TY - JOUR A1 - Chen, Ying A1 - Koch, Thorsten A1 - Peng, Hanqui A1 - Zhang, Hongrui T1 - Benchmarking of Quantum and Classical Computing in Large-Scale Dynamic Portfolio Optimization Under Market Frictions Y1 - 2025 ER - TY - JOUR A1 - Chen, Ying A1 - Xu, Xiuqin A1 - Koch, Thorsten T1 - Day-ahead high-resolution forecasting of natural gas demand and supply in Germany with a hybrid model JF - Applied Energy N2 - As the natural gas market is moving towards short-term planning, accurate and robust short-term forecasts of the demand and supply of natural gas is of fundamental importance for a stable energy supply, a natural gas control schedule, and transport operation on a daily basis. We propose a hybrid forecast model, Functional AutoRegressive and Convolutional Neural Network model, based on state-of-the-art statistical modeling and artificial neural networks. We conduct short-term forecasting of the hourly natural gas flows of 92 distribution nodes in the German high-pressure gas pipeline network, showing that the proposed model provides nice and stable accuracy for different types of nodes. It outperforms all the alternative models, with an improved relative accuracy up to twofold for plant nodes and up to fourfold for municipal nodes. For the border nodes with rather flat gas flows, it has an accuracy that is comparable to the best performing alternative model. KW - Natural gas flow forecasting KW - Neural network KW - Hybrid model KW - Functional autoregressive Y1 - 2020 U6 - https://doi.org/https://doi.org/10.1016/j.apenergy.2019.114486 VL - 262 IS - 114486 ER - TY - JOUR A1 - Tjusila, Gennesaret A1 - Besançon, Mathieu A1 - Turner, Mark A1 - Koch, Thorsten T1 - How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem JF - Operations Research Letters N2 - It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest. Y1 - 2024 U6 - https://doi.org/10.1016/j.orl.2024.107105 VL - 54 SP - 107105 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017. T3 - ZIB-Report - 23-17 KW - cutting plane selection KW - variable selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91120 SN - 1438-0064 ER - TY - JOUR A1 - Le, Thi Thai A1 - Fukumoto, Yasuhide A1 - Koch, Thorsten T1 - Linear stability of a simple shear layer between two parallel streams in a shallow water flow JF - Physics Letters A N2 - The stability of shear layers in fluid flows is a crucial factor in forming vortices and jets and plays a fundamental role in the development of turbulence. Such shear layer instabilities are ubiquitous in natural phenomena, such as atmospheric and oceanic flows, contributing to the formation of weather systems and predicting tsunamis. This study specifically focuses on the stability of a shear layer sandwiched between two semi-infinite layers within a two-dimensional flow. The velocity profile of the shear layer is assumed to be linearly dependent on the vertical coordinate, while the velocity of the other layers remains uniform with differing strengths. The effect of viscosity and surface tension is ignored to simplify the analysis. The shallow water equations are used to analyze the interface stability of the shear layer, and the resulting dispersion relation between wave frequency and other wave characteristics is obtained. This relation incorporates Whittaker functions and their first derivatives and is used to derive appropriate limits corresponding to various physical conditions. Our study thus contributes to a deeper understanding of the stability of shear layers and their implications for natural phenomena. Y1 - 2024 U6 - https://doi.org/10.1016/j.physleta.2023.129264 VL - 493 PB - Elservier ER - TY - GEN A1 - Tjusila, Gennesaret A1 - Besancon, Mathieu A1 - Turner, Mark A1 - Koch, Thorsten T1 - How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem N2 - It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest. T3 - ZIB-Report - 23-15 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90902 ER - TY - GEN A1 - Prause, Felix A1 - Hoppmann-Baum, Kai A1 - Defourny, Boris A1 - Koch, Thorsten T1 - The Maximum Diversity Assortment Selection Problem N2 - In this paper, we introduce the Maximum Diversity Assortment Selection Problem (MADASS), which is a generalization of the 2-dimensional Cutting Stock Problem (2CSP). Given a set of rectangles and a rectangular container, the goal of 2CSP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. In MADASS, we need to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as minimum or average normalized Hamming-Distance of all assortment pairs. The MADASS Problem was used in the 11th AIMMS-MOPTA Competition in 2019. The methods we describe in this article and the computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2CSP literature. T3 - ZIB-Report - 20-34 KW - Combinatorial Optimization KW - Mixed Integer Programming KW - 2-dim Cutting Stock Problem KW - Maximum Diversity Problem Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81039 SN - 1438-0064 ER - TY - GEN A1 - Anderson, Lovis A1 - Turner, Mark A1 - Koch, Thorsten T1 - Generative deep learning for decision making in gas networks N2 - A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%. T3 - ZIB-Report - 20-38 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81103 SN - 1438-0064 ER - TY - GEN A1 - Petkovic, Milena A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Deep learning for spatio-temporal supply and demand forecasting in natural gas transmission networks N2 - Germany is the largest market for natural gas in the European Union, with an annual consumption of approx. 95 billion cubic meters. Germany's high-pressure gas pipeline network is roughly 40,000 km long, which enables highly fluctuating quantities of gas to be transported safely over long distances. Considering that similar amounts of gas are also transshipped through Germany to other EU states, it is clear that Germany's gas transport system is essential to the European energy supply. Since the average velocity of gas in a pipeline is only 25km/h, an adequate high-precision, high-frequency forecasting of supply and demand is crucial for efficient control and operation of such a transmission network. We propose a deep learning model based on spatio-temporal convolutional neural networks (DLST) to tackle the problem of gas flow forecasting in a complex high-pressure transmission network. Experiments show that our model effectively captures comprehensive spatio-temporal correlations through modeling gas networks and consistently outperforms state-of-the-art benchmarks on real-world data sets by at least 21$\%$. The results demonstrate that the proposed model can deal with complex nonlinear gas network flow forecasting with high accuracy and effectiveness. T3 - ZIB-Report - 21-01 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81221 SN - 1438-0064 ER - TY - JOUR A1 - Le, Thi Thai A1 - Koch, Thorsten T1 - Instability of a tangential discontinuity surface in a three-dimensional compressible medium JF - Physics of Fluids N2 - Compressible flows appear in many natural and technological processes, for instance, the flow of natural gases in a pipe system. Thus, a detailed study of the stability of tangential velocity discontinuity in compressible media is relevant and necessary. The first early investigation in two-dimensional (2D) media was given more than 70 years ago. In this article, we continue investigating the stability in three-dimensional (3D) media. The idealized statement of this problem in an infinite spatial space was studied by Syrovatskii in 1954. However, the omission of the absolute sign of cos θ with θ being the angle between vectors of velocity and wave number in a certain inequality produced the inaccurate conclusion that the flow is always unstable for entire values of the Mach number M. First, we revisit this case to arrive at the correct conclusion, namely that the discontinuity surface is stabilized for a large Mach number with a given value of the angle θ. Next, we introduce a real finite spatial system such that it is bounded by solid walls along the flow direction. We show that the discontinuity surface is stable if and only if the dispersion relation equation has only real roots, with a large value of the Mach number; otherwise, the surface is always unstable. In particular, we show that a smaller critical value of the Mach number is required to make the flow in a narrow channel stable. Y1 - 2021 U6 - https://doi.org/10.1063/5.0033753 VL - 33 IS - 1 SP - 016106 ER - TY - JOUR A1 - Hoppmann-Baum, Kai A1 - Hennings, Felix A1 - Zittel, Janina A1 - Gotzes, Uwe A1 - Spreckelsen, Eva-Maria A1 - Spreckelsen, Klaus A1 - Koch, Thorsten T1 - An Optimization Approach for the Transient Control of Hydrogen Transport Networks JF - Mathematical Methods of Operations Research Y1 - 2021 IS - Special Issue on Energy Networks ER - TY - GEN A1 - Hoppmann-Baum, Kai A1 - Mexi, Gioni A1 - Burdakov, Oleg A1 - Casselgren, Carl Johan A1 - Koch, Thorsten T1 - Length-Constrained Cycle Partition with an Application to UAV Routing N2 - In this article, we discuss the Length-Constrained Cycle Partition Problem (LCCP). Besides edge weights, the undirected graph in LCCP features an individual critical weight value for each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is a feasible solution if the length of each cycle is not greater than the critical weight of each of the vertices in the cycle. The goal is to find a feasible partition with the minimum number of cycles. In this article, we discuss theoretical properties, preprocessing techniques, and two mixed-integer programming models (MIP) for LCCP both inspired by formulations for the closely related Travelling Salesperson Problem (TSP). Further, we introduce conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a report on computational experiments conducted on (A)TSPLIB-based instances. As an example, we use a routing problem in which a fleet of uncrewed aerial vehicles (UAVs) patrols a set of areas. T3 - ZIB-Report - 20-30 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-80489 SN - 1438-0064 ER - TY - JOUR A1 - Koch, Thorsten A1 - Schmidt, Martin A1 - Hiller, Benjamin A1 - Pfetsch, Marc A1 - Geißler, Björn A1 - Henrion, René A1 - Joormann, Imke A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Römisch, Werner A1 - Schewe, Lars A1 - Schultz, Rüdiger T1 - Capacity Evaluation for Large-Scale Gas Networks JF - German Success Stories in Industrial Mathematics Y1 - 2020 SN - 978-3-030-81454-0 U6 - https://doi.org/10.1007/978-3-030-81455-7 VL - 35 SP - 23 EP - 28 ER - TY - JOUR A1 - Chen, Ying A1 - Zakiyeva, Nazgul A1 - Zhu, Bangzhu A1 - Koch, Thorsten T1 - Modeling and Forecasting the Dynamics of the Natural Gas Transmission Network in Germany with the Demand and Supply Balance Constraint JF - Applied Energy Y1 - 2020 U6 - https://doi.org/10.1016/j.apenergy.2020.115597 N1 - https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3646636 IS - 278 ER - TY - JOUR A1 - Koch, Thorsten A1 - Chen, Ying A1 - Lim, Kian Guan A1 - Xu, Xiaofei A1 - Zakiyeva, Nazgul T1 - A review study of functional autoregressive models with application to energy forecasting JF - WIREs Computational Statistics Y1 - 2020 U6 - https://doi.org/10.1002/wics.1525 N1 - https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=7693&context=lkcsb_research ER - TY - CHAP A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - An exact high performance solver for Steiner tree problems in graphs and related problems T2 - Modeling, Simulation and Optimization of Complex Processes HPSC 2018 Y1 - 2020 PB - Springer ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Implications, conflicts, and reductions for Steiner trees T3 - ZIB-Report - 20-28 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-80039 SN - 1438-0064 ER - TY - GEN A1 - Hoppmann-Baum, Kai A1 - Hennings, Felix A1 - Zittel, Janina A1 - Gotzes, Uwe A1 - Spreckelsen, Eva-Maria A1 - Spreckelsen, Klaus A1 - Koch, Thorsten T1 - From Natural Gas towards Hydrogen - A Feasibility Study on Current Transport Network Infrastructure and its Technical Control N2 - This study examines the usability of a real-world, large-scale natural gas transport infrastructure for hydrogen transport. We investigate whether a converted network can transport the amounts of hydrogen necessary to satisfy current energy demands. After introducing an optimization model for the robust transient control of hydrogen networks, we conduct computational experiments based on real-world demand scenarios. Using a representative network, we demonstrate that replacing each turbo compressor unit by four parallel hydrogen compressors, each of them comprising multiple serial compression stages, and imposing stricter rules regarding the balancing of in- and outflow suffices to realize transport in a majority of scenarios. However, due to the reduced linepack there is an increased need for technical and non-technical measures leading to a more dynamic network control. Furthermore, the amount of energy needed for compression increases by 364% on average. T3 - ZIB-Report - 20-27 KW - Hydrogen Transport KW - Hydrogen Infrastructure KW - Network Flows KW - Mixed Integer Programming KW - Energiewende Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-79901 SN - 1438-0064 ER - TY - JOUR A1 - Hoppmann-Baum, Kai A1 - Hennings, Felix A1 - Lenz, Ralf A1 - Gotzes, Uwe A1 - Heinecke, Nina A1 - Spreckelsen, Klaus A1 - Koch, Thorsten T1 - Optimal Operation of Transient Gas Transport Networks JF - Optimization and Engineering N2 - In this paper, we describe an algorithmic framework for the optimal operation of transient gas transport networks consisting of a hierarchical MILP formulation together with a sequential linear programming inspired post-processing routine. Its implementation is part of the KOMPASS decision support system, which is currently used in an industrial setting. Real-world gas transport networks are controlled by operating complex pipeline intersection areas, which comprise multiple compressor units, regulators, and valves. In the following, we introduce the concept of network stations to model them. Thereby, we represent the technical capabilities of a station by hand-tailored artificial arcs and add them to network. Furthermore, we choose from a predefined set of flow directions for each network station and time step, which determines where the gas enters and leaves the station. Additionally, we have to select a supported simple state, which consists of two subsets of artificial arcs: Arcs that must and arcs that cannot be used. The goal is to determine a stable control of the network satisfying all supplies and demands. The pipeline intersections, that are represented by the network stations, were initially built centuries ago. Subsequently, due to updates, changes, and extensions, they evolved into highly complex and involved topologies. To extract their basic properties and to model them using computer-readable and optimizable descriptions took several years of effort. To support the dispatchers in controlling the network, we need to compute a continuously updated list of recommended measures. Our motivation for the model presented here is to make fast decisions on important transient global control parameters, i.e., how to route the flow and where to compress the gas. Detailed continuous and discrete technical control measures realizing them, which take all hardware details into account, are determined in a subsequent step. In this paper, we present computational results from the KOMPASS project using detailed real-world data. Y1 - 2020 U6 - https://doi.org/10.1007/s11081-020-09584-x VL - 22 SP - 735 EP - 781 ER - TY - CHAP A1 - Hoppmann-Baum, Kai A1 - Mexi, Gioni A1 - Burdakov, Oleg A1 - Casselgren, Carl Johan A1 - Koch, Thorsten ED - Hebrard, Emmanuel ED - Musliu, Nysret T1 - Minimum Cycle Partition with Length Requirements T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research N2 - 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. Y1 - 2020 SN - 978-3-030-58941-7 U6 - https://doi.org/10.1007/978-3-030-58942-4_18 VL - 12296 SP - 273 EP - 282 PB - Springer International Publishing CY - Cham ER - TY - JOUR A1 - Prause, Felix A1 - Hoppmann-Baum, Kai A1 - Defourny, Boris A1 - Koch, Thorsten T1 - The maximum diversity assortment selection problem JF - Mathematical Methods of Operations Research N2 - In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. MDASP is to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as the minimum or average normalized Hamming distance of all assortment pairs. MDASP was the topic of the 11th AIMMS-MOPTA Competition in 2019. The methods described in this article and the resulting computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2D-KP literature. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1007/s00186-021-00740-2 VL - 93 SP - 521 EP - 554 PB - Mathematical Methods of Operations Research ER - TY - GEN A1 - Yueksel-Erguen, Inci A1 - Zittel, Janina A1 - Wang, Ying A1 - Hennings, Felix A1 - Koch, Thorsten T1 - Lessons learned from gas network data preprocessing N2 - The German high-pressure natural gas transport network consists of thousands of interconnected elements spread over more than 120,000 km of pipelines built during the last 100 years. During the last decade, we have spent many person-years to extract consistent data out of the available sources, both public and private. Based on two case studies, we present some of the challenges we encountered. Preparing consistent, high-quality data is surprisingly hard, and the effort necessary can hardly be overestimated. Thus, it is particularly important to decide which strategy regarding data curation to adopt. Which precision of the data is necessary? When is it more efficient to work with data that is just sufficiently correct on average? In the case studies we describe our experiences and the strategies we adopted to deal with the obstacles and to minimize future effort. Finally, we would like to emphasize that well-compiled data sets, publicly available for research purposes, provide the grounds for building innovative algorithmic solutions to the challenges of the future. T3 - ZIB-Report - 20-13 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78262 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Franz, Henriette A1 - Koch, Thorsten T1 - Optimal Connected Subgraphs: Formulations and Algorithms T3 - ZIB-Report - 20-23 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-79094 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores N2 - Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper, we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances. T3 - ZIB-Report - 20-16 KW - Mixed Integer Programming, Parallel processing, Node merging, Racing, ParaSCIP, Ubiquity Generator Framework, MIPLIB Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78393 SN - 1438-0064 ER - TY - BOOK A1 - Hadjidimitriou, Natalia Selini A1 - Frangioni, Antonio A1 - Lodi, Andrea A1 - Koch, Thorsten ED - Hadjidimitriou, Natalia Selini ED - Frangioni, Antonio ED - Lodi, Andrea ED - Koch, Thorsten T1 - Mathematical Optimization for Efficient and Robust Energy Networks Y1 - 2020 SN - 978-3-030-57441-3 U6 - https://doi.org/10.1007/978-3-030-57442-0 VL - 4 PB - Springer ER - TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in Presolving for Mixed Integer Programming N2 - Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice. T3 - ZIB-Report - 13-48 KW - mixed-integer programming KW - presolving KW - preprocessing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42530 SN - 1438-0064 ER - TY - GEN A1 - Clarner, Jan-Patrick A1 - Tawfik, Christine A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Network-induced Unit Commitment - A model class for investment and production portfolio planning for multi-energy systems N2 - In light of the energy transition production planning of future decarbonized energy systems lead to very large and complex optimization problems. A widely used modeling paradigm for modeling and solving such problems is mathematical programming. While there are various scientific energy system models and modeling tools, most of them do not provide the necessary level of detail or the modeling flexibility to be applicable for industrial usage. Industrial modeling tools, on the other hand, provide a high level of detail and modeling flexibility. However, those models often exhibit a size and complexity that restricts their scope to a time horizon of several months, severely complicating long-term planning. As a remedy, we propose a model class that is detailed enough for real-world usage but still compact enough for long-term planning. The model class is based on a generalized unit commitment problem on a network with investment decisions. The focus lies on the topological dependency of different energy production and transportation units. T3 - ZIB-Report - 22-16 KW - Multi-energy systems KW - Unit commitment KW - Investment planning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87607 SN - 1438-0064 ER - TY - GEN A1 - Pedersen, Jaap A1 - Le, Thi Thai A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Optimal discrete pipe sizing for tree-shaped CO2 networks N2 - While energy-intensive industries like the steel industry plan to switch to renewable energy sources, other industries, such as the cement industry, have to rely on carbon capture storage and utilization technologies to reduce the inevitable carbon dioxide (CO2) emissions of their production processes. In this context, we investigate the problem of finding optimal pipeline diameters from a discrete set of diameters for a tree-shaped network transporting captured CO2 from multiple sources to a single sink. The general problem of optimizing arc capacities in potential-based fluid networks is a challenging mixed-integer nonlinear program. Additionally, the behaviour of CO2 is highly sensitive and nonlinear regarding temperature and pressure changes. We propose an iterative algorithm splitting the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modelling including mixing effects, the Joule-Thomson effect, and heat exchange with the surrounding environment. We show the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Western Germany. T3 - ZIB-Report - 22-15 KW - CO2 Transport KW - Network Design KW - Pipeline Sizing Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87574 SN - 1438-0064 ER - TY - JOUR A1 - Le, Thi Thai A1 - Koch, Thorsten T1 - Viscosity and porosity effects on tangential-discontinuity surface stability in 3D Compressible Media JF - Physics of Fluids N2 - The stability of a flow in porous media relates to the velocity rate of injecting and withdrawing natural gases inside porous storage. We thus aim to analyze the stability of flows in porous media to accelerate the energy transition process. This research examines a flow model of a tangential--velocity discontinuity with porosity and viscosity changes in a three-dimensional (3D) compressible medium because of a co-existence of different gases in a storage. The fluids are assumed to move in a relative motion where the plane y=0 is a tangential-velocity discontinuity surface. We obtain that the critical value of the Mach number to stabilize a tangential discontinuity surface of flows via porous media is smaller than the one of flows in a plane. The critical value of the Mach number M to stabilize a discontinuity surface of the 3D flow is different by a factor |cosθ| compared to the two-dimensional (2D) flow. Here, θ is the angle between velocity and wavenumber vectors. Our results also show that the flow model with viscosity and porosity effects is stable faster than those without these terms. Our analysis is done for both infinite and finite flows. The effect of solid walls along the flow direction could suppress the instability, i.e., the tangential-discontinuity surface is stabilized faster Y1 - 2022 U6 - https://doi.org/10.1063/5.0095970 VL - 34 IS - 7 PB - AIP Publishing ER - TY - JOUR A1 - Chen, Ying A1 - Koch, Thorsten A1 - Zakiyeva, Nazgul A1 - Liu, Kailiang A1 - Xu, Zhitong A1 - Chen, Chun-houh A1 - Nakano, Junji A1 - Honda, Keisuke T1 - Article's Scientific Prestige: Measuring the Impact of Individual Articles in the Web of Science N2 - We performed a citation analysis on the Web of Science publications consisting of more than 63 million articles and 1.45 billion citations on 254 subjects from 1981 to 2020. We proposed the Article’s Scientific Prestige (ASP) metric and compared this metric to number of citations (#Cit) and journal grade in measuring the scientific impact of individual articles in the large-scale hierarchical and multi-disciplined citation network. In contrast to #Cit, ASP, that is computed based on the eigenvector centrality, considers both direct and indirect citations, and provides steady-state evaluation cross different disciplines. We found that ASP and #Cit are not aligned for most articles, with a growing mismatch amongst the less cited articles. While both metrics are reliable for evaluating the prestige of articles such as Nobel Prize winning articles, ASP tends to provide more persuasive rankings than #Cit when the articles are not highly cited. The journal grade, that is eventually determined by a few highly cited articles, is unable to properly reflect the scientific impact of individual articles. The number of references and coauthors are less relevant to scientific impact, but subjects do make a difference. T3 - ZIB-Report - 22-07 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86380 VL - 17 IS - 1 SP - 101379 ER - TY - GEN A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming N2 - Cut selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP. T3 - ZIB-Report - 22-04 KW - cut selection KW - mixed-integer linear programming KW - reinforcement learning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86055 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - Faster exact solution of sparse MaxCut and QUBO problems T3 - ZIB-Report - 22-02 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85715 SN - 1438-0064 ER - TY - JOUR A1 - Hoppmann-Baum, Kai A1 - Burdakov, Oleg A1 - Mexi, Gioni A1 - Casselgren, Carl Johan A1 - Koch, Thorsten T1 - Length-Constrained Cycle Partition with an Application to UAV Routing JF - Optimization Methods and Software N2 - This article discusses the Length-Constrained Cycle Partition Problem (LCCP), which constitutes a new generalization of the Travelling Salesperson Problem (TSP). Apart from nonnegative edge weights, the undirected graph in LCCP features a nonnegative critical length parameter for each vertex. A cycle partition, i.e., a vertex-disjoint cycle cover, is a feasible solution for LCCP if the length of each cycle is not greater than the critical length of each vertex contained in it. The goal is to find a feasible partition having a minimum number of cycles. Besides analyzing theoretical properties and developing preprocessing techniques, we propose an elaborate heuristic algorithm that produces solutions of good quality even for large-size instances. Moreover, we present two exact mixed-integer programming formulations (MIPs) for LCCP, which are inspired by well-known modeling approaches for TSP. Further, we introduce the concept of conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a discussion on computational experiments that we conducted using (A)TSPLIB-based problem instances. As a motivating example application, we describe a routing problem where a fleet of uncrewed aerial vehicles (UAVs) must patrol a given set of areas. Y1 - 2022 U6 - https://doi.org/10.1080/10556788.2022.2053972 ER - TY - JOUR A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming JF - Open Journal of Mathematical Optimization N2 - Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP. Y1 - 2023 U6 - https://doi.org/10.5802/ojmo.25 VL - 4 SP - 5 ER - TY - GEN A1 - Charousset-Brignol, Sandrine A1 - van Ackooij, Wim A1 - Oudjane, Nadia A1 - Daniel, Dominique A1 - Noceir, Slimane A1 - Haus, Utz-Uwe A1 - Lazzaro, Alfio A1 - Frangioni, Antonio A1 - Lobato, Rafael A1 - Ghezelsoflu, Ali A1 - Iardella, Niccolò A1 - Galli, Laura A1 - Gorgone, Enrico A1 - dell’Amico, Mauro A1 - Giannelos, Spyros A1 - Moreira, Alex A1 - Strbac, Goran A1 - Borozan, Stefan A1 - Falugi, Paula A1 - Pudjianto, Danny A1 - Wyrwoll, Lothar A1 - Schmitt, Carlo A1 - Franken, Marco A1 - Beulertz, Daniel A1 - Schwaeppe, Henrik A1 - Most, Dieter A1 - Yüksel-Ergün, Inci A1 - Zittel, Janina A1 - Koch, Thorsten T1 - Synergistic approach of multi-energy models for a European optimal energy system management tool T2 - The Project Repository Journal Y1 - 2021 VL - 9 SP - 113 EP - 116 ER - TY - JOUR A1 - Dell’Amico, M. A1 - Hadjidimitriou, Natalia Selini A1 - Koch, Thorsten A1 - Petkovic, Milena T1 - Forecasting Natural Gas Flows in Large Networks JF - Machine Learning, Optimization, and Big Data. MOD 2017. N2 - Natural gas is the cleanest fossil fuel since it emits the lowest amount of other remains after being burned. Over the years, natural gas usage has increased significantly. Accurate forecasting is crucial for maintaining gas supplies, transportation and network stability. This paper presents two methodologies to identify the optimal configuration o parameters of a Neural Network (NN) to forecast the next 24 h of gas flow for each node of a large gas network. In particular the first one applies a Design Of Experiments (DOE) to obtain a quick initial solution. An orthogonal design, consisting of 18 experiments selected among a total of 4.374 combinations of seven parameters (training algorithm, transfer function, regularization, learning rate, lags, and epochs), is used. The best result is selected as initial solution of an extended experiment for which the Simulated Annealing is run to find the optimal design among 89.100 possible combinations of parameters. The second technique is based on the application of Genetic Algorithm for the selection of the optimal parameters of a recurrent neural network for time series forecast. GA was applied with binary representation of potential solutions, where subsets of bits in the bit string represent different values for several parameters of the recurrent neural network. We tested these methods on three municipal nodes, using one year and half of hourly gas flow to train the network and 60 days for testing. Our results clearly show that the presented methodologies bring promising results in terms of optimal configuration of parameters and forecast error. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1007/978-3-319-72926-8_14 VL - Lecture Notes in Computer Science IS - vol 10710 SP - 158 EP - 171 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem JF - SIAM Journal on Optimization N2 - Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced. Y1 - 2019 U6 - https://doi.org/10.1137/17M1145963 VL - 29 IS - 1 SP - 369 EP - 398 PB - Society for Industrial and Applied Mathematics ER - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten ED - Hamadi, Youssef T1 - Parallel Solvers for Mixed Integer Linear Optimization T2 - Handbook of Parallel Constraint Reasoning Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-63516-3_8 SP - 283 EP - 336 PB - Springer Nature ER - TY - CHAP A1 - Breuer, Thomas A1 - Bussieck, Michael A1 - Cao, Karl-Kien A1 - Cebulla, Felix A1 - Fiand, Frederik A1 - Gils, Hans Christian A1 - Gleixner, Ambros A1 - Khabi, Dmitry A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Wetzel, Manuel T1 - Optimizing Large-Scale Linear Energy System Problems with Block Diagonal Structure by Using Parallel Interior-Point Methods T2 - Operations Research Proceedings 2017 N2 - Current linear energy system models (ESM) acquiring to provide sufficient detail and reliability frequently bring along problems of both high intricacy and increasing scale. Unfortunately, the size and complexity of these problems often prove to be intractable even for commercial state-of-the-art linear programming solvers. This article describes an interdisciplinary approach to exploit the intrinsic structure of these large-scale linear problems to be able to solve them on massively parallel high-performance computers. A key aspect are extensions to the parallel interior-point solver PIPS-IPM originally developed for stochastic optimization problems. Furthermore, a newly developed GAMS interface to the solver as well as some GAMS language extensions to model block-structured problems will be described. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_85 SP - 641 EP - 647 PB - Springer International Publishing ER - TY - CHAP A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - SCIP-Jack—a solver for STP and variants with parallelization extensions: An update T2 - Operations Research Proceedings 2017 N2 - The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. Although the different Steiner tree problem variants are usually strongly related, solution approaches employed so far have been prevalently problem-specific. Against this backdrop, the solver SCIP-Jack was created as a general-purpose framework that can be used to solve the classical Steiner tree problem and 11 of its variants. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. Furthermore, SCIP-Jack includes various newly developed algorithmic components such as preprocessing routines and heuristics. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. After the introduction of SCIP-Jack at the 2014 DIMACS Challenge on Steiner problems, the overall performance of the solver has considerably improved. This article provides an overview on the current state. Y1 - 2018 SP - 191 EP - 196 ER - TY - GEN A1 - Gleixner, Ambros A1 - Bastubbe, Michael A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Schubert, Christoph A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Walter, Matthias A1 - Wegscheider, Fabian A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 6.0 N2 - 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 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders’ decomposition in a generic framework. GCG’s detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders’ framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 18-26 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69361 SN - 1438-0064 ER - TY - GEN A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Voß, Stefan T1 - SteinLib: An Updated Library on Steiner Tree Problems in Graphs N2 - In this paper we present the {\em SteinLib}, a library of data sets for the Steiner tree problem in graphs. This library extends former libraries on Steiner tree problems by many new interesting and difficult instances, most of them arising from real-world applications. We give a survey on the difficulty of these problem instances by giving references to state-of-the-art software packages that were the first or are currently among the best to solve these instances. T3 - ZIB-Report - 00-37 KW - Steiner Trees KW - Mathematical Programming Testdata Library Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6056 ER - TY - GEN A1 - Bley, Andreas A1 - Koch, Thorsten T1 - Integer programming approaches to access and backbone IP-network planning N2 - In this article we study the problem of designing a nation-wide communication network. Such networks usually consist of an access layer, a backbone layer, and maybe several intermediate layers. The nodes of each layer must be connected to those of the next layer in a tree-like fashion. The backbone layer has to satisfy certain survivability and routing constraints. Given the node locations, the demands between them, the possible connections and hardware configurations, and various other technical and administrational constraints, the goal is to decide, which node is assigned to which network level, how the nodes are connected, what hardware must be installed, and how traffic is routed in the backbone. Mixed integer linear programming models and solution methods are presented for both the access and the backbone network design problem. The focus is on the design of IP-over-SDH networks, but the access network design model and large parts of the backbone network design models are general and also applicable for other types of communication networks. Results obtained with these methods in the planning of the German research network are presented. T3 - ZIB-Report - 02-41 KW - Network design KW - Traffic enineering KW - Internet routing KW - Mixed-integer programming Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7081 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Koch, Thorsten A1 - Koster, Arie M.C.A. A1 - Martin, Alexander A1 - Pfender, Tobias A1 - Wegel, Oliver A1 - Wessäly, Roland T1 - Modelling Feasible Network Configurations for UMTS N2 - A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations. T3 - ZIB-Report - 02-16 KW - UMTS KW - radio interface KW - network planning KW - configuration KW - perfect power control KW - mathematical model KW - mixed integer programming KW - MOMENTUM KW - IST-20 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6837 ER - TY - GEN A1 - Koch, Thorsten T1 - The final NETLIB-LP results N2 - The NETLIB has now served for 18 years as a repository of LP problem instances. From the beginning to the present day there was some uncertainness about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the \emph{exact} optimal objective values for all NETLIB problems. T3 - ZIB-Report - 03-05 KW - Linear Programming KW - Simplex KW - Netlib KW - rational arithmetic Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7274 ER - TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Branching on History Information N2 - Mixed integer programs ($MIPs$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in $SIP$, a state-of-the-art $MIP$ solver. We give computational results that show the superiority of the new strategy. T3 - ZIB-Report - 02-32 KW - Mixed Integer Programming KW - Branch-and-Bound KW - Branching Rules KW - Pseudocost Branching Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6990 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Geerdes, Hans-Florian A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Optimization Methods for UMTS Radio Network Planning N2 - The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results. T3 - ZIB-Report - 03-41 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7637 ER - TY - THES A1 - Koch, Thorsten T1 - Rapid Mathematical Programming N2 - The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances. T3 - ZIB-Report - 04-58 KW - Modelling Languages KW - Mixed Integer Programming KW - Steiner Tree Packing in Graphs KW - Location Planning in Telecommunications KW - UMTS Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8346 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Geerdes, Hans-Florian A1 - Koch, Thorsten A1 - Türke, Ulrich T1 - MOMENTUM Data Scenarios for Radio Network Planning and Simulation (Extended Abstract) N2 - We present publicly available data sets related to research on wireless networks. The scenarios contain a wide range of data and are detailed in all aspects. To our knowledge, this is the most realistic, comprehensive, and detailed \emph{public} data collection on mobile networking. We indicate example uses of this data collection in applications related tu UMTS. T3 - ZIB-Report - 04-07 KW - Radio Network Planning KW - Simulation KW - UMTS KW - Realistic Data KW - XML Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7829 ER - TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Branching rules revisited N2 - Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy. T3 - ZIB-Report - 04-13 KW - Mixed-integer-programming KW - Branch-and-Bound KW - Variable selection KW - Pseudocost-Branching KW - Strong-Branching KW - Reliability-Branching Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7886 ER -