@incollection{AmbellanLameckervonTycowiczetal.2019, author = {Ambellan, Felix and Lamecker, Hans and von Tycowicz, Christoph and Zachow, Stefan}, title = {Statistical Shape Models - Understanding and Mastering Variation in Anatomy}, volume = {3}, booktitle = {Biomedical Visualisation}, number = {1156}, editor = {Rea, Paul M.}, edition = {1}, publisher = {Springer Nature Switzerland AG}, isbn = {978-3-030-19384-3}, doi = {10.1007/978-3-030-19385-0_5}, pages = {67 -- 84}, year = {2019}, abstract = {In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring.}, language = {en} } @incollection{GotzesBuchholzKallrathetal.2025, author = {Gotzes, Uwe and Buchholz, Annika and Kallrath, Josef and Lindner, Niels and Koch, Thorsten}, title = {Flexible Pooling Pattern Design with Integer Programming}, volume = {226}, booktitle = {Theory, Algorithms and Experiments in Applied Optimization. In Honor of the 70th Birthday of Panos Pardalos}, publisher = {Springer}, year = {2025}, abstract = {Sample pooling has the potential to significantly enhance large-scale screening procedures, especially in scenarios like the COVID-19 pandemic, where rapid and widespread PCR testing has been crucial. Efficient strategies are essential to increase the testing capacity, i.e., the number of tests that can be processed within a given timeframe. Non-adaptive pooling strategies can further streamline the testing process by reducing the required testing rounds. In contrast to adaptive strategies, where subsequent tests depend on prior results, non-adaptive pooling processes all samples in a single round, eliminating the need for sequential retesting and reducing delays. This paper presents a highly flexible method based on integer programming to design optimized pooling patterns suitable for various applications, including medical diagnostics and quality control in industrial production. Using coronavirus testing as a case study, we formulate and solve optimization and satisfiability models that compute efficient pool designs. Our optimized pooling does not only increase testing capacity, but also accelerates the testing process and reduces overall costs. The proposed method is adaptable and can be seamlessly integrated into automated testing systems.}, language = {en} } @incollection{DiekerhofMontiLebedevaetal.2020, author = {Diekerhof, M. and Monti, A. and Lebedeva, E. and Tkaczyk, A. H. and Y{\"u}ksel-Erg{\"u}n, I. and Zittel, J. and Escudero, L. F. and Soroudi, A. and Helmberg, C. and Kanov{\´i}c, Ž. and Petkovic, M. and Lacalandra, F. and Frangioni, A. and Lee, J. and De Filippo, A. and Lombardi, M. and Milano, M. and Ezran, P. and Haddad, Y.}, title = {Production and Demand Management}, volume = {4}, booktitle = {Mathematical Optimization for Efficient and Robust Energy Networks}, publisher = {Springer}, isbn = {978-3-030-57442-0}, doi = {https://doi.org/10.1007/978-3-030-57442-0_1}, year = {2020}, abstract = {Demand Side Management (DSM) is usually considered as a process of energy consumption shifting from peak hours to off-peak times. DSM does not always reduce total energy consumption, but it helps to meet energy demand and supply. For example, it balances variable generation from renewables (such as solar and wind) when energy demand differs from renewable generation.}, language = {en} } @incollection{SchwarzLacalandraScheweetal.2020, author = {Schwarz, R. and Lacalandra, F. and Schewe, L. and Bettinelli, A. and Vigo, D. and Bischi, A. and Parriani, T. and Martelli, E. and Vuik, K. and Lenz, R. and Madsen, H. and Blanco, I. and Guericke, D. and Y{\"u}ksel-Erg{\"u}n, I. and Zittel, J.}, title = {Network and Storage}, volume = {4}, booktitle = {Mathematical Optimization for Efficient and Robust Energy Networks}, publisher = {Springer}, isbn = {978-3-030-57442-0}, doi = {https://doi.org/10.1007/978-3-030-57442-0_6}, year = {2020}, abstract = {Natural gas is considered by many to be the most important energy source for the future. The objectives of energy commodities strategic problems can be mainly related to natural gas and deal with the definition of the "optimal" gas pipelines design which includes a number of related sub problems such as: Gas stations (compression) location and Gas storage locations, as well as compression station design and optimal operation.}, language = {en} } @incollection{PedersenLjubić2024, author = {Pedersen, Jaap and Ljubić, Ivana}, title = {Prize-Collecting Steiner Tree Problem and its Variants}, booktitle = {Encyclopedia of Optimization}, editor = {Pardalos, Panos M. and Prokopyev, Oleg A.}, publisher = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-030-54621-2_869-1}, year = {2024}, language = {en} } @incollection{HoppmannBaumMexiBurdakovetal.2020, author = {Hoppmann-Baum, Kai and Mexi, Gioni and Burdakov, Oleg and Casselgren, Carl Johan and Koch, Thorsten}, title = {Minimum Cycle Partition with Length Requirements}, volume = {12296}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, editor = {Hebrard, Emmanuel and Musliu, Nysret}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-58941-7}, doi = {10.1007/978-3-030-58942-4_18}, pages = {273 -- 282}, year = {2020}, abstract = {In this article we introduce a Minimum Cycle Partition Problem with Length Requirements (CPLR). This generalization of the Travelling Salesman Problem (TSP) originates from routing Unmanned Aerial Vehicles (UAVs). Apart from nonnegative edge weights, CPLR has an individual critical weight value associated with each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is regarded as a feasible solution if the length of each cycle, which is the sum of the weights of its edges, is not greater than the critical weight of each of its vertices. The goal is to find a feasible partition, which minimizes the number of cycles. In this article, a heuristic algorithm is presented together with a Mixed Integer Programming (MIP) formulation of CPLR. We furthermore introduce a conflict graph, whose cliques yield valid constraints for the MIP model. Finally, we report on computational experiments conducted on TSPLIB-based test instances.}, language = {en} } @incollection{BennerGrundelHimpeetal.2019, author = {Benner, Peter and Grundel, Sara and Himpe, Christian and Huck, Christoph and Streubel, Tom and Tischendorf, Caren}, title = {Gas Network Benchmark Models}, booktitle = {Applications of Differential-Algebraic Equations: Examples and Benchmarks}, publisher = {Springer International Publishing}, isbn = {978-3-030-03718-5}, doi = {10.1007/11221_2018_5}, pages = {171 -- 197}, year = {2019}, abstract = {The simulation of gas transportation networks becomes increasingly more important as its use-cases broaden to more complex applications. Classically, the purpose of the gas network was the transportation of predominantly natural gas from a supplier to the consumer for long-term scheduled volumes. With the rise of renewable energy sources, gas-fired power plants are often chosen to compensate for the fluctuating nature of the renewables, due to their on-demand power generation capability. Such an only short-term plannable supply and demand setting requires sophisticated simulations of the gas network prior to the dispatch to ensure the supply of all customers for a range of possible scenarios and to prevent damages to the gas network. In this work we describe the modeling of gas networks and present benchmark systems to test implementations and compare new or extended models.}, language = {en} } @incollection{GamrathBertholdHeinzetal.2015, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-Based Primal Heuristics for Mixed Integer Programming}, volume = {13}, booktitle = {Optimization in the Real World}, publisher = {Springer Japan}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_3}, pages = {37 -- 53}, 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} } @incollection{LameckerZachow2016, author = {Lamecker, Hans and Zachow, Stefan}, title = {Statistical Shape Modeling of Musculoskeletal Structures and Its Applications}, volume = {23}, booktitle = {Computational Radiology for Orthopaedic Interventions}, publisher = {Springer}, isbn = {978-3-319-23481-6}, doi = {10.1007/978-3-319-23482-3}, pages = {1 -- 23}, year = {2016}, abstract = {Statistical shape models (SSM) describe the shape variability contained in a given population. They are able to describe large populations of complex shapes with few degrees of freedom. This makes them a useful tool for a variety of tasks that arise in computer-aided madicine. In this chapter we are going to explain the basic methodology of SSMs and present a variety of examples, where SSMs have been successfully applied.}, language = {en} } @incollection{AnteghiniMartinsDosSantos2023, author = {Anteghini, Marco and Martins Dos Santos, Vitor}, title = {Computational Approaches for Peroxisomal Protein Localization}, volume = {2643}, booktitle = {Peroxisomes}, publisher = {Humana, New York}, isbn = {978-1-0716-3047-1}, doi = {10.1007/978-1-0716-3048-8_29}, pages = {405 -- 411}, year = {2023}, abstract = {Computational approaches are practical when investigating putative peroxisomal proteins and for sub-peroxisomal protein localization in unknown protein sequences. Nowadays, advancements in computational methods and Machine Learning (ML) can be used to hasten the discovery of novel peroxisomal proteins and can be combined with more established computational methodologies. Here, we explain and list some of the most used tools and methodologies for novel peroxisomal protein detection and localization.}, language = {de} } @incollection{YokoyamaShinano2015, author = {Yokoyama, Ryohei and Shinano, Yuji}, title = {MILP Approaches to Optimal Design and Operation of Distributed Energy Systems}, volume = {Volume 13}, booktitle = {Optimization in the Real World}, publisher = {Springer}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_9}, pages = {157 -- 176}, year = {2015}, abstract = {Energy field is one of the practical areas to which optimization can contribute significantly. In this chapter, the application of mixed-integer linear programming (MILP) approaches to optimal design and operation of distributed energy systems is described. First, the optimal design and operation problems are defined, and relevant previous work is reviewed. Then, an MILP method utilizing the hierarchical relationship between design and operation variables is presented. In the optimal design problem, integer variables are used to express the types, capacities, numbers, operation modes, and on/off states 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. The presented method can change the enumeration tree for the branching and bounding procedures, and can search the optimal solution very efficiently. Finally, future work in relation to this method is described.}, language = {en} } @incollection{KochPfetschRoevekamp2015, author = {Koch, Thorsten and Pfetsch, Marc and R{\"o}vekamp, Jessica}, title = {Introduction}, booktitle = {Evaluating Gas Network Capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {9781611973686}, pages = {3 -- 16}, year = {2015}, language = {en} } @incollection{WuMaher2017, author = {Wu, Cheng-Lung and Maher, Stephen J.}, title = {Airline scheduling and disruption management}, booktitle = {L. Budd, S. Ison, eds., Air transportation management: an international perspective}, publisher = {Routledge}, address = {New York}, isbn = {9781472451064}, pages = {151 -- 167}, year = {2017}, language = {en} } @incollection{ReutherSchlechte2018, author = {Reuther, Markus and Schlechte, Thomas}, title = {Optimization of Rolling Stock Rotations}, volume = {268}, booktitle = {Handbook of Optimization in the Railway Industry}, publisher = {Springer International Publishing}, isbn = {978-3-319-72152-1}, doi = {https://doi.org/10.1007/978-3-319-72153-8}, pages = {213 -- 241}, year = {2018}, abstract = {This chapter shows a successful approach how to model and optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical optimization problem is described in detail and solved by RotOR, i.e., a complex optimization algorithm based on linear programming and combinatorial methods. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. We focus on main modeling and solving components, i.e. a hypergraph model and a coarse-to-fine column generation approach. Finally, the chapter concludes with a complex industrial re-optimization application showing the effectiveness of the approach for real world challenges.}, language = {en} } @incollection{Klug2018, author = {Klug, Torsten}, title = {Freight Train Routing}, volume = {268}, booktitle = {Handbook of Optimization in the Railway Industry}, publisher = {Springer International Publishing}, isbn = {978-3-319-72152-1}, doi = {10.1007/978-3-319-72153-8}, pages = {73 -- 92}, year = {2018}, abstract = {This chapter is about strategic routing of freight trains in railway transportation networks with mixed traffic. A good utilization of a railway transportation network is important since in contrast to road and air traffic the routing through railway networks is more challenging and the extension of capacities is expensive and a long-term projects. Therefore, an optimized routing of freight trains have a great potential to exploit remaining capacity since the routing has fewer restrictions compared to passenger trains. In this chapter we describe the freight train routing problem in full detail and present a mixed-integer formulation. Wo focus on a strategic level that take into account the actual immutable passenger traffic. We conclude the chapter with a case study for the German railway network.}, language = {en} } @incollection{HaynHumpolaKochetal.2015, author = {Hayn, Christine and Humpola, Jesco and Koch, Thorsten and Schewe, Lars and Schweiger, Jonas and Spreckelsen, Klaus}, title = {Perspectives}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, year = {2015}, abstract = {After we discussed approaches to validate nominations and to verify bookings, we consider possible future research paths. This includes determining technical capacities and planning of network extensions.}, language = {en} } @incollection{BargmannEbbersHeineckeetal.2015, author = {Bargmann, Dagmar and Ebbers, Mirko and Heinecke, Nina and Koch, Thorsten and K{\"u}hl, Veronika and Pelzer, Antje and Pfetsch, Marc and R{\"o}vekamp, Jessica and Spreckelsen, Klaus}, title = {State-of-the-art in evaluating gas network capacities}, booktitle = {Evaluating Gas Network Capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {9781611973686}, pages = {65 -- 84}, year = {2015}, language = {en} } @incollection{ScheweKochMartinetal.2015, author = {Schewe, Lars and Koch, Thorsten and Martin, Alexander and Pfetsch, Marc}, title = {Mathematical optimization for evaluating gas network capacities}, booktitle = {Evaluating Gas Network Capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {9781611973686}, pages = {87 -- 102}, year = {2015}, language = {en} } @incollection{HillerHumpolaLehmannetal.2015, author = {Hiller, Benjamin and Humpola, Jesco and Lehmann, Thomas and Lenz, Ralf and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Willert, Bernhard}, title = {Computational results for validation of nominations}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, year = {2015}, abstract = {The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances.}, language = {en} } @incollection{HumpolaFuegenschuhHilleretal.2015, author = {Humpola, Jesco and F{\"u}genschuh, Armin and Hiller, Benjamin and Koch, Thorsten and Lehmann, Thomas and Lenz, Ralf and Schwarz, Robert and Schweiger, Jonas}, title = {The Specialized MINLP Approach}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, year = {2015}, abstract = {We propose an approach to solve the validation of nominations problem using mixed-integer nonlinear programming (MINLP) methods. Our approach handles both the discrete settings and the nonlinear aspects of gas physics. Our main contribution is an innovative coupling of mixed-integer (linear) programming (MILP) methods with nonlinear programming (NLP) that exploits the special structure of a suitable approximation of gas physics, resulting in a global optimization method for this type of problem.}, language = {en} } @incollection{GotzesHeineckeHilleretal.2015, author = {Gotzes, Uwe and Heinecke, Nina and Hiller, Benjamin and R{\"o}vekamp, Jessica and Koch, Thorsten}, title = {Regulatory rules for gas markets in Germany and other European countries}, booktitle = {Evaluating gas network capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {978-1-611973-68-6}, pages = {45 -- 64}, year = {2015}, language = {en} } @incollection{CaimiFischerSchlechte2018, author = {Caimi, Gabrio and Fischer, Frank and Schlechte, Thomas}, title = {Railway Track Allocation}, volume = {268}, booktitle = {Handbook of Optimization in the Railway Industry}, publisher = {Springer International Publishing}, isbn = {978-3-319-72152-1}, doi = {https://doi.org/10.1007/978-3-319-72153-8}, pages = {141 -- 160}, year = {2018}, abstract = {This chapter addresses the classical task to decide which train runs on which track in a railway network. In this context a track allocation defines the precise routing of trains through a railway network, which usually has only a limited capacity. Moreover, the departure and arrival times at the visited stations of each train must simultaneously meet several operational and safety requirements. The problem to find the 'best possible' allocation for all trains is called the track allocation problem (TTP). Railway systems can be modeled on a very detailed scale covering the behavior of individual trains and the safety system to a large extent. However, those microscopic models are too big and not scalable to large networks, which make them inappropriate for mathematical optimization on a network wide level. Hence, most network optimization approaches consider simplified, so called macroscopic, models. In the first part we take a look at the challenge to construct a reliable and condensed macroscopic model for the associated microscopic model and to facilitate the transition between both models of different scale. In the main part we focus on the optimization problem for macroscopic models of the railway system. Based on classical graph-theoretical tools the track allocation problem is formulated to determine conflict-free paths in corresponding time-expanded graphs. We present standard integer programming model formulations for the track allocation problem that model resource or block conflicts in terms of packing constraints. In addition, we discuss the role of maximal clique inequalities and the concept of configuration networks. We will also present classical decomposition approaches like Lagrangian relaxation and bundle methods. Furthermore, we will discuss recently developed techniques, e.g., dynamic graph generation. Finally, we will discuss the status quo and show a vision of mathematical optimization to support real world track allocation, i.e. integrated train routing and scheduling, in a data-dominated and digitized railway future.}, 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} }