TY - GEN A1 - Hosoda, Junko A1 - Maher, Stephen J. A1 - Shinano, Yuji A1 - Villumsen, Jonas Christoffer T1 - A parallel branch-and-bound heuristic for the integrated long-haul and local vehicle routing problem on an adaptive transportation network N2 - Consolidation of commodities and coordination of vehicle routes are fundamental features of supply chain management problems. While locations for consolidation and coordination are typically known a priori, in adaptive transportation networks this is not the case. The identification of such consolidation locations forms part of the decision making process. Supply chain management problems integrating the designation of consolidation locations with the coordination of long haul and local vehicle routing is not only challenging to solve, but also very difficult to formulate mathematically. In this paper, the first mathematical model integrating location clustering with long haul and local vehicle routing is proposed. This mathematical formulation is used to develop algorithms to find high quality solutions. A novel parallel framework is developed that combines exact and heuristic methods to improve the search for high quality solutions and provide valid bounds. The results demonstrate that using exact methods to guide heuristic search is an effective approach to find high quality solutions for difficult supply chain management problems. T3 - ZIB-Report - 23-02 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89700 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Ebert, Patricia T1 - Forward and Line-Based Cycle Bases for Periodic Timetabling N2 - The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks, and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances. T3 - ZIB-Report - 23-05 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89731 SN - 1438-0064 ER - TY - GEN A1 - Fujii, Koichi A1 - Kim, Sunyoung A1 - Kojima, Masakazu A1 - Mittelmann, Hans D. A1 - Shinano, Yuji T1 - An Exceptionally Difficult Binary Quadratic Optimization Problem with Symmetry: a Challenge for The Largest Unsolved QAP Instance Tai256c N2 - Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB. It is known that QAP tai256c can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92. As the BQOP is much simpler than the original QAP, the conversion increases the possibility to solve the QAP. Solving exactly the BQOP, however, is still very difficult. Indeed, a 1.48% gap remains between the best known upper bound (UB) and lower bound (LB) of the unknown optimal value. This paper shows that the BQOP admits a nontrivial symmetry, a property that makes the BQOP very hard to solve. The symmetry induces equivalent subproblems in branch and bound (BB) methods. To effectively improve the LB, we propose an efficient BB method that incorporates a doubly nonnegative relaxation, the standard orbit branching and a technique to prune equivalent subproblems. With this BB method, a new LB with 1.25% gap is successfully obtained, and computing an LB with 1.0% gap is shown to be still quite difficult. T3 - ZIB-Report - 23-27 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93072 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 - 大規模二次割当問題への挑戦 T2 - 統計数理研究所共同研究リポート 453 最適化:モデリングとアルゴリズム33 2022年3月 「大規模二次割当問題への挑戦」 p.84-p.92 N2 - 二次割当問題は線形緩和が弱いことが知られ,強化のため多様な緩和手法が考案されているが,その一つである二重非負値計画緩和( DNN 緩和)及びその解法として近年研究が進んでいるニュートン・ブラケット法を紹介し,それらに基づく分枝限定法の実装及び数値実験結果について報告する. T2 - Solving Large Scale QAPs with DNN-based Branch-and-bound : a progress report T3 - ZIB-Report - 22-11 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86779 SN - 1438-0064 ER - TY - THES A1 - Paskin, Martha T1 - Estimating 3D Shape of the Head Skeleton of Basking Sharks Using Annotated Landmarks on a 2D Image N2 - Basking sharks are thought to be one of the most efficient filter-feeding fish in terms of the throughput of water filtered through their gills. Details about the underlying morphology of their branchial region have not been studied due to various challenges in acquiring real-world data. The present thesis aims to facilitate this, by developing a mathematical shape model which constructs the 3D structure of the head skeleton of a basking shark using annotated landmarks on a single 2D image. This is an ill-posed problem as estimating the depth of a 3D object from a single 2D view is, in general, not possible. To reduce this ambiguity, we create a set of pre-defined training shapes in 3D from CT scans of basking sharks. First, the damaged structures of the sharks in the scans are corrected via solving a set of optimization problems, before using them as accurate 3D representations of the object. Then, two approaches are employed for the 2D-to-3D shape fitting problem–an Active Shape Model approach and a Kendall’s Shape Space approach. The former represents a shape as a point on a high-dimensional Euclidean space, whereas the latter represents a shape as an equivalence class of points in this Euclidean space. Kendall’s shape space approach is a novel technique that has not yet been applied in this context, and a comprehensive comparison of the two approaches suggests this approach to be superior for the problem at hand. This can be credited to an improved interpolation of the training shapes. N2 - Riesenhaie zählen zu den effizientesten Filtrierern hinsichtlich des durch die Kiemen gefilterten Wasservolumens. Die Kiemenregion dieser Tiere besitzt eine markante Morphologie, die jedoch bisher nicht umfassend erforscht werden konnte, da es schwierig ist, reale Daten dieser Tiere zu erheben. Die vorliegende Arbeit zielt darauf ab, dies durch die Entwicklung eines mathematischen Formmodels zu ermöglichen, das es erlaubt, die 3D-Struktur des Schädelskeletts anhand von Landmarken, die auf einem 2D-Bild platziert werden, zu rekonstruieren. Die hierzu benötigte Tiefenbestimmung der Landmarken aus einer 2D-Projektion ist ein unterbestimmtes Problem. Wir lösen dies durch die Hinzunahme von Trainingsformen, welche wir aus CT-Scans von Riesenhaien gewinnen. Der Zustand der tomografierten Exemplare erfordert jedoch einen vorhergehenden Korrekturschritt, den wir mit Hilfe eines Optimierungsansatzes lösen, bevor die extrahierten Strukturen als 3D-Trainingsformen dienen können. Um die 3D-Struktur des Schädelskelettes aus 2D-Landmarken zu rekonstruieren, vergleichen wir zwei Ansätze – den sogenannten Active-Shape-Model (ASM)-Ansatz und einen Ansatz basierend auf Kendalls Formenraum. Während eine Form des ASM-Ansatzes durch einen Punkt in einem hochdimensionalen Euklidischen Raum repräsentiert ist, repräsentiert eine Form im Kendall-Formenraum eine Äquivalenzklasse von Punkten des Euklidischen Raumes. Die Anwendung des Kendall-Formenraumes für das beschriebene Problem ist neu und ein umfassender Vergleich der Methoden hat ergeben, dass dieser Ansatz für die spezielle Anwendung zu besseren Ergebnissen führt. Wir führen dies auf die überlegene Interpolation der Trainingsformen in diesem Raum zurück. Y1 - 2022 UR - https://arxiv.org/abs/2207.12687 ER - TY - GEN A1 - Paskin, Martha A1 - Baum, Daniel A1 - Dean, Mason N. A1 - von Tycowicz, Christoph T1 - A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks -- Source Code and Data N2 - Source code and novel dataset of basking shark head skeletons facilitating the reproduction of the results presented in 'A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks' - ECCV 2022. Y1 - 2022 U6 - https://doi.org/10.12752/8730 ER - TY - GEN A1 - Ambellan, Felix A1 - Hanik, Martin A1 - von Tycowicz, Christoph T1 - Morphomatics: Geometric morphometrics in non-Euclidean shape spaces N2 - Morphomatics is an open-source Python library for (statistical) shape analysis developed within the geometric data analysis and processing research group at Zuse Institute Berlin. It contains prototype implementations of intrinsic manifold-based methods that are highly consistent and avoid the influence of unwanted effects such as bias due to arbitrary choices of coordinates. KW - shape analysis KW - geometric statistics KW - geometric morphometrics Y1 - 2021 U6 - https://doi.org/10.12752/8544 N1 - https://morphomatics.github.io/ 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 - TY - GEN A1 - Shinano, Yuji T1 - UG - Ubiquity Generator Framework v1.0.0beta N2 - UG is a generic framework to parallelize branch-and-bound based solvers (e.g., MIP, MINLP, ExactIP) in a distributed or shared memory computing environment. It exploits the powerful performance of state-of-the-art "base solvers", such as SCIP, CPLEX, etc. without the need for base solver parallelization. UG framework, ParaSCIP(ug[SCIP,MPI]) and FiberSCIP (ug[SCIP,Pthreads]) are available as a beta version. v1.0.0: new documentation and cmake, generalization of ug framework, implementation of selfsplitrampup for fiber- and parascip, better memory and time limit handling. KW - parallelization framework KW - branch-and-bound parallelization KW - integer optimization Y1 - 2021 U6 - https://doi.org/10.12752/8521 ER - TY - THES A1 - Krause, Jan T1 - Investigation of Options to Handle 3D MRI Data via Convolutional Neural Networks Application in Knee Osteoarthritits Classification KW - Machine Learning KW - Computational Diagnosis KW - Knee Osteoarthritis Y1 - 2021 ER -