TY - JOUR A1 - Fritsch, Markus A1 - Haupt, Harry A1 - Schnurbus, Joachim T1 - Efficiency of poll-based multi-period forecasting systems for German state elections JF - International Journal of Forecasting (Online ISSN: 1872-8200) N2 - Election polls are frequently employed to reflect voter sentiment with respect to a particular election (or fixed-event). Despite their widespread use as forecasts and inputs for predictive algorithms, there is substantial uncertainty regarding their efficiency. This uncertainty is amplified by judgment in the form of pollsters applying unpublished weighting schemes to ensure the representativeness of the sampled voters for the underlying population. Efficient forecasting systems incorporate past information instantly, which renders a given fixed-event unpredictable based on past information. This results in all sequential adjustments of the fixed-event forecasts across adjacent time periods (or forecast revisions) being martingale differences. This paper illustrates the theoretical conditions related to weak efficiency of fixed-event forecasting systems based on traditional least squares loss and asymmetrically weighted least absolute deviations (or quantile) loss. Weak efficiency of poll-based multi-period forecasting systems for all German federal state elections since the year 2000 is investigated. The inefficiency of almost all considered forecasting systems is documented and alternative explanations for the findings are discussed. KW - Fixed-event forecasting KW - Multiple lead times KW - Forecast efficiency KW - Weak efficiency concepts KW - Quantile loss KW - Election forecasting Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-18793 VL - 41 (2025) IS - 2 SP - 670 EP - 688 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Lechl, Michael A1 - de Meer, Hermann A1 - Fürmann, Tim T1 - A stochastic flexibility calculus for uncertainty-aware energy flexibility management JF - Applied Energy N2 - The increasing share of volatile renewables in power systems requires more reserves to balance forecast errors in renewable generation and power fluctuations. In contrast, common reserves such as gas-fired power plants are phased out, impeding the procurement of sufficient reserves. Alternative reserves, particularly on the demand side, such as battery storage systems, also exhibit some degree of freedom to deviate from their scheduled operating point to supply or consume more or less power, thus providing a flexibility potential. However, demand-side flexibility potentials are generally subject to uncertainties, and so is the generation of volatile renewables. The challenge is incorporating the uncertainties on both sides to procure sufficient (uncertain) flexibility potential in advance. Considering uncertainty is important to avoid additional, drastic measures in real-time to balance generation and demand, such as curtailing renewable generation or load shedding. This work presents a stochastic flexibility calculus that provides an indicator for computing the risk of insufficient flexibility potentials or, conversely, guarantees for sufficient flexibility potentials. Thus, the stochastic flexibility calculus contributes to overcoming the challenge of procuring sufficient flexibility potentials in renewable-based systems. An evaluation based on real data is performed using an example of a renewable energy community consisting of households equipped with photovoltaic power plants and battery storage systems. The newly introduced stochastic flexibility calculus computes the number of households that must operate their battery storage systems flexibly to balance forecast errors locally. The results show that the forecast method significantly influences this number. Some numerical results appear unexpected, as too many flexibility-friendly households can negatively impact the aggregated household flexibility potential. KW - Stochastic network calculus KW - Probabilistic flexibility guarantees KW - Power system flexibility KW - Renewable energy community KW - Uncertainty modeling KW - Battery storage system Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-19233 VL - 2025 IS - 379 ER - TY - JOUR A1 - Goerigk, Marc A1 - Kurtz, Jannis T1 - Data-driven prediction of relevant scenarios for robust combinatorial optimization JF - Computers & Operations Research N2 - We study iterative constraint and variable generation methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. The goal of this work is to find a set of starting scenarios that provides strong lower bounds early in the process. To this end we define the Relevant Scenario Recognition Problem (RSRP) which finds the optimal choice of scenarios which maximizes the corresponding objective value. We show for classical and two-stage robust optimization that this problem can be solved in polynomial time if the number of selected scenarios is constant and NP-hard if it is part of the input. Furthermore, we derive a linear mixed-integer programming formulation for the problem in both cases. Since solving the RSRP is not possible in reasonable time, we propose a machine-learning-based heuristic to determine a good set of starting scenarios. To this end, we design a set of dimension-independent features, and train a Random Forest Classifier on already solved small-dimensional instances of the problem. Our experiments show that our method is able to improve the solution process even for larger instances than contained in the training set, and that predicting even a small number of good starting scenarios can considerably reduce the optimality gap. Additionally, our method provides a feature importance score which can give new insights into the role of scenario properties in robust optimization. KW - Robust optimization KW - Two-stage robust optimization KW - Data-driven optimization KW - Machine learning for optimization Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-19207 SN - 1873-765X VL - 2025 IS - 174 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Łatuszyński, Krzysztof A1 - Rudolf, Daniel T1 - Convergence of hybrid slice sampling via spectral gap JF - Advances in Applied Probability N2 - It is known that the simple slice sampler has robust convergence properties; however, the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where another Markov chain approximately samples the uniform distribution on each slice. Under appropriate assumptions on the Markov chain on the slice, we give a lower bound and an upper bound of the spectral gap of the hybrid slice sampler in terms of the spectral gap of the simple slice sampler. An immediate consequence of this is that the spectral gap and geometric ergodicity of the hybrid slice sampler can be concluded from the spectral gap and geometric ergodicity of the simple version, which is very well understood. These results indicate that robustness properties of the simple slice sampler are inherited by (appropriately designed) easily implementable hybrid versions. We apply the developed theory and analyze a number of specific algorithms, such as the stepping-out shrinkage slice sampling, hit-and-run slice sampling on a class of multivariate targets, and an easily implementable combination of both procedures on multidimensional bimodal densities. KW - Slice sampler KW - spectral gap KW - geometric ergodicity Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-19264 SN - 1475-6064 VL - 56 (2024) IS - 4 SP - 1440 EP - 1466 PB - Cambridge University Press CY - Cambridge ER - TY - THES A1 - Danner, Julian T1 - SAT Solving Using XOR-OR-AND Normal Forms and Cryptographic Fault Attacks N2 - The Boolean satisfiability problem (SAT) lies at the core of computational logic and has found many applications in verification, cryptography, and artificial intelligence. While conflict-driven SAT solvers (CDCL) excel on large industrial instances, they struggle with XOR-rich instances arising frequently in cryptanalysis, due to the inefficiency of CNF encodings of linear constraints. Conversely, algebraic approaches can work with linear XOR constraints naturally but fail to scale to relevant sizes. Bridging these complementary paradigms with a focus on cryptographic problems is at the heart of this thesis. On one hand, this dissertation advances SAT solving by introducing the XOR-OR-AND normal form (XNF) as a generalization of the conjunctive normal form (CNF), where literals are replaced by XOR chains of literals. This allows for a native representation of XOR constraints. We generalize the CDCL architecture to the richer language of XNFs. The underlying reasoning based on the proof system SRES which is shown to be exponentially stronger than classical resolution. An implementation demonstrates competitive performance and often surpasses state-of-the-art algebraic and logic solvers on random and cryptographic benchmarks. Furthermore, we prove that every XNF formula can be converted in polynomial time to a formula in 2-XNF, enabling a graph-based approach similar to 2-SAT. Building on this, we propose advanced in- and pre-processing techniques, and construct a simple DPLL-based solving framework. Our implementation, 2-Xornado, outperforms modern algebraic and logic solving approaches on many random and some structured cryptographic problems. On the other hand, we apply combined algebraic and logical techniques to cryptanalysis of stream ciphers. We introduce a formal guess-and-determine (GD) framework using a logical abstraction of the information flow in the internal state. From an algebraic point of view, we can then find optimal GD attacks utilizing a Gröbner basis. As a case study, we apply this method to aid in the construction of novel fault attacks on the ciphers KCipher-2 and Enocoro-128v2. Using ad hoc methods combining algebraic and logical approaches, we show that both ciphers are vulnerable to active side-channel attacks under rather weak fault models. Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-19171 ER - TY - THES A1 - Ellinger, Simon T1 - On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients N2 - In this dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, such as the Euler-Maruyama scheme or a transformed Milstein scheme, for classes of piecewise Lipschitz continuous, Hölder continuous and Sobolev regular drift coefficients. To do this, we derive the optimal error rates for the different classes of irregular drift coefficients. Furthermore, we show that the solution of an SDE with piecewise Hölder continuous drift coefficient has a regular local density, which is used in the proofs of the lower bounds. KW - Complexity KW - Error rates KW - Stochastic differential equations KW - Non-Lipschitz drift coefficient KW - Strong approximation KW - Lower error bounds Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-19634 ER - TY - THES A1 - Khosravi, Mohammad T1 - Hard Instances, Improved Algorithms and New Interdiction Models for Robust Optimization N2 - Robust combinatorial optimization seeks solutions that remain effective across all possible realizations of an uncertainty set, making the choice of this set a crucial factor in both the complexity and practical applicability of robust models. A key challenge in this field is striking a balance between computational tractability and solution quality, particularly when dealing with large uncertainty sets. This dissertation advances the field of robust optimization by addressing three central themes: (i) methods for generating hard instances and establishing a benchmark library, (ii) high-quality exact solution methods and approximation algorithms, and (iii) the modeling of uncertainty sets and their impact on problem complexity. The absence of a benchmark library for robust optimization problems makes it difficult to conduct fair and effective comparisons of different solution methods. As a result, researchers often rely on randomly generated instances, which may hinder meaningful evaluations. To address this issue, this work develops optimization-based and heuristic methods for generating challenging instances of robust problems. Additionally, to facilitate more consistent and insightful comparisons of solution algorithms with minimal effort, we introduce a standardized benchmark library for use by the research community. To tackle the computational challenges posed by large uncertainty sets, this dissertation proposes scenario reduction techniques specifically designed for robust optimization. These methods aim to reduce the size of the uncertainty set while preserving the objective value as accurately as possible. Unlike traditional clustering approaches, this formulation treats scenario reduction as an optimization problem independent of the underlying decision-making model, enabling structured reductions with theoretical performance guarantees. Experimental results demonstrate that this approach produces solutions of comparable or superior quality compared to those obtained through general-purpose clustering techniques. Building on this framework, we further refine scenario reduction by incorporating information about the structure of feasible solutions. While previous reduction methods focused exclusively on the uncertainty set, we show that integrating knowledge of feasible solutions leads to improved uncertainty sets and more accurate robust models. Through a combination of theoretical analysis and computational experiments, we establish the effectiveness of this approach in enhancing both tractability and solution quality in robust combinatorial optimization. Finally, we introduce a novel variant of discrete budgeted uncertainty for cardinality-based constraints or objectives, incorporating a weight vector into the budget constraint. Our theoretical analysis reveals that while the adversarial problem can be solved in linear time, the robust problem becomes NP-hard and non-approximable. Nonetheless, we propose and evaluate alternative modeling approaches that demonstrate promising scalability in practice. This dissertation contributes to robust optimization by offering new perspectives on uncertainty modeling, algorithmic techniques for scenario reduction, and complexity analyses of key robust problems. The proposed methods provide both theoretical guarantees and practical advancements, paving the way for more efficient and scalable robust optimization models. Y1 - 2026 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus4-20399 ER -