@misc{Shinano, author = {Shinano, Yuji}, title = {UG - Ubiquity Generator Framework v1.0.0beta}, doi = {10.12752/8521}, abstract = {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.}, language = {en} } @misc{MunguiaOxberryRajanetal., author = {Munguia, Lluis-Miquel and Oxberry, Geoffrey and Rajan, Deepak and Shinano, Yuji}, title = {Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs}, number = {ZIB-Report 17-58}, issn = {1438-0064}, doi = {10.1007/s10589-019-00074-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65517}, abstract = {PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch \& Bound (B\&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B\&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B\&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores.}, language = {en} } @misc{GriewankStreubelLehmannetal., author = {Griewank, Andreas and Streubel, Tom and Lehmann, Lutz and Hasenfelder, Richard and Radons, Manuel}, title = {Piecewise linear secant approximation via Algorithmic Piecewise Differentiation}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1387256}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61642}, abstract = {It is shown how piecewise differentiable functions \(F: R^n → R^m\) that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points x̌ and x̂. We show that the discrepancy between function and model at any point x is of the bilinear order O(||x - x̌|| ||x - x̂||). This is a little surprising since x ∈ R^n may vary over the whole Euclidean space, and we utilize only two function samples F̌ = F(x̌) and F̂ = F(x̂), as well as the intermediates computed during their evaluation. As an application of the piecewise linearization procedure we devise a generalized Newton's method based on successive piecewise linearization and prove for it sufficient conditions for convergence and convergence rates equaling those of semismooth Newton. We conclude with the derivation of formulas for the numerically stable implementation of the aforedeveloped piecewise linearization methods.}, language = {en} } @misc{LindnerReisch, author = {Lindner, Niels and Reisch, Julian}, title = {Parameterized Complexity of Periodic Timetabling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78314}, abstract = {Public transportation networks are typically operated with a periodic timetable. The Periodic Event Scheduling Problem (PESP) is the standard mathematical modelling tool for periodic timetabling. Since PESP can be solved in linear time on trees, it is a natural question to ask whether there are polynomial-time algorithms for input networks of bounded treewidth. We show that deciding the feasibility of a PESP instance is NP-hard even when the treewidth is 2, the branchwidth is 2, or the carvingwidth is 3. Analogous results hold for the optimization of reduced PESP instances, where the feasibility problem is trivial. To complete the picture, we present two pseudo-polynomial-time dynamic programming algorithms solving PESP on input networks with bounded tree- or branchwidth. We further analyze the parameterized complexity of PESP with bounded cyclomatic number, diameter, or vertex cover number. For event-activity networks with a special -- but standard -- structure, we give explicit and sharp bounds on the branchwidth in terms of the maximum degree and the carvingwidth of an underlying line network. Finally, we investigate several parameters on the smallest instance of the benchmarking library PESPlib.}, language = {en} } @misc{Witzig, type = {Master Thesis}, author = {Witzig, Jakob}, title = {Reoptimization Techniques in MIP Solvers}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54067}, pages = {176}, abstract = {Many optimization problems can be modeled as Mixed Integer Programs (MIPs). In general, MIPs cannot be solved efficiently, since solving MIPs is NP-hard, see, e.g., Schrijver, 2003. Common methods for solving NP-hard problems are branch-and-bound and column generation. In the case of column generation, the original problem becomes decomposed or re-formulated into one ore more smaller subproblems, which are easier to solve. Each of these subproblems is solved separately and recurrently, which can be interpreted as solving a sequence of optimization problems. In this thesis, we consider a sequence of MIPs which only differ in the respective objective functions. Furthermore, we assume each of these MIPs get solved with a branch-and-bound algorithm. This thesis aims to figure out whether the solving process of a given sequence of MIPs can be accelerated by reoptimization. As reoptimization we understand starting the solving process of a MIP of this sequence at a given frontier of a search tree corresponding to another MIP of this sequence. At the beginning we introduce an LP-based branch-and-bound algorithm. This algorithm is inspired by the reoptimizing algorithm of Hiller, Klug, and the author of this thesis, 2013. Since most of the state-of-the-art MIP solvers come to decisions based on dual information, which leads to the loss of feasible solutions after changing the objective function, we present a technique to guarantee optimality despite using these information. A decision is based on a dual information if this decision is valid for at least one feasible solution, whereas a decision is based on a primal information if this decision is valid for all feasible solutions. Afterwards, we consider representing the search frontier of the tree by a set of nodes of a given size. We call this the Tree Compression Problem. Moreover, we present a criterion characterizing the similarity of two objective functions. To evaluate our approach of reoptimization we extend the well-known and well-maintained MIP solver SCIP to an LP-based branch-and-bound framework, introduce two heuristics for solving the Tree Compression Problem, and a primal heuristic which is especially fitted to column generation. Finally, we present computational experiments on several problem classes, e.g., the Vertex Coloring and k-Constrained Shortest Path. Our experiments show, that a straightforward reoptimization, i.e., without additional heuristics, provides no benefit in general. However, in combination with the techniques and methods presented in this thesis, we can accelerate the solving of a given sequence up to the factor 14. For this purpose it is essential to take the differences of the objective functions into account and to restart the reoptimization, i.e., solve the subproblem from scratch, if the objective functions are not similar enough. Finally, we discuss the possibility to parallelize the solving process of the search frontier at the beginning of each solving process.}, language = {en} } @masterthesis{Witzig, type = {Bachelor Thesis}, author = {Witzig, Jakob}, title = {Effiziente Reoptimierung in Branch\&Bound-Verfahren f{\"u}r die Steuerung von Aufz{\"u}gen}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42210}, school = {Zuse Institute Berlin (ZIB)}, pages = {111}, abstract = {Heutzutage ist eine Vielzahl der mehrst{\"o}ckigen Geb{\"a}ude mit Personenaufzugsgruppen ausgestattet. Uns wohl bekannt sind die sogenannten konventionellen Systeme. Bei diesen Systemen bet{\"a}tigt jeder ankommende Passagier eine der beiden Richtungstasten und teilt dem dahinterstehenden Steuerungsalgorithmus seine gew{\"u}nschte Startetage und Fahrtrichtung mit. Betreten wird der zuerst auf der Startetage ankommende Aufzug mit gleicher Fahrtrichtung und ausreichend Kapazit{\"a}t. Die entsprechende Zieletage wird dem System erst nach dem Betreten der Fahrgastkabine mitgeteilt. Neben diesen konventionellen Systemen gibt es Aufzugsgruppen mit Zielrufsteuerung. Die Besonderheit eines zielrufgesteuerten Systems ist, dass ein ankommender Passagier bereits auf der Startetage seine gew{\"u}nschte Zieletage angibt und eine R{\"u}ckmeldung vom System erh{\"a}lt, welchen Aufzug er nutzen soll. Diese Zuweisung durch das System hat das Ziel, die Warte- und Reisezeiten der Passagiere zu minimieren. Ein wesentlicher Faktor bei der Berechnung warte- und reisezeitminimaler Fahrpl{\"a}ne ist das momentane Verkehrsmuster. Eine Einteilung der Verkehrsszenarien l{\"a}sst sich am besten bei B{\"u}rogeb{\"a}uden vornehmen. So ist es typisch f{\"u}r die Morgenstunden, dass jeder Passagier auf einer Zugangsebene seine Fahrt beginnt und alle Passagiere die gleiche Fahrtrichtung haben. Unter einer Zugangsebene ist z. B. der Haupteingang oder ein Parkdeck zu verstehen. Ein weiterer wesentlicher Punkt bei Zielrufsystemen ist die Art der Zuweisung der Passagiere durch das System. Zum einen gibt es unmittelbar zuweisende (UZ-) Systeme. In einem UZ-System wird nach jeder Ankunft eines Passagiers eine Momentaufnahme des momentanen Verkehrs erstellt und es findet eine Neuplanung und Zuweisung statt. Eine solche Momentaufnahme werden wir im sp{\"a}teren Verkauf als Schnappschussproblem bezeichnen. Jeder Passagier bekommt im Anschluss an die L{\"o}sung des Schnappschussproblems eine Mitteilung vom System, z. B. {\"u}ber ein Display, welchen Aufzug er benutzen soll. Zum anderen gibt es verz{\"o}gert zuweisende (VZ-) Systeme. In diesen Systemen wird die Erstellung und L{\"o}sung eines Schnappschussproblems bis kurz vor Ankunft eines Aufzuges auf einer Etage verz{\"o}gert. In einem VZ-System teilt das System allen wartenden Passagieren die geplanten Zieletagen des ankommenden Aufzugs mit. Jeder Passagier, der einen Ruf get{\"a}tigt hat und zu einer dieser Zieletagen fahren will, kann jetzt diesen Aufzug betreten. Durch die Verz{\"o}gerung muss im Vergleich zu einem UZ-System eine weitaus gr{\"o}ßere Menge von Passagieren zugewiesen werden. Dadurch kann der L{\"o}sungsprozess bedeutend aufw{\"a}ndiger werden. Vorteil eines VZ-Systems ist hingegen der gr{\"o}ßere Freiheitsgrad bei der Optimierung, da aufgrund der sp{\"a}ten Zuweisung die weitere Verkehrsentwicklung mit einbezogen werden kann. VZ-Systeme sind aufgrund des gr{\"o}ßeren Freiheitsgrades interessant f{\"u}r die Praxis ist, wir uns demzufolge in dieser Arbeit mit einer effizienteren L{\"o}sung dieser Art von Schnappschussproblemen befassen. Es gen{\"u}gt dabei den L{\"o}sungsprozess eines Schnappschussproblems zu betrachten. Das Ziel ist eine Reduzierung der ben{\"o}tigten Rechenzeit. Unter Reoptimierung verstehen wir die Konstruktion zul{\"a}ssiger Spalten in den jeweiligen Iterationsrunden der Spaltengenerierung innerhalb eines Schnappschussproblems. Als eine Iterationsrunde bezeichnet wir einer Menge zul{\"a}ssiger Touren mit negativen reduzierten Kosten. Eine effiziente Reoptimierung zeichnet sich durch die Wiederverwendung und Aufbereitung von Informationen aus vorangegangenen Iterationsrunden desselben Schnappschussproblems aus. Zu den wichtigen Informationen geh{\"o}rt der konstruierte Suchbaum der vorherigen Iterationsrunde mit seinen ausgeloteten (abgeschnittenen) Bl{\"a}ttern sowie konstruierten Touren bzw. Spalten, welche in der Iterationsrunde ihrer Konstruktion nicht zur L{\"o}sung des Teilproblems der Spaltengenerierung beitrugen. Eine solche Wiederverwendung und Aufbereitung von Informationen nennen wir Warmstart.}, language = {de} } @misc{OezelKulkarniHasanetal., author = {{\"O}zel, M. Neset and Kulkarni, Abhishek and Hasan, Amr and Brummer, Josephine and Moldenhauer, Marian and Daumann, Ilsa-Maria and Wolfenberg, Heike and Dercksen, Vincent J. and Kiral, F. Ridvan and Weiser, Martin and Prohaska, Steffen and von Kleist, Max and Hiesinger, Peter Robin}, title = {Serial synapse formation through filopodial competition for synaptic seeding factors}, issn = {1438-0064}, doi = {10.1016/j.devcel.2019.06.014}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74397}, abstract = {Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses.}, language = {en} } @misc{MasingLindnerEbert, author = {Masing, Berenike and Lindner, Niels and Ebert, Patricia}, title = {Forward and Line-Based Cycle Bases for Periodic Timetabling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89731}, abstract = {The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks, and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances.}, language = {en} } @misc{RiberaBorrellQuerRichteretal., author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, issn = {1438-0064}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @misc{Paskin, type = {Master Thesis}, author = {Paskin, Martha}, title = {Estimating 3D Shape of the Head Skeleton of Basking Sharks Using Annotated Landmarks on a 2D Image}, abstract = {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.}, language = {en} }