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Gray Wolf Optimization (GWO), inspired by the social hierarchy and cooperative hunting behavior of gray wolves, is a widely used metaheuristic algorithm for solving complex optimization problems in various domains, including engineering design, image processing, and machine learning. However, standard GWO can suffer from premature convergence and sensitivity to parameter settings. To address these limitations, this paper introduces the Hierarchical Multi-Step Gray Wolf Optimization (HMS-GWO) algorithm. HMS-GWO incorporates a novel hierarchical decision-making framework that more closely mimics the observed hierarchical behavior of wolf packs, enabling each wolf type (Alpha, Beta, Delta, and Omega) to execute a structured multi-step search process. This hierarchical approach enhances exploration and exploitation, improves solution diversity, and prevents stagnation. The performance of HMS-GWO is evaluated on a benchmark suite of 23 functions, showing a 99% accuracy, with a computational time of 3 s and a stability score of 0.9. Compared to other advanced optimization techniques such as standard GA, PSO, MMSCC-GWO, WCA, and CCS-GWO, HMS-GWO demonstrates significantly better performance, including faster convergence and improved solution accuracy. While standard GWO suffers from premature convergence, HMS-GWO mitigates this issue by employing a multi-step search process and better solution diversity. These results confirm that HMS-GWO outperforms other techniques in terms of both convergence speed and solution quality, making it a promising approach for solving complex optimization problems across various domains with enhanced robustness and efficiency.

Modern active distribution networks are increasingly characterized by high complexity, uncertainty, and distributed clustering, posing challenges for traditional model-based simulations in capturing nonlinear dynamics and stochastic variations. This study develops a data–model hybrid-driven simulation architecture that integrates a Federated Evolutionary Monte Carlo Optimization (FEMCO) algorithm for distribution network optimization. The model-driven module employs spectral clustering to decompose the network into multiple autonomous subsystems and performs distributed reconstruction through gradient descent. The data-driven module, built upon Long Short-Term Memory (LSTM) networks, learns temporal dependencies between load curves and operational parameters to enhance predictive accuracy. These two modules are fused via a Random Forest ensemble, while FEMCO jointly leverages Monte Carlo global sampling, Federated Learning-based distributed training, and Genetic Algorithm-driven evolutionary optimization. Simulation studies on the IEEE 33 bus distribution system demonstrate that the proposed framework reduces power losses by 25–45% and voltage deviations by 75–85% compared with conventional Genetic Algorithm and Monte Carlo approaches. The results confirm that the proposed hybrid architecture effectively improves convergence stability, optimization precision, and adaptability, providing a scalable solution for the intelligent operation and distributed control of modern power distribution systems.

Distributed energy technologies are gaining popularity nowadays; however, due to the highly intermittent characteristics of distributed energy resources, a larger penetration of these resources into the distribution grid network becomes of major concern. The main issue is to cope with the intermittent nature of the renewable sources alongside the requirements for power quality and system stability. Unlike traditional power systems, the control and optimization of complex energy systems comprising of wind, solar, thermal, and energy storage becomes difficult in many aspects, such as modelling, integration, operation, coordination and planning etc. This means that energy conversion as per the standards imposed by the energy market is unachievable without adequate control, management, and optimization. This edited book serves as a resource for the engineers, scientists and professionals working on distributed energy systems. The book is an extensive collection of state-of-the-art studies on advanced control paradigms for complex energy systems, with emphasis on the optimization and management of the high penetration of distributed energy resources into power distribution networks. Readers will find the book inspiring and useful whilst carrying out their own research in distributed energy systems. Key features: • An extensive collection of state-of-the-art studies on advanced control paradigms for complex energy systems. • Emphasis on the optimization and management of high penetration of distributed energy resources into power/energy distribution networks. • Serves as a valuable resource for engineers, scientists, academicians, experienced professionals, and research scholars who are working in management of energy systems.

The model of voting originated social dynamics in a stochastic environment (the ViSE model) is considered. Within this model, the influence of the heaviness of distribution tails on the effectiveness of egoistic and altruistic strategies in terms of maximizing two criteria, the average capital increment and the number of non-bankrupt participants, is investigated. Homogeneous societies and four types of distributions used to generate proposals (Gaussian, logistic, Student’s with 3 degrees of freedom, and symmetrized Pareto distributions) are studied. To assess the effect of tail heaviness, all distributions are unified by quartile using scatter. Such an approach can be used to compare the heavy-tailed distributions that are commensurable by density with other distributions under consideration on an interval containing 90% of observations.

We have theoretically and experimentally demonstrated an RF compression-based jitter-amplification effect in high-brightness electron source ultrafast electron diffraction (UED), which degrades the temporal resolution significantly. A detailed analysis and simulations reveal the crucial role of the longitudinal and transverse Coulomb interaction for this jitter-amplification effect, which accord very well with experimental results. An optimized compact UED structure for full compression has been proposed, which can suppress the jitter by half and improve the temporal resolution to sub-100 fs. This Coulomb interaction-induced jitter amplification exists in nearly the whole ultrafast physics field where laser-electron synchronization is required. Moreover, it cannot be suppressed completely. The quantified explanation for the mechanism and optimization provides important guidance for photocathode accelerators and other compression-based ultrashort electron pulse generation and precise control.

In next-generation wireless communication systems, non-orthogonal multiple access (NOMA) has been recognized as essential technology for improving the spectrum efficiency. NOMA allows multiple users transmit data using the same resource block simultaneously with proper user pairing. Most of the pairing schemes, however, require prior information, such as location information of the users, leading to difficulties in realizing prompt user pairing. To realize real-time operations without prior information in NOMA, a bandit algorithm using chaotically oscillating time series, which we refer to as the laser chaos decision-maker, was demonstrated. However, this scheme did not consider the detailed communication processes, e.g., modulation, error correction code, etc. In this study, in order to adapt the laser chaos decision-maker to real communication systems, we propose a user pairing scheme based on acknowledgment (ACK) and negative acknowledgment (NACK) information considering detailed communication channels. Furthermore, based on the insights gained by the analysis of parameter dependencies, we introduce an adaptive pairing method to minimize the bit error rate of the NOMA system under study. The numerical results show that the proposed method achieves superior performances than the traditional using pairing schemes, i.e., Conventional-NOMA pairing scheme (C-NOMA) and Unified Channel Gain Difference pairing scheme (UCGD-NOMA), and ϵ-greedy-based user pairing scheme. As the cell radius of the NOMA system gets smaller, the superior on the BER of our proposed scheme gets bigger. Specifically, our proposed scheme can decrease the BER from 10−1 to 10−5 compared to the conventional schemes when the cell radius is 400 m.

Digital Twin (DT) refers to the virtual copy or model of any physical entity (physical twin) both of which are interconnected via exchange of data in real time. Conceptually, a DT mimics the state of its physical twin in real time and vice versa. Application of DT includes real-time monitoring, designing/planning, optimization, maintenance, remote access, etc. Its implementation is expected to grow exponentially in the coming decades. The advent of Industry 4.0 has brought complex industrial systems that are more autonomous, smart, and highly interconnected. These systems generate considerable amounts of data useful for several applications such as improving performance, predictive maintenance, training, etc. A sudden influx in the number of publications related to ‘Digital Twin’ has led to confusion between different terminologies related to the digitalization of industries. Another problem that has arisen due to the growing popularity of DT is a lack of consensus on the description of DT as well as so many different types of DT, which adds to the confusion. This paper intends to consolidate the different types of DT and different definitions of DT throughout the literature for easy identification of DT from the rest of the complimentary terms such as ‘product avatar’, ‘digital thread’, ‘digital model’, and ‘digital shadow’. The paper looks at the concept of DT since its inception to its predicted future to realize the value it can bring to certain sectors. Understanding the characteristics and types of DT while weighing its pros and cons is essential for any researcher, business, or sector before investing in the technology.

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

We consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost In this paper we show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set The analysis requires (1) (2) (3) (4)

Change points are a very common feature of 'big data' that arrive in the form of a data stream. We study high dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the co-ordinates. The challenge is to borrow strength across the co-ordinates to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called inspect for estimation of the change points: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimization problem derived from the cumulative sum transformation of the time series. We then apply an existing univariate change point estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated change points and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data-generating mechanisms. Software implementing the methodology is available in the R package InspectChangepoint.