TY - CHAP A1 - Borndörfer, Ralf A1 - Schwartz, Stephan A1 - Surau, William T1 - Finding Minimum Balanced Separators - an Exact Approach T2 - Operations Research Proceedings 2021 N2 - Balanced separators are node sets that split the graph into size bounded components. They find applications in different theoretical and practical problems. In this paper we discuss how to find a minimum set of balanced separators in node weighted graphs. Our contribution is a new and exact algorithm that solves Minimum Balanced Separators by a sequence of Hitting Set problems. The only other exact method appears to be a mixed-integer program (MIP) for the edge weighted case. We adapt this model to node weighted graphs and compare it to our approach on a set of instances, resembling transit networks. It shows that our algorithm is far superior on almost all test instances. T3 - ZIB-Report - 21-25 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83138 SN - 1438-0064 SP - 154 EP - 159 ER - TY - GEN A1 - Pedersen, Jaap A1 - Hoppmann-Baum, Kai A1 - Zittel, Janina A1 - Koch, Thorsten T1 - Blending hydrogen into natural gas: An assessment of the capacity of the German gas grid; Technical Report N2 - In the transition towards a pure hydrogen infrastructure, utilizing the existing natural gas infrastructure is a necessity. In this study, the maximal technically feasible injection of hydrogen into the existing German natural gas transmission network is analysed with respect to regulatory limits regarding the gas quality. We propose a transient tracking model based on the general pooling problem including linepack. The analysis is conducted using real-world hourly gas flow data on a network of about 10,000 km length. T3 - ZIB-Report - 21-21 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82838 SN - 1438-0064 ER - TY - GEN A1 - Tateiwa, Nariaki A1 - Shinano, Yuji A1 - Yamamura, Keiichiro A1 - Yoshida, Akihiro A1 - Kaji, Shizuo A1 - Yasuda, Masaya A1 - Fujisawa, Katsuki T1 - CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems N2 - Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments. T3 - ZIB-Report - 21-16 KW - Discrete optimization KW - Lattice problem KW - Lattice-based cryptography KW - Shortest vector problem KW - Parallel algorithms KW - Ubiquity Generator Framework Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82802 SN - 1438-0064 N1 - Revised version is accepted to HiPC 2021 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian A1 - Masing, Berenike T1 - Forward Cycle Bases and Periodic Timetabling N2 - Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance \texttt{R1L1} of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds. T3 - ZIB-Report - 21-18 KW - Periodic Timetabling KW - Cycle Bases KW - Mixed Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82756 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Maristany de las Casas, Pedro A1 - Schiewe, Philine T1 - Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data N2 - We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport. T3 - ZIB-Report - 21-17 KW - Preprocessing Shortest Path Problems KW - Interval Data KW - Graph Algorithms Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82716 SN - 1438-0064 ER - TY - GEN A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics N2 - Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal. T3 - ZIB-Report - 21-15 KW - linear reaction networks KW - cross-correlation KW - neurotransmission Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82674 SN - 1438-0064 ER - TY - GEN A1 - Rusch, Beate A1 - Peters-Kottig, Wolfgang A1 - Boltze, Julia A1 - Brandtner, Andreas A1 - Degkwitz, Andreas A1 - Kirsch, Simona A1 - Koch, Thorsten A1 - Lohrum, Stefan A1 - Müller, Anja A1 - Mutter, Moritz A1 - Seeliger, Frank A1 - Stanek, Ursula T1 - KOBV Jahresbericht 2019-2020 N2 - Der aktuelle KOBV-Jahresbericht informiert darüber, was in den Mitgliedsbibliotheken und Partnerprojekten in den letzten beiden Jahren passiert ist und was sich in der Verbundzentrale und in der Bibliothekslandschaft ändert. Die Ausgabe 2019/2020 enthält den Schwerpunktteil »Digitalisierung« mit verschiedenen Perspektiven auf die digitale Arbeitswelt. T3 - KOBV-Jahresbericht - 2019-2020 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82474 SN - 1438-0064 CY - Berlin ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schwartz, Stephan A1 - Surau, William T1 - Vertex Covering with Capacitated Trees N2 - The covering of a graph with (possibly disjoint) connected subgraphs is a fundamental problem in graph theory. In this paper, we study a version to cover a graph's vertices by connected subgraphs subject to lower and upper weight bounds, and propose a column generation approach to dynamically generate feasible and promising subgraphs. Our focus is on the solution of the pricing problem which turns out to be a variant of the NP-hard Maximum Weight Connected Subgraph Problem. We compare different formulations to handle connectivity, and find that a single-commodity flow formulation performs best. This is notable since the respective literature seems to have dismissed this formulation. We improve it to a new coarse-to-fine flow formulation that is theoretically and computationally superior, especially for large instances with many vertices of degree 2 like highway networks, where it provides a speed-up factor of 10 over the non-flow-based formulations. We also propose a preprocessing method that exploits a median property of weight constrained subgraphs, a primal heuristic, and a local search heuristic. In an extensive computational study we evaluate the presented connectivity formulations on different classes of instances, and demonstrate the effectiveness of the proposed enhancements. Their speed-ups essentially multiply to an overall factor of 20. Overall, our approach allows the reliabe solution of instances with several hundreds of nodes in a few minutes. These findings are further corroborated in a comparison to existing districting models on a set of test instances from the literature. T3 - ZIB-Report - 21-14 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82616 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Denißen, Jonas A1 - Heller, Simon A1 - Klug, Torsten A1 - Küpper, Michael A1 - Lindner, Niels A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Söhlke, Andreas A1 - Steadman, William T1 - Microscopic Timetable Optimization for a Moving Block System N2 - 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. T3 - ZIB-Report - 21-13 KW - Moving Block KW - Railway Track Allocation KW - Railway Timetabling KW - Train Routing Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82547 SN - 1438-0064 ER - TY - THES A1 - Badel, Raphael T1 - Registration-based Tracking of Regions Defined by Level Sets of Time-dependent Scalar Fields N2 - This thesis is concerned with the wide field of feature tracking in time-dependent data. Many solutions already exist for the tracking of various features in scalar fields that are given as discrete time steps. In the field of meteorology, recently published precipitation data of the COSMO-REA2 reanalysis system gave rise to the analysis of precipitation at a convective scale for which a tracking of precipitation cells over time is desired. A previous study indicated that a tracking based on the widely used overlap criterion does not perform well for the reanalysis data. Based on a novel set of requirements, a new approach to the tracking of regions in time-dependent scalar fields is developed in the course of this thesis and applied in a prototypical study to example datasets of the COSMO-REA2 system. Despite the concrete motivation of using the developed method for subsequent studies of precipitation, the tracking approach is designed to be applicable for arbitrary scalar quantities that can conceptually be given on uniform grids of arbitrary dimensions. Based on a detailed description of the utilized methods, this thesis presents a novel tracking solution whose correspondence identification is based on image registration of successive time steps in combination with a hierarchical watershed segmentation by means of which features are extracted. The proposed implementation allows for an efficient generation of tracking results under the premise that the registration-based correspondence information has been precomputed. Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82264 ER - TY - GEN A1 - Schmitt, Carlo A1 - Wyrwoll, Lothar A1 - Moser, Albert A1 - Yueksel-Erguen, Inci T1 - Integration of Flexible Distributed Energy Resource Models into a Market Coupling-based Lagrangian Relaxation of the pan-European Electricity Market N2 - This report presents a method to integrate highly flexible technology models for distributed energy resources such as electric vehicles, power-to-heat systems, or home battery systems into a Lagrangian relaxation of the pan-European day-ahead electricity market (EULR). These flexible technology models are highly sensitive to the changes of Lagrangian multipliers within the iterative Lagrangian relaxation process, leading to volatile behavior. Furthermore, they show a high concurrency in their market behavior due to their technical homogeneity. Therefore, the method proposed in this report is an extension of the existing EULR modeling approach to improve the model's convergence. The methodological extension comprises a convex combination of iteration solutions for the Lagrangian relaxation subproblems similar to Dantzig-Wolfe decomposition. An exemplary case study shows the effectiveness of this extended approach. T3 - ZIB-Report - 21-11 KW - Electricity Market Simulation KW - Lagrangian Relaxation KW - Distributed Energy Resources Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82238 SN - 1438-0064 ER - TY - GEN A1 - Lenz, Ralf T1 - Pipe Merging for Transient Gas Network Problems N2 - In practice, transient gas transport problems frequently have to be solved for large-scale gas networks. Gas network optimization problems typically belong to the class of Mixed-Integer Nonlinear Programming Problems (MINLP). However current state-of-the-art MINLP solvers are not yet mature enough to solve large-scale real-world instances. Therefore, an established approach in practice is to solve the problems with respect to a coarser representation of the network and thereby reducing the size of the underlying model. Two well-known aggregation methods that effectively reduce the network size are parallel and serial pipe merges. However, these methods have only been studied in stationary gas transport problems so far. This paper closes this gap and presents parallel and serial pipe merging methods in the context of transient gas transport. To this end, we introduce the concept of equivalent and heuristic subnetwork replacements. For the heuristic methods, we conduct a huge empirical evaluation based on real-world data taken from one of the largest gas networks in Europe. It turns out that both, parallel and serial pipe merging can be considered as appropriate aggregation methods for real-world transient gas flow problems. T3 - ZIB-Report - 21-10 KW - Pipe merging KW - Network aggregation KW - Gas network optimization KW - Transient gas flow transport KW - Nonlinear Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82116 SN - 1438-0064 ER - TY - GEN A1 - Ambellan, Felix A1 - Zachow, Stefan A1 - von Tycowicz, Christoph T1 - Geodesic B-Score for Improved Assessment of Knee Osteoarthritis N2 - Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions. T3 - ZIB-Report - 21-09 KW - Statistical shape analysis KW - Osteoarthritis KW - Geometric statistics KW - Riemannian manifolds Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81930 SN - 1438-0064 ER - TY - GEN A1 - Hennings, Felix T1 - Large-scale empirical study on the momentum equation's inertia term N2 - A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations. An example is the inertia term of the momentum equation since it is said to be of negligible size under real-world operating conditions. However, this justification has always only been based on experience or single sets of artificial data points. This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network. Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km. We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes. On average, such an event occurs less often than once every ten days. Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems. T3 - ZIB-Report - 21-08 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81881 SN - 1438-0064 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Gleixner, Ambros A1 - Vigerske, Stefan T1 - A Computational Study of Perspective Cuts N2 - The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time. T3 - ZIB-Report - 21-07 KW - perspective cuts, mixed-integer nonlinear programming, nonconvex optimization, computational study Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81821 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Timetable Merging for the Periodic Event Scheduling Problem N2 - We propose a new mixed integer programming based heuristic for computing new benchmark primal solutions for instances of the PESPlib. The PESPlib is a collection of instances for the Periodic Event Scheduling Problem (PESP), comprising periodic timetabling problems inspired by real-world railway timetabling settings, and attracting several international research teams during the last years. We describe two strategies to merge a set of good periodic timetables. These make use of the instance structure and minimum weight cycle bases, finally leading to restricted mixed integer programming formulations with tighter variable bounds. Implementing this timetable merging approach in a concurrent solver, we improve the objective values of the best known solutions for the smallest and largest PESPlib instances by 1.7 and 4.3 percent, respectively. T3 - ZIB-Report - 21-06 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Railway Timetabling KW - PESPlib KW - Benchmark Solutions KW - Mixed Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81587 SN - 1438-0064 ER - TY - GEN A1 - Bertelmann, Roland A1 - Boltze, Julia A1 - Ceynowa, Klaus A1 - Christof, Jürgen A1 - Faensen, Katja A1 - Groß, Matthias A1 - Hoffmann, Cornelia A1 - Koch, Thorsten A1 - Kuberek, Monika A1 - Lohrum, Stefan A1 - Pampel, Heinz A1 - Putnings, Markus A1 - Retter, Regina A1 - Rusch, Beate A1 - Schäffler, Hildegard A1 - Söllner, Konstanze A1 - Steffen, Ronald A1 - Wannick, Eike T1 - DeepGreen: Open-Access-Transformation in der Informationsinfrastruktur – Anforderungen und Empfehlungen, Version 1.0 N2 - DeepGreen ist ein Service, der es teilnehmenden institutionellen Open-Access-Repositorien,Open-Access-Fachrepositorien und Forschungsinformationssystemen erleichtert, für sie relevante Verlagspublikationen in zyklischer Abfolge mithilfe von Schnittstellen Open Access zur Verfügung zu stellen. Die entsprechende Bandbreite an Relationen zwischen den Akteuren, diverse lizenzrechtliche Rahmenbedingungen sowie technische Anforderungen gestalten das Thema komplex. Ziel dieser Handreichung ist es, neben all diesen Themen, die begleitend beleuchtet werden, im Besonderen Empfehlungen für die reibungslose Nutzung der Datenübertragung zu liefern. Außerdem werden mithilfe einer vorangestellten Workflow- Evaluierung Unterschiede und Besonderheiten in den Arbeitsschritten bei institutionellen Open-Access-Repositorien und Open-Access-Fachrepositorien aufgezeigt und ebenfalls mit Empfehlungen angereichert. T3 - ZIB-Report - 21-03 KW - Open Access KW - Zweitveröffentlichung KW - Bibliotheken KW - Verlage Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81503 SN - 1438-0064 ER - TY - GEN A1 - Lenz, Ralf A1 - Serrano, Felipe T1 - Tight Convex Relaxations for the Expansion Planning Problem N2 - Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improve the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58%. T3 - ZIB-Report - 21-05 KW - Convex envelopes KW - Mixed-Integer Nonlinear Programming KW - Expansion planning of energy networks Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81459 SN - 1438-0064 ER - TY - GEN A1 - Fujii, Koichi A1 - Ito, Naoki A1 - Kim, Sunyoung A1 - Kojima, Masakazu A1 - Shinano, Yuji A1 - Toh, Kim-Chuan T1 - Solving Challenging Large Scale QAPs N2 - We report our progress on the project for solving larger scale quadratic assignment problems (QAPs). Our main approach to solve large scale NP-hard combinatorial optimization problems such as QAPs is a parallel branch-and-bound method efficiently implemented on a powerful computer system using the Ubiquity Generator(UG) framework that can utilize more than 100,000 cores. Lower bounding procedures incorporated in the branch-and-bound method play a crucial role in solving the problems. For a strong lower bounding procedure, we employ the Lagrangian doubly nonnegative (DNN) relaxation and the Newton-bracketing method developed by the authors’ group. In this report, we describe some basic tools used in the project including the lower bounding procedure and branching rules, and present some preliminary numerical results. Our next target problem is QAPs with dimension at least 50, as we have succeeded to solve tai30a and sko42 from QAPLIB for the first time. T3 - ZIB-Report - 21-02 KW - QAP KW - Parallel Branch-and-Bound Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81303 SN - 1438-0064 ER -