In bilevel optimization, some of the variables of an optimization problem have to be an optimal solution to another nested optimization problem. This specific structure renders bilevel optimization a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. Due to their nested structure, however, bilevel problems are also inherently hard to solve—both in theory and in practice. Further challenges arise if, e.g., bilevel problems under uncertainty are considered. In this dissertation, we address different types of uncertainties in bilevel optimization using techniques from robust optimization. We study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we tackle using the notion of Gamma-robustness. We present two exact branch-and-cut approaches to solve these Gamma-robust bilevel problems, along with cuts tailored to the important class of monotone interdiction problems. Given the overall hardness of the considered problems, we additionally propose heuristic approaches for mixed-integer, linear, and Gamma-robust bilevel problems. The latter rely on solving a linear number of deterministic bilevel problems so that no problem-specific tailoring is required. We assess the performance of both the exact and the heuristic approaches through extensive computational studies. In addition, we study the problem of determining optimal tolls in a traffic network in which the network users hedge against uncertain travel costs in a robust way. The overall toll-setting problem can be seen as a single-leader multi-follower problem with multiple robustified followers. We model this setting as a mathematical problem with equilibrium constraints, for which we present a mixed-integer, nonlinear, and nonconvex reformulation that can be tackled using state-of-the-art general-purpose solvers. We further illustrate the impact of considering robustified followers on the toll-setting policies through a case study. Finally, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to single-level optimization. To this end, we study two aspects related to so-called decision uncertainty. First, we propose a strictly robust approach in which the follower hedges against erroneous observations of the leader's decision. Second, we consider an exemplary bilevel problem with a continuous but nonconvex lower level in which algorithmic necessities prevent the follower from making a globally optimal decision in an exact sense. The example illustrates that even very small deviations in the follower's decision may lead to arbitrarily large discrepancies between exact and computationally obtained bilevel solutions.

This dissertation addresses the measurement and evaluation of the energy and resource efficiency of software systems. Studies show that the environmental impact of Information and Communications Technologies (ICT) is steadily increasing and is already estimated to be responsible for 3 % of the total greenhouse gas (GHG) emissions. Although it is the hardware that consumes natural resources and energy through its production, use, and disposal, software controls the hardware and therefore has a considerable influence on the used capacities. Accordingly, it should also be attributed a share of the environmental impact. To address this softwareinduced impact, the focus is on the continued development of a measurement and assessment model for energy and resource-efficient software. Furthermore, measurement and assessment methods from international research and practitioner communities were compared in order to develop a generic reference model for software resource and energy measurements. The next step was to derive a methodology and to define and operationalize criteria for evaluating and improving the environmental impact of software products. In addition, a key objective is to transfer the developed methodology and models to software systems that cause high consumption or offer optimization potential through economies of scale. These include, e. g., Cyber-Physical Systems (CPS) and mobile apps, as well as applications with high demands on computing power or data volumes, such as distributed systems and especially Artificial Intelligence (AI) systems. In particular, factors influencing the consumption of software along its life cycle are considered. These factors include the location (cloud, edge, embedded) where the computing and storage services are provided, the role of the stakeholders, application scenarios, the configuration of the systems, the used data, its representation and transmission, or the design of the software architecture. Based on existing literature and previous experiments, distinct use cases were selected that address these factors. Comparative use cases include the implementation of a scenario in different programming languages, using varying algorithms, libraries, data structures, protocols, model topologies, hardware and software setups, etc. From the selection, experimental scenarios were devised for the use cases to compare the methods to be analyzed. During their execution, the energy and resource consumption was measured, and the results were assessed. Subtracting baseline measurements of the hardware setup without the software running from the scenario measurements makes the software-induced consumption measurable and thus transparent. Comparing the scenario measurements with each other allows the identification of the more energyefficient setup for the use case and, in turn, the improvement/optimization of the system as a whole. The calculated metrics were then also structured as indicators in a criteria catalog. These indicators represent empirically determinable variables that provide information about a matter that cannot be measured directly, such as the environmental impact of the software. Together with verification criteria that must be complied with and confirmed by the producers of the software, this creates a model with which the comparability of software systems can be established. The gained knowledge from the experiments and assessments can then be used to forecast and optimize the energy and resource efficiency of software products. This enables developers, but also students, scientists and all other stakeholders involved in the life cycleof software, to continuously monitor and optimize the impact of their software on energy and resource consumption. The developed models, methods, and criteria were evaluated and validated by the scientific community at conferences and workshops. The central outcomes of this thesis, including a measurement reference model and the criteria catalog, were disseminated in academic journals. Furthermore, the transfer to society has been driven forward, e. g., through the publication of two book chapters, the development and presentation of exemplary best practices at developer conferences, collaboration with industry, and the establishment of the eco-label “Blue Angel” for resource and energy-efficient software products. In the long term, the objective is to effect a change in societal attitudes and ultimately to achieve significant resource savings through economies of scale by applying the methods in the development of software in general and AI systems in particular.

Globalization significantly transforms labor markets. Advances in production technologies, transportation, and political integration reshape how and where goods and services are produced. Local economic conditions and diverse policy responses create varying speeds of change, affecting regions' attractiveness for living and working -- and promoting mobility. Competition for talent necessitates a deep understanding of why individuals choose specific destinations, how to ensure their effective labor market integration, and what workplace factors affect workers' well-being. This thesis focuses on two crucial aspects of labor market change -- Migration and workplace technological change. It contributes to our understanding of the determinants of labor mobility, the factors facilitating migrant integration, and the role of workplace automation for worker well-being. Chapter 2 investigates the relationship between minimum wages (MWs) and regional worker mobility in the EU. EU citizens are free to work anywhere in the common market, which allows them to take advantage of the significant variation in MWs across the EU. However, although MWs are set at the national level, it is also their local relevance that varies substantially -- depending on factors such as the share of affected workers or the extent to which they shift local compensation levels. These variations may attract workers from elsewhere, from within a country or from abroad. Analyzing regional variations in the Kaitz index, a measure of local MW impact, reveals that higher MWs can significantly increase inflows of low-skilled EU workers, particularly in central Europe. Chapter 3 examines the inequality in returns to skills experienced by immigrants, focusing on the role of linguistic proximity between migrants' origin and destination countries. Harmonized individual-level data from nine linguistically diverse migrant-hosting economies allows for an analysis of the wage gaps faced by immigrants from various origins, implicitly indicating how well they and their skills are integrated into the local labor markets. The analysis reveals that greater linguistic distance is associated with a higher wage penalty for highly skilled immigrants and a lower position in the wage distribution for those without tertiary education. Chapter 4 investigates an institutional factor potentially relevant for the integration of immigrants -- the labor market impact of Confucius Institutes (CIs), Chinese government-sponsored institutions that promote Chinese language and culture abroad. CIs have been found to foster trade and cultural exchange, indicating their potential relevance in shaping attitudes and trust of natives towards China and Chinese individuals. Examining the relationship between local CI presence and the wages of Chinese immigrants in local labor markets of the United States, the analysis reveals that CIs associate with significantly reduced wages for nearby residing Chinese immigrants. An event study demonstrates that the mere announcement of a new CI negatively impacts local wages for Chinese immigrants, independent of the CI's actual opening. Chapter 5 explores how working in automatable jobs affects life satisfaction in Germany. Following earlier literature, we classify occupations by potential for automation, and define the top third of occupations in this metric as \textit{automatable jobs}. We find workers in highly automatable jobs reporting a lower life satisfaction. Moreover, we detect a non-linearity, where workers in moderately automatable jobs (the second third of the distribution) experience a positive association with life satisfaction. Overall, the negative relationship of automation is most pronounced among younger and blue-collar workers, irrespective of the non-linearity.

Case-Based Reasoning (CBR) is a symbolic Artificial Intelligence (AI) approach that has been successfully applied across various domains, including medical diagnosis, product configuration, and customer support, to solve problems based on experiential knowledge and analogy. A key aspect of CBR is its problem-solving procedure, where new solutions are created by referencing similar experiences, which makes CBR explainable and effective even with small amounts of data. However, one of the most significant challenges in CBR lies in defining and computing meaningful similarities between new and past problems, which heavily relies on domain-specific knowledge. This knowledge, typically only available through human experts, must be manually acquired, leading to what is commonly known as the knowledge-acquisition bottleneck. One way to mitigate the knowledge-acquisition bottleneck is through a hybrid approach that combines the symbolic reasoning strengths of CBR with the learning capabilities of Deep Learning (DL), a sub-symbolic AI method. DL, which utilizes deep neural networks, has gained immense popularity due to its ability to automatically learn from raw data to solve complex AI problems such as object detection, question answering, and machine translation. While DL minimizes manual knowledge acquisition by automatically training models from data, it comes with its own limitations, such as requiring large datasets, and being difficult to explain, often functioning as a "black box". By bringing together the symbolic nature of CBR and the data-driven learning abilities of DL, a neuro-symbolic, hybrid AI approach can potentially overcome the limitations of both methods, resulting in systems that are both explainable and capable of learning from data. The focus of this thesis is on integrating DL into the core task of similarity assessment within CBR, specifically in the domain of process management. Processes are fundamental to numerous industries and sectors, with process management techniques, particularly Business Process Management (BPM), being widely applied to optimize organizational workflows. Process-Oriented Case-Based Reasoning (POCBR) extends traditional CBR to handle procedural data, enabling applications such as adaptive manufacturing, where past processes are analyzed to find alternative solutions when problems arise. However, applying CBR to process management introduces additional complexity, as procedural cases are typically represented as semantically annotated graphs, increasing the knowledge-acquisition effort for both case modeling and similarity assessment. The key contributions of this thesis are as follows: It presents a method for preparing procedural cases, represented as semantic graphs, to be used as input for neural networks. Handling such complex, structured data represents a significant challenge, particularly given the scarcity of available process data in most organizations. To overcome the issue of data scarcity, the thesis proposes data augmentation techniques to artificially expand the process datasets, enabling more effective training of DL models. Moreover, it explores several deep learning architectures and training setups for learning similarity measures between procedural cases in POCBR applications. This includes the use of experience-based Hyperparameter Optimization (HPO) methods to fine-tune the deep learning models. Additionally, the thesis addresses the computational challenges posed by graph-based similarity assessments in CBR. The traditional method of determining similarity through subgraph isomorphism checks, which compare nodes and edges across graphs, is computationally expensive. To alleviate this issue, the hybrid approach seeks to use DL models to approximate these similarity calculations more efficiently, thus reducing the computational complexity involved in graph matching. The experimental evaluations of the corresponding contributions provide consistent results that indicate the benefits of using DL-based similarity measures and case retrieval methods in POCBR applications. The comparison with existing methods, e.g., based on subgraph isomorphism, shows several advantages but also some disadvantages of the compared methods. In summary, the methods and contributions outlined in this work enable more efficient and robust applications of hybrid CBR and DL in process management applications.

The goal of this work is to compare operators that are defined on probably varying Hilbert spaces. Distance concepts for operators as well as convergence concepts for such operators are explained and examined. For distance concepts we present three main notions. All have in common that they use space-linking operators that connect the spaces. At first, we look at unitary maps and compare the unitary orbits of the operators. Then, we consider isometric embeddings, which is based on a concept of Joachim Weidmann. Then we look at contractions but with more norm equations in comparison. The latter idea is based on a concept of Olaf Post called quasi-unitary equivalence. Our main result is that the unitary and isometric distances are equal provided the operators are both self-adjoint and have 0 in their essential spectra. In the third chapter, we focus specifically on the investigation of these distance terms for compact operators or operators in p-Schatten classes. In this case, the interpretation of the spectra as null sequences allows further distance investigation. Chapter four deals mainly with convergence terms of operators on varying Hilbert spaces. The analyses in this work deal exclusively with concepts of norm resolvent convergence. The main conclusion of the chapter is that the generalisation for norm resolvent convergence of Joachim Weidmann and the generalisation of Olaf Post, called quasi-unitary equivalence, are equivalent to each other. In addition, we specify error bounds and deal with the convergence speed of both concepts. Two important implications of these convergence notions are that the approximation is spectrally exact, i.e., the spectra converge suitably, and that the convergence is transferred to the functional calculus of the bounded functions vanishing at infinity.