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 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Teckentrup, Aretha T1 - Random forward models and log-likelihoods in Bayesian inverse problems T2 - SIAM/ASA Journal on Uncertainty Quantification N2 - We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations. T3 - ZIB-Report - 18-03 KW - Bayesian inverse problem KW - random likelihood KW - surrogate model KW - posterior consistency KW - probabilistic numerics KW - uncertainty quantification KW - randomised misfit Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66324 SN - 1438-0064 VL - 6 IS - 4 SP - 1600 EP - 1629 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 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Probabilistic alternatives for competitive analysis N2 - In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis. T3 - ZIB-Report - 11-55 KW - online algorithms KW - probabilistic analysis KW - competitive analysis KW - survey Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15131 SN - 1438-0064 ER - TY - GEN A1 - D'Andreagiovanni, Fabio A1 - Krolikowski, Jonatan A1 - Pulaj, Jonad T1 - A hybrid primal heuristic for Robust Multiperiod Network Design N2 - We investigate the Robust Multiperiod Network Design Problem, a generalization of the classical Capacitated Network Design Problem that additionally considers multiple design periods and provides solutions protected against traffic uncertainty. Given the intrinsic difficulty of the problem, which proves challenging even for state-of-the art commercial solvers, we propose a hybrid primal heuristic based on the combination of ant colony optimization and an exact large neighborhood search. Computational experiments on a set of realistic instances from the SNDlib show that our heuristic can find solutions of extremely good quality with low optimality gap. T3 - ZIB-Report - 13-78 KW - Multiperiod Network Design, Traffic Uncertainty, Robust Optimization, Multiband Robustness, Hybrid Heuristics Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44081 SN - 1438-0064 ER - TY - GEN A1 - D'Andreagiovanni, Fabio A1 - Raymond, Annie T1 - Multiband Robust Optimization and its Adoption in Harvest Scheduling N2 - A central assumption in classical optimization is that all the input data of a problem are exact. However, in many real-world problems, the input data are subject to uncertainty. In such situations, neglecting uncertainty may lead to nominally optimal solutions that are actually suboptimal or even infeasible. Robust optimization offers a remedy for optimization under uncertainty by considering only the subset of solutions protected against the data deviations. In this paper, we provide an overview of the main theoretical results of multiband robustness, a new robust optimization model that extends and refines the classical theory introduced by Bertsimas and Sim. After introducing some new results for the special case of pure binary programs, we focus on the harvest scheduling problem and show how multiband robustness can be adopted to tackle the uncertainty affecting the volume of produced timber and grant a reduction in the price of robustness. T3 - ZIB-Report - 13-76 KW - Data Uncertainty KW - Robust Optimization KW - Multiband Robustness KW - Harvest Scheduling Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43380 SN - 1438-0064 ER - TY - GEN A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio A1 - Raymond, Annie T1 - 0-1 Multiband Robust Optimization N2 - We provide an overview of new theoretical results that we obtained while further investigating multiband robust optimization, a new model for robust optimization that we recently proposed to tackle uncertainty in mixed-integer linear programming. This new model extends and refines the classical Gamma-robustness model of Bertsimas and Sim and is particularly useful in the common case of arbitrary asymmetric distributions of the uncertainty. Here, we focus on uncertain 0-1 programs and we analyze their robust counterparts when the uncertainty is represented through a multiband set. Our investigations were inspired by the needs of our industrial partners in the research project ROBUKOM. T3 - ZIB-Report - 13-77 KW - Combinatorial Optimization, Robust Optimization, Multiband Robustness, Network Design Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44093 SN - 1438-0064 ER - TY - GEN A1 - Bley, Andreas A1 - D'Andreagiovanni, Fabio A1 - Karch, Daniel T1 - Scheduling technology migration in WDM Networks N2 - The rapid technological evolution of telecommunication networks demands service providers to regularly update their technology, with the aim of remaining competitive in the marketplace. However, upgrading the technology in a network is not a trivial task. New hardware components need to be installed in the network and during the installation network connectivity may be temporarily compromised. The Wavelength Division Multiplexing (WDM) technology, whose upgrade is considered in here, shares fiber links among several optical connections and tearing down a single link may disrupt several optical connections at once. When the upgrades involve large parts of a network, typically not all links can be upgraded in parallel, which may lead to an unavoidable longer disruption of some connections. A bad scheduling of the overall endeavor, however, can dramatically increase the disconnection time of parts of the networks, causing extended service disruption. In this contribution, we study the problem of finding a schedule of the fiber link upgrades that minimizes the total service disruption time. To the best of our knowledge, this problem has not yet been formalized and investigated. The aim of our work is to close this gap by presenting a mathematical optimization model for the problem and an innovative solution algorithm that tackles the intrinsic difficulties of the problem. Computational experience on realistic instances completes our study. Our original investigations have been driven by real needs of DFN, operator of the German National Research and Education Network and our partner in the BMBF research project ROBUKOM (http://www.robukom.de/). T3 - ZIB-Report - 13-62 KW - Scheduling, Extended Formulations, Network Migration, WDM Networks Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42654 UR - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6507677&isnumber=6507670 SN - 1438-0064 ER - TY - GEN A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio T1 - A new theoretical framework for Robust Optimization under multi-band uncertainty N2 - We provide an overview of our main results about studying Linear Programming Problems whose coefficient matrix is subject to uncertainty and the uncertainty is modeled through a multi-band set. Such an uncertainty set generalizes the classical one proposed by Bertsimas and Sim and is particularly suitable in the common case of arbitrary non-symmetric distributions of the parameters. Our investigations were inspired by practical needs of our industrial partner in ongoing projects with focus on the design of robust telecommunications networks. T3 - ZIB-Report - 13-61 KW - Robust Optimization, Uncertainty Set, Multiband Robustness, Network Design Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42644 UR - http://www.springer.com/business+%26+management/operations+research/book/978-3-319-00794-6 SN - 1438-0064 ER - TY - GEN A1 - Zakrzewska, Anna A1 - D'Andreagiovanni, Fabio A1 - Ruepp, Sarah A1 - Berger, Michael S. T1 - Biobjective Optimization of Radio Access Technology Selection and Resource Allocation in Heterogeneous Wireless Networks N2 - We propose a novel optimization model for resource assignment in heterogeneous wireless network. The model adopts two objective functions maximizing the number of served users and the minimum granted utility at once. A distinctive feature of our new model is to consider two consecutive time slots, in order to include handover as an additional decision dimension. Furthermore, the solution algorithm that we propose refines a heuristic solution approach recently proposed in literature, by considering a real joint optimization of the considered resources. The simulation study shows that the new model leads to a significant reduction in handover frequency, when compared to a traditional scheme based on maximum SNR. T3 - ZIB-Report - 13-63 KW - Heterogeneous Wireless Networks, Biobjective Optimization, Mixed Integer Linear Programming, Simulation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42675 UR - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6576416&isnumber=6576384 SN - 1438-0064 ER - TY - GEN A1 - Bauschert, Thomas A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio A1 - Koster, Arie M.C.A. A1 - Kutschka, Manuel A1 - Steglich, Uwe T1 - Network Planning under Demand Uncertainty with Robust Optimization N2 - The planning of a communication network is inevitably depending on the quality of both the planning tool and the demand forecast used. In this article, we show exemplarily how the emerging area of Robust Optimization can advance the network planning by a more accurate mathematical description of the demand uncertainty. After a general introduction of the concept and its application to a basic network design problem, we present two applications: multi-layer and mixed-line-rate network design. We conclude with a discussion of extensions of the robustness concept to increase the accuracy of handling uncertainties. T3 - ZIB-Report - 13-59 KW - Network Design, Demand Uncertainty, Robust Optimization, Telecommunications Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42557 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 - 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 T1 - The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound N2 - Mixed integer linear programming (MIP) is a general form to model combinatorial optimization problems and has many industrial applications. The performance of MIP solvers has improved tremendously in the last two decades and these solvers have been used to solve many real-word problems. However, against the backdrop of modern computer technology, parallelization is of pivotal importance. In this way, ParaSCIP is the most successful parallel MIP solver in terms of solving previously unsolvable instances from the well-known benchmark instance set MIPLIB by using supercomputers. It solved two instances from MIPLIB2003 and 12 from MIPLIB2010 for the first time to optimality by using up to 80,000 cores on supercomputers. ParaSCIP has been developed by using the Ubiquity Generator (UG) framework, which is a general software package to parallelize any state-of-the-art branch-and-bound based solver. This paper discusses 7 years of progress in parallelizing branch-and-bound solvers with UG. T3 - ZIB-Report - 17-60 KW - Parallelization, Branch-and-bound, Mixed Integer Programming, UG, ParaSCIP, FiberSCIP, ParaXpress, FiberXpress, SCIP-Jack Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65545 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 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Stochastic dominance analysis of Online Bin Coloring algorithms N2 - This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations. T3 - ZIB-Report - 12-42 KW - online algorithms, stochastic dominance, algorithm analysis, Markov chains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16502 SN - 1438-0064 ER - TY - GEN A1 - Pfeuffer, Frank A1 - Werner, Axel T1 - Adaptive telecommunication network operation with a limited number of reconfigurations N2 - Rising traffic in telecommunication networks lead to rising energy costs for the network operators. Meanwhile, increased flexibility of the networking hardware may help to realize load-adaptive operation of the networks to cut operation costs. To meet network operators’ concerns over stability, we propose to switch network configurations only a limited number of times per day. We present a method for the integrated computation of optimal switching times and network configurations that alternatingly solves mixed-integer programs and constrained shortest cycle problems in a certain graph. Similarly to the Branch & Bound Algorithm, it uses lower and upper bounds on the optimum value and allows for pivoting strategies to guide the computation and avoid the solution of irrelevant subproblems. The algorithm can act as a framework to be adapted and applied to suitable problems of different origin. T3 - ZIB-Report - 15-36 KW - Telecommunication KW - Network Design KW - Dynamic Traffic KW - Branch and Bound Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55547 SN - 1438-0064 ER - TY - GEN A1 - Griewank, Andreas A1 - Streubel, Tom A1 - Lehmann, Lutz A1 - Hasenfelder, Richard A1 - Radons, Manuel T1 - Piecewise linear secant approximation via Algorithmic Piecewise Differentiation N2 - 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. T3 - ZIB-Report - 16-54 KW - Automatic differentiation KW - Computational graph KW - Lipschitz continuity KW - Generalized Hermite interpolation KW - ADOL-C Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61642 SN - 1438-0064 ER -