. We show that deciding the feasibility of a PESP instance is NP-hard even when the treewidth is 2, the branchwidth is 2, or the carvingwidth is 3. Analogous results hold for the optimization of reduced PESP instances, where the feasibility problem is trivial. Moreover, we show W[1]-hardness of the general feasibility problem with respect to treewidth, which means that we can most likely only accomplish pseudo-polynomial-time algorithms on input networks with bounded tree- or branchwidth. We present two such algorithms based on dynamic programming. We further analyze the parameterized complexity of PESP with bounded cyclomatic number, diameter, or vertex cover number. For event-activity networks with a special—but standard—structure, we give explicit and sharp bounds on the branchwidth in terms of the maximum degree and the carvingwidth of an underlying line network. Finally, we investigate several parameters on the smallest instance of the benchmarking library PESPlib.}, language = {en} } @inproceedings{MasingLindnerBorndoerfer2022, author = {Masing, Berenike and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {Optimal Line Plans in the Parametric City and the Impact of In-Motion Costs}, booktitle = {Operations Research Proceedings 2021}, editor = {Trautmann, Norbert and Dr{\"a}gi, Mario}, publisher = {Springer, Cham}, isbn = {978-3-031-08623-6}, doi = {10.1007/978-3-031-08623-6_44}, pages = {295 -- 301}, year = {2022}, abstract = {Line planning in public transport involves determining vehicle routes and assigning frequencies of service such that travel demands are satisfied. We evaluate how line plans, which are optimal with respect to in-motion costs (IMC), the objective function depending purely on arc-lengths for both user and operator costs, performs with respect to the value of resources consumed (VRC). The latter is an elaborate, socio-economic cost function which includes discomfort caused by delay, boarding and alighting times, and transfers. Even though discomfort is a large contributing factor to VRC and is entirely disregarded in IMC,  we observe that the two cost functions are qualitatively comparable.}, language = {en} } @article{SchieweGoerigkLindner2023, author = {Schiewe, Philine and Goerigk, Marc and Lindner, Niels}, title = {Introducing TimPassLib - A Library for Integrated Periodic Timetabling and Passenger Routing}, volume = {4}, journal = {Operations Research Forum}, number = {3}, doi = {10.1007/s43069-023-00244-1}, pages = {64}, year = {2023}, abstract = {Classic models to derive a timetable for public transport often face a chicken-and-egg situation: A good timetable should offer passengers routes with small travel times, but the route choice of passengers depends on the timetable. While models that fix passenger routes were frequently considered in the literature, integrated models that simultaneously optimize timetables and passenger routes have seen increasing attention lately. This creates a growing need for a set of instances that allows to test and compare new algorithmic developments for the integrated problem. Our paper addresses this requirement by presenting TimPassLib, a new benchmark library of instances for integrated periodic timetabling and passenger routing.}, language = {en} } @inproceedings{BlancoBorndoerferMaristanydelasCasas2022, author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Maristany de las Casas, Pedro}, title = {An A* Algorithm for Flight Planning Based on Idealized Vertical Profiles}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, doi = {10.4230/OASIcs.ATMOS.2022.1}, pages = {1:1 -- 1:15}, year = {2022}, abstract = {The Flight Planning Problem is to find a minimum fuel trajectory between two airports in a 3D airway network under consideration of the wind. We show that this problem is NP-hard, even in its most basic version. We then present a novel A∗ heuristic, whose potential function is derived from an idealized vertical profile over the remaining flight distance. This potential is, under rather general assumptions, both admissible and consistent and it can be computed efficiently. The method outperforms the state-of-the-art heuristic on real-life instances.}, language = {en} } @article{MasingLindnerBorndoerfer2022, author = {Masing, Berenike and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {The price of symmetric line plans in the Parametric City}, volume = {166}, journal = {Transportation Research Part B: Methodological}, doi = {10.1016/j.trb.2022.10.009}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88613}, pages = {419 -- 443}, year = {2022}, abstract = {We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. We prove that the symmetry gap is small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations.}, language = {de} } @article{Beckenbach2020, author = {Beckenbach, Isabel}, title = {Von Graphen zu Hypergraphen}, journal = {OR News}, number = {70}, issn = {1437-2045}, year = {2020}, language = {en} } @inproceedings{GrimmBorndoerferBushe2023, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Bushe, Julian}, title = {Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, doi = {https://doi.org/10.4230/OASIcs.ATMOS.2023.13}, pages = {13:1 -- 13:15}, year = {2023}, abstract = {The fundamental task of every passenger railway operator is to offer an attractive railway timetable to the passengers while operating it as cost efficiently as possible. The available rolling stock has to be assigned to trips so that all trips are operated, operational requirements are satisfied, and the operating costs are minimum. This so-called Rolling Stock Rotation Problem (RSRP) is well studied in the literature. In this paper we consider an acyclic version of the RSRP that includes vehicle maintenance. As the latter is an important aspect, maintenance services have to be planned simultaneously to ensure the rotation's feasibility in practice. Indeed, regular maintenance is important for the safety and reliability of the rolling stock as well as enforced by law in many countries. We present a new integer programming formulation that links a hyperflow to model vehicle compositions and their coupling decisions to a set of path variables that take care of the resource consumption of the individual vehicles. To solve the model we developed different column generation algorithms which are compared to each other as well as to the MILP flow formulation of [Ralf Bornd{\"o}rfer et al., 2016] on a test set of real world instances.}, language = {en} } @inproceedings{BorndoerferGrimmSchade2023, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Schade, Stanley}, title = {A Robustness Analysis of Long Distance Train Crew Schedules in Germany}, volume = {CCC 1}, booktitle = {Proceedings Of The Fifth Iinternational Conference On Railway Technology: Research, Development and Maintenance}, issn = {2753-3239}, doi = {10.4203/ccc.1.23.17}, year = {2023}, abstract = {Nowadays railway networks are highly complex and often very fragile systems. A wide variety of individual operations that influence each other have to go hand in hand to end up with a smoothly and efficiently running system. Many of these operations suffer from uncertainty as trains could be delayed, the signaling system be disrupted or scheduled crews could be ill. Usually these opartions could be organized hierarchically from long term strategical decisions to real time decision management. Each stage in the hierarchy defines a different mathematical optimization problem, which is solved sequentially. At every stage the knowledge about preceding or succeeding planning stages may vary and also the interaction between two stages in this chain of problems may vary from almost no interaction to highly dependent situations. This paper deals with a topic that is an example for the latter case, namely the interaction between vehicle schedules, vehicle punctuality, and crew schedules. To reduce the number of potential rescheduling actions we developed a software tool in cooperation with our practical partner DB Fernverkehr AG (DBF) to predict a certain set of critical crew schedules. This tool evaluates, predicts, and determines "bottlenecks" in the crew schedule in the sense of potentially required rescheduling actions due to likely delays. The approach was tested on real life crew and train timetable data of DBF and can be regarded as the computation of key performance indicators, which is often desired. For our experiments we had access to the operated timetable and crew schedule of DBF for periods of two and six weeks in 2019.}, language = {en} } @inproceedings{BortolettoLindnerMasing2022, author = {Bortoletto, Enrico and Lindner, Niels and Masing, Berenike}, title = {Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, doi = {10.4230/OASIcs.ATMOS.2022.3}, pages = {3:1 -- 3:19}, year = {2022}, abstract = {Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [Bornd{\"o}rfer et al., 2020]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [Bortoletto et al., 2022]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances.}, language = {en} } @inproceedings{BortolettoLindnerMasing2023, author = {Bortoletto, Enrico and Lindner, Niels and Masing, Berenike}, title = {Periodic Timetabling with Cyclic Order Constraints}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.7}, pages = {7:1 -- 7:18}, year = {2023}, abstract = {Periodic timetabling for highly utilized railway networks is a demanding challenge. We formulate an infrastructure-aware extension of the Periodic Event Scheduling Problem (PESP) by requiring that not only events, but also activities using the same infrastructure must be separated by a minimum headway time. This extended problem can be modeled as a mixed-integer program by adding constraints on the sum of periodic tensions along certain cycles, so that it shares some structural properties with standard PESP. We further refine this problem by fixing cyclic orders at each infrastructure element. Although the computational complexity remains unchanged, the mixed-integer programming model then becomes much smaller. Furthermore, we also discuss how to find a minimal subset of infrastructure elements whose cyclic order already prescribes the order for the remaining parts of the network, and how cyclic order information can be modeled in a mixed-integer programming context. In practice, we evaluate the impact of cyclic orders on a real-world instance on the S-Bahn Berlin network, which turns out to be computationally fruitful.}, language = {en} } @inproceedings{MasingLindnerLiebchen2023, author = {Masing, Berenike and Lindner, Niels and Liebchen, Christian}, title = {Integrating Line Planning for Construction Sites into Periodic Timetabling via Track Choice}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.5}, pages = {5:1 -- 5:15}, year = {2023}, abstract = {We consider maintenance sites for urban rail systems, where unavailable tracks typically require changes to the regular timetable, and often even to the line plan. In this paper, we present an integrated mixed-integer linear optimization model to compute an optimal line plan that makes best use of the available tracks, together with a periodic timetable, including its detailed routing on the tracks within the stations. The key component is a flexible, turn-sensitive event-activity network that allows to integrate line planning and train routing using a track choice extension of the Periodic Event Scheduling Problem (PESP). Major goals are to maintain as much of the regular service as possible, and to keep the necessary changes rather local. Moreover, we present computational results on real construction site scenarios on the S-Bahn Berlin network. We demonstrate that this integrated problem is indeed solvable on practically relevant instances.}, language = {en} } @inproceedings{Masing2022, author = {Masing, Berenike}, title = {Optimal Line Planning in the Parametric City}, booktitle = {Operations Research Proceedings 2021. OR 2021.}, editor = {Trautmann, Norbert and Dr{\"a}gi, Mario}, publisher = {Springer, Cham}, isbn = {978-3-031-08623-6}, doi = {10.1007/978-3-031-08623-6_7}, pages = {39 -- 44}, year = {2022}, abstract = {We formulate the line planning problem in public transport as a mixed integer linear program (MILP), which selects both passenger and vehicle routes, such that travel demands are met with respect to minimized travel times for both operators and users. We apply MILP to the Parametric City, a generic city model developed by Fielbaum et al. [2]. While the infrastructure graph and demand are entirely rotation symmetric, asymmetric optimal line plans can occur. Using group theory, we analyze the properties of symmetric solutions and introduce a symmetry gap to measure their deviation of the optimum. We also develop a 1+1+2√g-approximation algorithm, depending only on the cost related parameter g. Supported by computational experiments, we conclude that in practice symmetric line plans provide good solutions for the line planning problem in the Parametric City.}, language = {en} } @inproceedings{LindnervanLieshout2022, author = {Lindner, Niels and van Lieshout, Rolf}, title = {Benders Decomposition for the Periodic Event Scheduling Problem}, booktitle = {Operations Research Proceedings 2021}, publisher = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-031-08623-6_43}, pages = {289 -- 294}, year = {2022}, 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{OPUS4-8811, title = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, volume = {106}, editor = {D'Emidio, Mattia and Lindner, Niels}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, isbn = {978-3-95977-259-4}, doi = {10.4230/OASIcs.ATMOS.2022}, year = {2022}, abstract = {OASIcs, Volume 106, ATMOS 2022, Complete Volume}, language = {en} } @misc{MaristanydelasCasasBorndoerferKrausetal.2020, author = {Maristany de las Casas, Pedro and Bornd{\"o}rfer, Ralf and Kraus, Luitgard and Sede{\~n}o-Noda, Antonio}, title = {An FPTAS for Dynamic Multiobjective Shortest Path Problems}, doi = {https://doi.org/10.3390/a14020043}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-80954}, year = {2020}, abstract = {We propose in this paper the Dynamic Multiobjective Shortest Problem. It features multidimensional states that can depend on several variables and not only on time; this setting is motivated by flight planning and electric vehicle routing applications. We give an exact algorithm for the FIFO case and derive from it an FPTAS, which is computationally efficient. It also features the best known complexity in the static case.}, language = {en} } @inproceedings{PrauseBorndoerfer2024, author = {Prause, Felix and Bornd{\"o}rfer, Ralf}, title = {A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance}, volume = {123}, booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)}, doi = {10.4230/OASIcs.ATMOS.2024.13}, pages = {13:1 -- 13:19}, year = {2024}, abstract = {We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach.}, language = {en} } @misc{BestuzhevaBesanconChenetal.2021, author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc E. and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 8.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85309}, year = {2021}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.}, language = {en} } @misc{BolusaniBesanconBestuzhevaetal.2024, author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Bestuzheva, Ksenia and Chmiela, Antonia and Dion{\´i}sio, Jo{\~a}o and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Ghannam, Mohammed and Gleixner, Ambros and Graczyk, Christoph and Halbig, Katrin and Hedtke, Ivo and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Kamp, Dominik and Koch, Thorsten and Kofler, Kevin and Lentz, Jurgen and Manns, Julian and Mexi, Gioni and M{\"u}hmer, Erik and E. Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Turner, Mark and Vigerske, Stefan and Weninger, Dieter and Xu, Liding}, title = {The SCIP Optimization Suite 9.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-95528}, year = {2024}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.}, language = {en} } @misc{TurnerChmielaKochetal.2023, author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93095}, year = {2023}, abstract = {A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.}, language = {en} } @article{BestuzhevaBesanconChenetal.2023, author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {Enabling research through the SCIP optimization suite 8.0}, volume = {49}, journal = {ACM Transactions on Mathematical Software}, number = {2}, doi = {10.1145/3585516}, pages = {1 -- 21}, year = {2023}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.}, language = {en} } @inproceedings{TurnerChmielaKochetal.2025, author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, volume = {15763}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2025}, doi = {10.1007/978-3-031-95976-9_14}, year = {2025}, abstract = {A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.}, language = {en} } @article{BestuzhevaChmielaMuelleretal.2023, author = {Bestuzheva, Ksenia and Chmiela, Antonia and M{\"u}ller, Benjamin and Serrano, Felipe and Vigerske, Stefan and Wegscheider, Fabian}, title = {Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0}, journal = {Journal of Global Optimization}, doi = {10.1007/s10898-023-01345-1}, year = {2023}, abstract = {For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.}, language = {en} } @article{ChmielaMunozSerrano2025, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {Monoidal strengthening and unique lifting in MIQCPs}, volume = {210}, journal = {Mathematical Programming B}, doi = {10.1007/s10107-024-02112-0}, pages = {189 -- 222}, year = {2025}, language = {en} } @article{ChmielaMunozSerrano2023, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, volume = {197}, journal = {Mathematical Programming B}, doi = {10.1007/s10107-022-01808-5}, pages = {549 -- 586}, year = {2023}, language = {en} } @inproceedings{ChmielaKhalilGleixneretal.2021, author = {Chmiela, Antonia and Khalil, Elias B. and Gleixner, Ambros and Lodi, Andrea and Pokutta, Sebastian}, title = {Learning to Schedule Heuristics in Branch and Bound}, booktitle = {Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021}, arxiv = {http://arxiv.org/abs/2103.10294}, year = {2021}, abstract = {Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49\% on a class of challenging instances.}, language = {en} } @inproceedings{ChmielaMunozSerrano2023, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {Monoidal strengthening and unique lifting in MIQCPs}, volume = {13904}, booktitle = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, doi = {10.1007/978-3-031-32726-1_7}, pages = {87 -- 99}, year = {2023}, abstract = {Using the recently proposed maximal quadratic-free sets and the well-known monoidal strengthening procedure, we show how to improve inter- section cuts for quadratically-constrained optimization problems by exploiting integrality requirements. We provide an explicit construction that allows an efficient implementation of the strengthened cuts along with computational results showing their improvements over the standard intersection cuts. We also show that, in our setting, there is unique lifting which implies that our strengthening procedure is generating the best possible cut coefficients for the integer variables.}, language = {en} } @inproceedings{ChmielaMunozSerrano2021, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, volume = {22}, booktitle = {Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021}, doi = {10.1007/978-3-030-73879-2_10}, pages = {134 -- 147}, year = {2021}, abstract = {The generation of strong linear inequalities for QCQPs has been recently tackled by a number of authors using the intersection cut paradigm - a highly studied tool in integer programming whose flexibility has triggered these renewed efforts in non-linear settings. In this work, we consider intersection cuts using the recently proposed construction of maximal quadratic-free sets. Using these sets, we derive closed-form formulas to compute intersection cuts which allow for quick cut-computations by simply plugging-in parameters associated to an arbitrary quadratic inequality being violated by a vertex of an LP relaxation. Additionally, we implement a cut-strengthening procedure that dates back to Glover and evaluate these techniques with extensive computational experiments.}, language = {en} } @article{KotilPelofskeRiedmuelleretal.2025, author = {Kotil, Ayse and Pelofske, Elijah and Riedm{\"u}ller, Stephanie and Egger, Daniel J. and Eidenbenz, Stephan and Koch, Thorsten and Woerner, Stefan}, title = {Quantum Approximate Multi-Objective Optimization}, journal = {Nature Computational Science}, arxiv = {http://arxiv.org/abs/2503.22797}, doi = {10.1038/s43588-025-00873-y}, pages = {1168 -- 1177}, year = {2025}, abstract = {The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. In this work, we use low-depth Quantum Approximate Optimization Algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with Matrix Product State numerical simulation, and show its potential to outperform classical approaches.}, language = {en} } @inproceedings{BortolettoLindner2025, author = {Bortoletto, Enrico and Lindner, Niels}, title = {Scaling and Rounding Periodic Event Scheduling Instances to Different Period Times}, booktitle = {Operations Research Proceedings 2023}, editor = {Voigt, Guido and Fliedner, Malte and Haase, Knut and Br{\"u}ggemann, Wolfgang and Hoberg, Kai and Meissner, J{\"o}rn}, doi = {10.1007/978-3-031-58405-3_51}, pages = {397 -- 402}, year = {2025}, abstract = {The Periodic Event Scheduling Problem (PESP) is a notoriously hard combinatorial optimization problem, essential for the design of periodic timetables in public transportation. The coefficients of the integer variables in the standard mixed integer linear programming formulations of PESP are the period time, e.g., 60 for a horizon of one hour with a resolution of one minute. In many application scenarios, lines with different frequencies have to be scheduled, leading to period times with many divisors. It then seems natural to consider derived instances, where the period time is a divisor of the original one, thereby smaller, and bounds are scaled and rounded accordingly. To this end, we identify two rounding schemes: wide and tight. We then discuss the approximation performance of both strategies, in theory and practice.}, language = {en} } @article{SikelerKempterSekulicetal.2025, author = {Sikeler, Christoph and Kempter, Susanne and Sekulic, Ivan and Burger, Sven and Liedl, Tim}, title = {Chiral Plasmonic Crystals Self-Assembled by DNA Origami}, volume = {129}, journal = {J. Phys. Chem. C}, number = {10}, doi = {10.1021/acs.jpcc.4c08768}, pages = {5116 -- 5121}, year = {2025}, language = {en} } @article{ZittelPetkovicEinck2025, author = {Zittel, Janina and Petkovic, Milena and Einck, Mathias}, title = {Forecasting Hourly Gas Flows}, volume = {79}, journal = {Foresight - The International Journal of Applied Forecasting}, pages = {40 -- 44}, year = {2025}, language = {en} } @article{WoodstockPokutta2025, author = {Woodstock, Zev and Pokutta, Sebastian}, title = {Splitting the conditional gradient algorithm}, volume = {35}, journal = {SIAM Journal on Optimization}, number = {1}, doi = {10.1137/24M1638008}, pages = {347 -- 368}, year = {2025}, language = {en} } @article{ShimadaMakoYaegashietal.2025, author = {Shimada, Naoki and Mako, Sato and Yaegashi, Yuta and Koch, Thorsten and Le, Thi Thai}, title = {An Application of Modified S-CLSVOF Method to Kelvin-Helmholtz Instability and Comparison with Theoretical Result}, volume = {58}, journal = {Journal of Chemical Engineering of Japan}, number = {1}, publisher = {Taylor and Francis}, doi = {10.1080/00219592.2025.2451953}, year = {2025}, abstract = {This study focuses on validating a two-phase flow solver based on the modified Simple Coupled Level Set and Volume of Fluid method (Uchihashi et al. (2023)) through viscous Kelvin-Helmholtz instability simulations. Our numerical simulation results are compared with the ones given by Funada and Joseph (2001) to provide reliable predictions of interface behavior under the influence of viscosity. The primary goal is to accurately assess the solver's ability to replicate theoretical analysis of interface behaviors under various conditions. First, the wave between two fluids of identical density is calculated. In addition, the effect of surface tension is investigated. By comparing growth rates, numerical simulations obtain well-agreements with the analytical results on the effect of the fluid viscosity, the wave number, and the surface tension. Finally, fluid density is changed to an air-water system. When relative velocity U is smaller than the criteria of relative velocity U_c given by analytical solutions, the wave is not broken. However, waves are splashed into droplets in the condition of U>U_c. This result agrees with the analysis by Funada and Joseph (2001). These findings provide a robust framework for applying the solver to more complex two-phase flow problems, supporting advancements in numerical simulations of fluid interfaces.}, language = {en} } @article{RongChenKochetal.2026, author = {Rong, Guoyang and Chen, Ying and Koch, Thorsten and Honda, Keisuke}, title = {Assessing data quality in citation analysis: A case study of web of science and Crossref}, volume = {20}, journal = {Journal of Informetrics}, number = {1}, publisher = {Elsevier BV}, issn = {1751-1577}, doi = {10.1016/j.joi.2026.101775}, year = {2026}, language = {en} } @inproceedings{EbertMasingLindneretal.2025, author = {Ebert, Patricia and Masing, Berenike and Lindner, Niels and Gleixner, Ambros}, title = {Sorting Criteria for Line-based Periodic Timetabling Heuristics}, booktitle = {Operations Research Proceedings 2024. OR 2024}, pages = {348 -- 354}, year = {2025}, abstract = {It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2\%.}, language = {en} } @misc{VanaretLeyffer2026, author = {Vanaret, Charlie and Leyffer, Sven}, title = {Implementing a unified solver for nonlinearly constrained optimization}, arxiv = {http://arxiv.org/abs/2406.13454}, year = {2026}, abstract = {SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno's software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at this https URL and via its C, Julia, Python, Fortran, and AMPL interfaces.}, language = {en} } @article{HalbigHoenGleixneretal.2025, author = {Halbig, Katrin and Hoen, Alexander and Gleixner, Ambros and Witzig, Jakob and Weninger, Dieter}, title = {A diving heuristic for mixed-integer problems with unbounded semi-continuous variables}, volume = {13}, journal = {EURO Journal on Computational Optimization}, doi = {10.1016/j.ejco.2025.100107}, year = {2025}, language = {en} } @article{BestuzhevaGleixnerAchterberg2025, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Achterberg, Tobias}, title = {Efficient separation of RLT cuts for implicit and explicit bilinear terms}, volume = {210}, journal = {Mathematical Programming}, doi = {10.1007/s10107-024-02104-0}, pages = {47 -- 74}, year = {2025}, language = {en} } @inproceedings{GhannamGleixner2025, author = {Ghannam, Mohammed and Gleixner, Ambros}, title = {Hybrid Genetic Search for Dynamic Vehicle Routing with Time Windows}, booktitle = {Operations Research Proceedings 2023. OR 2023}, doi = {10.1007/978-3-031-58405-3_35}, year = {2025}, language = {en} } @article{HoenKampGleixner2025, author = {Hoen, Alexander and Kamp, Dominik and Gleixner, Ambros}, title = {MIP-DD: Delta Debugging for Mixed-Integer Programming Solvers}, journal = {INFORMS Journal on Computing}, doi = {10.1287/ijoc.2024.0844}, year = {2025}, language = {en} } @article{MehrmannJohnyEbbinghausetal.2026, author = {Mehrmann, Carolin and Johny, Jacob and Ebbinghaus, Petra and Hammerschmidt, Martin and Das, Ankita and Wei, Xin and Tesch, Marc F. and Rabe, Martin}, title = {Nano IR spectroscopy on Silicon-Supported Organic-Inorganic Hybrid Materials}, journal = {Phys. Chem. Chem. Phys.}, publisher = {Royal Society of Chemistry (RSC)}, doi = {10.1039/D5CP03815D}, year = {2026}, language = {en} } @inproceedings{PedersenLindnerRehfeldtetal.2026, author = {Pedersen, Jaap and Lindner, Niels and Rehfeldt, Daniel and Koch, Thorsten}, title = {Comparing Branching Rules for the Quota Steiner Tree Problem with Interference}, booktitle = {Operations Research Proceedings 2025}, year = {2026}, abstract = {Branching decisions play a crucial role in branch-and-bound algorithms for solving combinatorial optimization problems. In this paper, we investigate several branching rules applied to the Quota Steiner Tree Problem with Interference (QSTPI). The Quota Steiner Tree Problem (QSTP) generalizes the classical Steiner Tree Problem (STP) in graphs by seeking a minimum-cost tree that connects a subset of profit-associated vertices whose cumulative profit meets or exceeds a given quota. The QSTPI introduces interference among vertices: Selecting certain vertices simultaneously reduces their individual contributions to the overall profit. This problem arises, for example, in positioning and connecting wind turbines, where turbines possibly shadow other turbines, reducing their energy yield. Unlike classical STP variants, large QSTPI instances require significantly more branching to compute provably optimal solutions. In contrast to branching on variables, we utilize the combinatorial structure of the QSTPI by branching on the graph's vertices. We adapt classical and problem-specific branching rules and present a comprehensive computational study comparing the effectiveness of these branching strategies.}, language = {en} } @inproceedings{FrankeHamacherManns2026, author = {Franke, Paula and Hamacher, Kay and Manns, Paul}, title = {Minimizing and Maximizing the Shannon Entropy for Fixed Marginals}, booktitle = {Operations Research Proceedings 2025}, year = {2026}, abstract = {The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distri- bution is the variable part under fixed marginals. We aim to minimize and maximize it to obtain the largest and smallest MI possible in this case, leading to a scaled MI ratio for better comparability. We present algorithmic approaches and optimal solutions for a set of problem instances based on data from molecular evolution. We show that this allows us to construct a sensible, systematic correction to raw MI values.}, language = {en} }