TY - GEN A1 - Kaplan, Bernhard A1 - Laufer, Jan A1 - Prohaska, Steffen A1 - Buchmann, Jens T1 - Monte-Carlo-based inversion scheme for 3D quantitative photoacoustic tomography N2 - The goal of quantitative photoacoustic tomography (qPAT) is to recover maps of the chromophore distributions from multiwavelength images of the initial pressure. Model-based inversions that incorporate the physical processes underlying the photoacoustic (PA) signal generation represent a promising approach. Monte-Carlo models of the light transport are computationally expensive, but provide accurate fluence distributions predictions, especially in the ballistic and quasi-ballistic regimes. Here, we focus on the inverse problem of 3D qPAT of blood oxygenation and investigate the application of the Monte-Carlo method in a model-based inversion scheme. A forward model of the light transport based on the MCX simulator and acoustic propagation modeled by the k-Wave toolbox was used to generate a PA image data set acquired in a tissue phantom over a planar detection geometry. The combination of the optical and acoustic models is shown to account for limited-view artifacts. In addition, the errors in the fluence due to, for example, partial volume artifacts and absorbers immediately adjacent to the region of interest are investigated. To accomplish large-scale inversions in 3D, the number of degrees of freedom is reduced by applying image segmentation to the initial pressure distribution to extract a limited number of regions with homogeneous optical parameters. The absorber concentration in the tissue phantom was estimated using a coordinate descent parameter search based on the comparison between measured and modeled PA spectra. The estimated relative concentrations using this approach lie within 5 % compared to the known concentrations. Finally, we discuss the feasibility of this approach to recover the blood oxygenation from experimental data. T3 - ZIB-Report - 17-04 KW - quantitative photoacoustic tomography KW - model-based inversion KW - oxygen saturation KW - chromophore concentration KW - photoacoustic imaging KW - Monte Carlo methods for light transport KW - boundary conditions KW - coordinate search Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62318 SN - 1438-0064 ER - TY - GEN A1 - Tateiwa, Nariaki A1 - Shinano, Yuji A1 - Yasuda, Masaya A1 - Kaji, Shizuo A1 - Yamamura, Keiichiro A1 - Fujisawa, Katsuki T1 - Massively parallel sharing lattice basis reduction N2 - For cryptanalysis in lattice-based schemes, the performance evaluation of lattice basis reduction using high-performance computers is becoming increasingly important for the determination of the security level. We propose a distributed and asynchronous parallel reduction algorithm based on randomization and DeepBKZ, which is an improved variant of the block Korkine-Zolotarev (BKZ) reduction algorithm. Randomized copies of a lattice basis are distributed to up to 103,680 cores and independently reduced in parallel, while some basis vectors are shared asynchronously among all processes via MPI. There is a trade-off between randomization and information sharing; if a substantial amount of information is shared, all processes will work on the same problem, thereby diminishing the benefit of parallelization. To monitor this balance between randomness and sharing, we propose a metric to quantify the variety of lattice bases. We empirically find an optimal parameter of sharing for high-dimensional lattices. We demonstrate the efficacy of our proposed parallel algorithm and implementation with respect to both performance and scalability through our experiments. T3 - ZIB-Report - 21-38 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-85209 SN - 1438-0064 N1 - under review ER - TY - GEN A1 - Clasen, Malte A1 - Paar, Philip A1 - Prohaska, Steffen T1 - Level of Detail for Trees Using Clustered Ellipsoids N2 - We present a level of detail method for trees based on ellipsoids and lines. We leverage the Expectation Maximization algorithm with a Gaussian Mixture Model to create a hierarchy of high-quality leaf clusterings, while the branches are simplified using agglomerative bottom-up clustering to preserve the connectivity. The simplification runs in a preprocessing step and requires no human interaction. For a fly by over and through a scene of 10k trees, our method renders on average at 40 ms/frame, up to 6 times faster than billboard clouds with comparable artifacts. T3 - ZIB-Report - 11-41 KW - level of detail KW - rendering KW - natural scene KW - Gaussian mixture model Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14251 SN - 1438-0064 ER - TY - GEN A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics N2 - 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. T3 - ZIB-Report - 21-40 KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2021 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 - Shinano, Yuji A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - FiberSCIP - A shared memory parallelization of SCIP N2 - Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated. T3 - ZIB-Report - 13-55 KW - parallel KW - branch-and-bound KW - deterministic parallelism KW - constraint integer programming KW - mixed integer programming KW - mixed integer nonlinear programming KW - SCIP KW - MIP KW - MINLP Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42595 SN - 1438-0064 ER - TY - GEN A1 - Ehlke, Moritz A1 - Ramm, Heiko A1 - Lamecker, Hans A1 - Hege, Hans-Christian A1 - Zachow, Stefan T1 - Fast Generation of Virtual X-ray Images from Deformable Tetrahedral Meshes N2 - We propose a novel GPU-based approach to render virtual X-ray projections of deformable tetrahedral meshes. These meshes represent the shape and the internal density distribution of a particular anatomical structure and are derived from statistical shape and intensity models (SSIMs). We apply our method to improve the geometric reconstruction of 3D anatomy (e.g.\ pelvic bone) from 2D X-ray images. For that purpose, shape and density of a tetrahedral mesh are varied and virtual X-ray projections are generated within an optimization process until the similarity between the computed virtual X-ray and the respective anatomy depicted in a given clinical X-ray is maximized. The OpenGL implementation presented in this work deforms and projects tetrahedral meshes of high resolution (200.000+ tetrahedra) at interactive rates. It generates virtual X-rays that accurately depict the density distribution of an anatomy of interest. Compared to existing methods that accumulate X-ray attenuation in deformable meshes, our novel approach significantly boosts the deformation/projection performance. The proposed projection algorithm scales better with respect to mesh resolution and complexity of the density distribution, and the combined deformation and projection on the GPU scales better with respect to the number of deformation parameters. The gain in performance allows for a larger number of cycles in the optimization process. Consequently, it reduces the risk of being stuck in a local optimum. We believe that our approach contributes in orthopedic surgery, where 3D anatomy information needs to be extracted from 2D X-rays to support surgeons in better planning joint replacements. T3 - ZIB-Report - 13-38 KW - digitally reconstructed radiographs KW - volume rendering KW - mesh deformation KW - statistical shape and intensity models KW - image registration KW - GPU acceleration Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-41896 SN - 1438-0064 ER - TY - GEN A1 - Orlowski, Sebastian A1 - Werner, Axel A1 - Wessäly, Roland T1 - Estimating trenching costs in FTTx network planning N2 - In this paper we assess to which extent trenching costs of an FTTx network are unavoidable, even if technical side constraints are neglected. For that purpose we present an extended Steiner tree model. Using a variety of realistic problem instances we demonstrate that the total trenching cost can only be reduced by about 5 percent in realistic scenarios. This work has been funded by BMBF (German Federal Ministry of Education and Research) within the program "KMU-innovativ". T3 - ZIB-Report - 11-49 KW - Optical access networks KW - Optimization KW - Steiner trees Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14884 SN - 1438-0064 ER - TY - GEN A1 - Becker, Kai-Helge A1 - Hiller, Benjamin T1 - Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited N2 - In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested. T3 - ZIB-Report - 20-05 KW - acyclic orientations KW - enumeration algorithm KW - multiple sources and sinks KW - bipolar orientations Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77684 SN - 1438-0064 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Kunt, Tim A1 - Katamish, Bassel A1 - Vanaret, Charlie A1 - Sasanpour, Shima A1 - Clarner, Jan-Patrick A1 - Koch, Thorsten T1 - Developing heuristic solution techniques for large-scale unit commitment models N2 - Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and operational decision-making. ESOMs are frequently formulated as linear (LPs) and mixed-integer linear (MIP) problems. MIPs allow continuous and discrete decision variables. Consequently, they are substantially more expressive than LPs but also more challenging to solve. The ever-growing size and complexity of ESOMs take a toll on the computational time of state-of-the-art commercial solvers. Indeed, for large-scale ESOMs, solving the LP relaxation -- the basis of modern MIP solution algorithms -- can be very costly. These time requirements can render ESOM MIPs impractical for real-world applications. This article considers a set of large-scale decarbonization-focused unit commitment models with expansion decisions based on the REMix framework (up to 83 million variables and 900,000 discrete decision variables). For these particular instances, the solution to the LP relaxation and the MIP optimum lie close. Based on this observation, we investigate the application of relaxation-enforced neighborhood search (RENS), machine learning guided rounding, and a fix-and-propagate (FP) heuristic as a standalone solution method. Our approach generated feasible solutions 20 to 100 times faster than GUROBI, achieving comparable solution quality with primal-dual gaps as low as 1% and up to 35%. This enabled us to solve numerous scenarios without lowering the quality of our models. For some instances that Gurobi could not solve within two days, our FP method provided feasible solutions in under one hour. T3 - ZIB-Report - 25-03 KW - Energy system optimization models KW - Unit commitment KW - Mixed-integer programming KW - Large-scale optimization KW - Primal heuristics Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99555 SN - 1438-0064 ER -