Interactive analysis of high-dimensional association structures with graphical models

Graphical chain models are a capable tool for analyzing multivariate data. However, their practical use may still be cumbersome in some respect since fitting the model requires the application of an intensive selection strategy based on the calculation of an enormous number of different regressions. In this paper, we present a computer system especially designed for the calculation of graphical chain models which is not only planned to automatically carry out the model search but also to visualize the corresponding graph at each stage of the model fit on request by the user. It additionally allows to modify the graph and the model fit interactively

Unaccompanied minors in Bremen - A case study on how empowerment is implemented in the work with young refugees in Bremen

The number of people escaping from wars and conflicts to European welfare states is increasing. Many of them are children; some come as unaccompanied minors (UMs), fleeing without parents or any other responsible family member, entering and living in the country of refuge on their own. The “United Nations” (UN) and its “Convention on the Rights of the Child” from 1989 secures them special protection in any country of refuge. How does Germany and in particular the federal city state of Bremen support UMs? This case study investigates policies and practices for UMs in Bremen and applies empowerment theory. Accordingly, the focus of the thesis will be on the policy-implementation of empowerment-based goals. Withal, empowerment is understood as participation. How do stakeholders in fact participate UMs? The research retrieves qualitative evidence from semi-structured interviews with stakeholders in Bremen. Findings demonstrate a discrepancy between the obligation to participate and its implementation

Landscapes (re) mediated between image-matrix and matrix-image

This article aims to analyze the series of engravings called Passagens entre Paisagens, in which different media are used, such as digital photography, the engraving of matrices, printing, scanning and reprinting of images on other media. These works present different granulations and textures, whose characteristics are problematized by the operations of contact between image-matrix and matrix-image, between traditional media and (re) mediation by numerical means; conceptual issues regarding the matrix, image and (re) mediation are addressed according to authors such as Vilém Flusser (2008), David Bolter and Richard Grusin (2000), Edmond Couchot (2003), among others

Vehicle Routing in Theory and Practice

In this thesis, we study combinatorial optimization problems that arise in logistics and can be summarized under the name vehicle routing. We tackle these problems from two different points of view. First, we study their computational complexity. All problems we look at are generalizations of the famous traveling salesperson problem, TSP for short: a driver needs to visit certain customers (e.g., to deliver goods) and return to the starting point at the end of the tour. The goal is to compute a tour of minimum length (or cost). We provide improved approximation guarantees for two well-known natural generalizations of this problem. Both variants are of high relevance in logistics. In the first variant, known as the prize-collecting TSP, we are allowed to reject customer requests, which comes at customer-specific penalties. The goal is then to optimize the sum of tour length and total penalty for rejected inquiries. We improve the best known approximation ratio of roughly 1.914 (due to Goemans) to 1.599, which significantly reduces the gap between the approximability of the TSP and its prize-collecting variant. The second variant of the TSP for which we provide improved approximation guarantees is the capacitated vehicle routing problem. In many applications, the goods that need to be delivered to customers exceed the capacity of a single vehicle. Hence, we need to distribute the goods to several vehicles and compute an efficient route for each of these such that the sum of tour lengths is minimized. We improve and simplify an approach that was initiated in my master’s thesis, which led to the first improvement of the approximation ratio of the classical tour partitioning approach. We obtain a better approximation ratio for several major variants of the problem. Second, we study vehicle routing problems from a practical point of view. On typical real-world instances, the approximation algorithms discussed in the first part of this thesis are not practical, neither in terms of solution quality nor in terms of running time. Moreover, we need to satisfy various additional constraints such as time windows, working time limits, and limited heterogeneous vehicle fleets. We present an algorithm called BonnTour that covers a wide class of vehicle routing problems and provides high-quality solutions in reasonable computation time. On numerous benchmarks, the cost of the computed solution comes close to the optimum or the best known. On some benchmark instances, we present new best known solutions. Our algorithm takes into account time-dependent travel time fluctuations that are caused by congestion, which leads to much more reliable tour plans. We provide a new set of realistic and large-scale benchmark instances for vehicle routing with time-dependent travel times to foster future research on this problem. BonnTour is developed in cooperation with our industry partner Greenplan, and is used on a daily basis to solve real-world vehicle routing problems for various companies

Space Mapping for PDE Constrained Shape Optimization

The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model optimization problem. In this paper, we propose novel space mapping methods for solving shape optimization problems constrained by partial differential equations (PDEs). We present the methods in a Riemannian setting based on Steklov-Poincar\'e-type metrics and discuss their numerical discretization and implementation. We investigate the numerical performance of the space mapping methods on several model problems. Our numerical results highlight the methods' great efficiency for solving complex shape optimization problems

Version 2.0 -- cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software

In this paper, we present version 2.0 of cashocs. Our software automates the solution of PDE constrained optimization problems for shape optimization and optimal control. Since its inception, many new features and useful tools have been added to cashocs, making it even more flexible and efficient. The most significant additions are a framework for space mapping, the ability to solve topology optimization problems with a level-set approach, the support for parallelism via MPI, and the ability to handle additional (state) constraints. In this software update, we describe the key additions to cashocs, which is now even better-suited for solving complex PDE constrained optimization problems

Quasi-Newton Methods for Topology Optimization Using a Level-Set Method

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andr\"a (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier-Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization