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Keywords = improved grey wolf optimizer

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24 pages, 4947 KB  
Article
A GWO–Fisher Hybrid Model for Rapid and Interpretable Mine Water Inrush Source Identification with Multi-Spring Domain Validation
by Hongfu Sun, Yihao Zhang, Jie He, Wenxi Wu, Shu Wang, Kongyu Zhao and Fenghua Zhao
Water 2026, 18(15), 1813; https://doi.org/10.3390/w18151813 - 26 Jul 2026
Abstract
Rapid and accurate identification of mine water inrush sources is critical for hazard control in underground coal mining. Conventional Fisher discriminant analysis is often limited by feature redundancy and multicollinearity when applied to small-sample, high-dimensional hydrochemical data. To address this, we propose GWO–Fisher, [...] Read more.
Rapid and accurate identification of mine water inrush sources is critical for hazard control in underground coal mining. Conventional Fisher discriminant analysis is often limited by feature redundancy and multicollinearity when applied to small-sample, high-dimensional hydrochemical data. To address this, we propose GWO–Fisher, a hybrid model integrating the Grey Wolf Optimizer (GWO) with Fisher discriminant analysis. The model employs correlation-based pre-screening followed by global optimization, using a fitness function that combines Fisher accuracy with a feature-size penalty, to achieve a compact and interpretable feature set. Trained on data from the Xiegou Coal Mine (Shanxi, China), it reduced 17 hydrochemical indicators to 12 key features, achieving 92.98% training accuracy and 86.21% test accuracy—an improvement of 10.35 percentage points over conventional Fisher. When independently validated across four mines in three spring domains, the model maintained over 83% accuracy, consistently selecting TDS, K+, and HCO3 as core features. Misclassification patterns were cross-domain consistent and linked to hydrogeological conditions. The proposed GWO–Fisher model balances predictive accuracy with hydrogeological interpretability, demonstrating reliable performance across both single-mine and cross-spring-domain scenarios. Full article
(This article belongs to the Section Hydrology)
45 pages, 783 KB  
Article
Optimal Placement of Sectionalizing Devices in Radial Distribution Networks for Reliability Improvement Using the Aquila Optimizer
by Juan José Gaibor Fierro, Alexander Aguila Téllez and Manuel Darío Jaramillo Monge
Energies 2026, 19(15), 3472; https://doi.org/10.3390/en19153472 - 23 Jul 2026
Viewed by 156
Abstract
Radial distribution networks are highly exposed to sustained service interruptions because faults occurring along upstream feeder sections can affect large groups of downstream customers. This condition motivates the development of cost-effective planning strategies capable of reducing expected energy not supplied (EENS) and improving [...] Read more.
Radial distribution networks are highly exposed to sustained service interruptions because faults occurring along upstream feeder sections can affect large groups of downstream customers. This condition motivates the development of cost-effective planning strategies capable of reducing expected energy not supplied (EENS) and improving reliability indices such as the System Average Interruption Frequency Index (SAIFI), System Average Interruption Duration Index (SAIDI), and Customer Average Interruption Duration Index (CAIDI). This study formulates the optimal placement of sectionalizing devices as a binary combinatorial optimization problem in which the objective function minimizes the total expected cost, defined as the sum of customer interruption cost and the annualized investment and installation cost of the selected devices. The formulation considers candidate-branch eligibility, the maximum number of devices, the available investment budget, and the maximum allowable restoration time, while preserving the radial topology of the base feeder by construction. The Aquila Optimizer (AO) is implemented and compared with the Grey Wolf Optimizer (GWO) and a hybrid Genetic Algorithm–Particle Swarm Optimization (GA-PSO) algorithm using the IEEE 69-bus test system under identical population size, iteration budget, number of independent runs, and pseudo-random seed conditions. The results show that the best identified installation of eight sectionalizing devices reduces SAIDI by approximately 58% and the total expected cost by nearly 50% with respect to the base case. SAIFI remains unchanged because the analyzed radial configuration does not include load-transfer paths; therefore, sectionalizing primarily reduces interruption duration rather than interruption frequency. The three algorithms reached solutions of comparable quality around the best identified configuration. GWO exhibited the highest robustness, AO showed a slightly lower computational time than GWO under the adopted MATLAB R2025b-based evaluator, and GA-PSO converged to the same best identified configuration found by GWO. These findings indicate that AO is a competitive computational alternative for sectionalizing-device placement and that a moderate investment in sectionalizing infrastructure can support economically justified reliability improvements in radial distribution networks. Full article
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24 pages, 1666 KB  
Article
DGWO: A Deep Reinforcement Learning-Driven Grey Wolf Optimizer for Feature Selection in Network Intrusion Detection Systems
by Qianqian Zhang, Ting Shu and Jinsong Xia
Symmetry 2026, 18(8), 1249; https://doi.org/10.3390/sym18081249 - 23 Jul 2026
Viewed by 185
Abstract
With the continuous evolution of network attack techniques, efficiently selecting the most discriminative feature subset from massive network traffic data has become a key issue for improving the performance of intrusion detection systems. Metaheuristic algorithms, as a core approach for wrapper-based feature selection, [...] Read more.
With the continuous evolution of network attack techniques, efficiently selecting the most discriminative feature subset from massive network traffic data has become a key issue for improving the performance of intrusion detection systems. Metaheuristic algorithms, as a core approach for wrapper-based feature selection, directly determine the quality of the selected feature subset through their optimization capability. The Grey Wolf Optimizer (GWO) is popular due to its simple structure and few parameters, where three leader wolves guide the search through weighted cooperation. However, its static weight mechanism cannot adapt to dynamic changes in individual search states and population evolution stages, limiting optimization capability and convergence performance. To address this issue, this study proposes a Deep Reinforcement Learning-based Grey Wolf Optimizer (DGWO), which pre-trains a weight adjustment decision model offline and dynamically adjusts the guiding weights of leader wolves during the online search process, thereby improving the optimization ability of the algorithm. Experimental results on NSL-KDD, UNSW-NB15, and CIC-IDS-2017 datasets show that DGWO outperforms seven comparative feature selection methods. It achieves classification accuracies of 93.59%, 93.40%, and 94.84%, respectively, demonstrating superior performance in accuracy, precision, recall, and F1-score. DGWO promotes symmetry between cybersecurity requirements and reliable intrusion detection. Full article
(This article belongs to the Section A: Computer Science)
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22 pages, 5757 KB  
Article
Accelerating the Design of Double-Absorber Solar Cells: From Surrogate Model-Assisted Reinforcement Learning and Multi-Algorithm Optimization Comparison to Transfer Learning
by Yuhan Zhang, Qiaochu Sun and Jiang Zhao
Materials 2026, 19(14), 3091; https://doi.org/10.3390/ma19143091 - 17 Jul 2026
Viewed by 242
Abstract
Lead-free double-absorber perovskite solar cells offer broad-spectrum absorption and environmental benefits, but their multilayer heterostructure creates computational challenges for conventional design optimization. This study introduces an automated framework integrating SCAPS-1D simulation, multilayer perceptron (MLP) surrogate modeling, metaheuristic algorithms, and reinforcement learning (RL). Using [...] Read more.
Lead-free double-absorber perovskite solar cells offer broad-spectrum absorption and environmental benefits, but their multilayer heterostructure creates computational challenges for conventional design optimization. This study introduces an automated framework integrating SCAPS-1D simulation, multilayer perceptron (MLP) surrogate modeling, metaheuristic algorithms, and reinforcement learning (RL). Using FTO/ZnO/Cs2TiBr6/RbGeI3/CuI/Au cells, the MLP model trained on Latin hypercube sampling data achieved high accuracy (R2 > 0.95). The proximal policy optimization (PPO) RL agent converged to 27.41% power conversion efficiency (PCE) in approximately 20 steps. For direct 15-dimensional optimization, simulated annealing and particle swarm optimization reached 98% target PCE with 138 and 111 function evaluations, respectively, while Grey Wolf Optimizer (GWO) yielded the highest average PCE. Transfer learning successfully adapted the pretrained model to a novel FASnI3/Sb2S3 structure, improving the prediction accuracy of PCE, JSC, and FF. This work systematically optimizes Cs2TiBr6/RbGeI3 solar cells while establishing an efficient, generalizable paradigm for intelligent photovoltaic device design, validation, and material discovery. Full article
(This article belongs to the Section Energy Materials)
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24 pages, 18515 KB  
Article
Wind Turbine Blade Fault Diagnosis Integrating Multi-Scale Enhanced Hierarchical Fuzzy Entropy, Isolation Forest and GWO-GRU
by Min Wang, Xiao-Fei Zhang, Guo-Jun Qin and Ming Liu
Entropy 2026, 28(7), 810; https://doi.org/10.3390/e28070810 - 16 Jul 2026
Viewed by 229
Abstract
To effectively extract fault characteristics from complex vibration signals and improve the diagnostic performance of deep learning networks, this paper introduces a wind turbine blade fault diagnosis method that combines Multi-scale Enhanced Hierarchical Fuzzy Entropy (MEHFE), Isolation Forest, and the Grey Wolf Optimization [...] Read more.
To effectively extract fault characteristics from complex vibration signals and improve the diagnostic performance of deep learning networks, this paper introduces a wind turbine blade fault diagnosis method that combines Multi-scale Enhanced Hierarchical Fuzzy Entropy (MEHFE), Isolation Forest, and the Grey Wolf Optimization (GWO) algorithm for optimizing the Gated Recurrent Unit (GRU). Initially, the MEHFE algorithm is applied to decompose and reconstruct three-directional vibration signals at the blade root, thereby extracting “scale-frequency” dual-dimensional features that represent the evolution of fault frequency structure and complexity across multiple scales. Subsequently, Isolation Forest is employed to assess and filter feature importance, constructing an optimal feature subset to mitigate redundancy and noise interference. Finally, the optimal features are fed into the GRU network for fault pattern recognition, and the GWO algorithm is utilized to adaptively optimize network hyperparameters, thereby enhancing classification accuracy and noise resilience. Simulation experiments on typical wind turbine blade faults reveal that when GRU serves as the classifier, the diagnostic accuracy of MEHFE exceeds 76%. After feature optimization with Isolation Forest and network parameter optimization with GWO, the diagnostic accuracy surpasses 93%, demonstrating notable advantages in both classification capability and stability. Even under conditions of noise interference, the accuracy remains above 90%. The research substantiates that the proposed method can effectively extract pattern information indicative of blade structural damage from vibration data, achieving high fault recognition accuracy and robustness. Full article
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37 pages, 5096 KB  
Article
Dynamic Dual-Mutation Strategy-Based Grey Wolf Optimizer for Solving Discrete Wind Farm Layout Optimization Problem
by Pengfei Wang, Hua Qin, Rufa Zhao, Haodong Wang, Feifei Li and Shaonan Chen
Electronics 2026, 15(14), 3122; https://doi.org/10.3390/electronics15143122 - 15 Jul 2026
Viewed by 180
Abstract
Discrete wind farm layout optimization (WFLO) involves discontinuous and highly combinatorial solution spaces, where existing swarm intelligence methods exhibit weak discrete local search and aerodynamic adaptability, limiting power generation and cost efficiency improvements. This study proposes a dynamic dual-mutation strategy-based grey wolf optimizer [...] Read more.
Discrete wind farm layout optimization (WFLO) involves discontinuous and highly combinatorial solution spaces, where existing swarm intelligence methods exhibit weak discrete local search and aerodynamic adaptability, limiting power generation and cost efficiency improvements. This study proposes a dynamic dual-mutation strategy-based grey wolf optimizer (DDMS-GWO) to solve discrete WFLO problems. The method utilizes three leading grey wolves for local search, integrating a Hadamard product mutation strategy for elite gene recombination to preserve favorable aerodynamic topologies, and an elite pool-guided differential mutation strategy to enrich population diversity and avoid premature convergence. The two mutation strategies are adaptively scheduled through a dynamic probability, while a first-order exponential smoothing mechanism is employed to stabilize iterative control parameters. DDMS-GWO was validated against nine baseline algorithms across three wind scenarios. Results demonstrate that DDMS-GWO achieves superior normalized cost of energy (CoE), total power output, and overall efficiency. Specifically, in Scenarios 2 and 3, it improves total power output by up to 0.98% and 1.85% while reducing average CoE by up to 1.72% and 2.42%, respectively. Further analyses of convergence, layout topology, and probability-weighted wake exposure confirm that DDMS-GWO generates more coordinated layouts with reduced wake exposure and enhanced aerodynamic rationality. Full article
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42 pages, 7382 KB  
Article
Glide Trajectory Optimization of Guided Projectiles Using an Improved Grey Wolf Optimizer and hp-Adaptive Radau Pseudospectral Method
by Chen Zhao, Yuhao Wu and Jun Guan
Aerospace 2026, 13(7), 644; https://doi.org/10.3390/aerospace13070644 - 15 Jul 2026
Viewed by 192
Abstract
This study proposes an NSL-GWO-hpRPM framework for constrained glide trajectory optimization of guided projectiles. The method combines an improved Grey Wolf Optimizer with the hp-adaptive Radau pseudospectral method to reduce the dependence of hpRPM on initial guesses and improve global search performance. In [...] Read more.
This study proposes an NSL-GWO-hpRPM framework for constrained glide trajectory optimization of guided projectiles. The method combines an improved Grey Wolf Optimizer with the hp-adaptive Radau pseudospectral method to reduce the dependence of hpRPM on initial guesses and improve global search performance. In the improved GWO, Sobol low-discrepancy sequence initialization is used to enhance population diversity, a nonlinear convergence strategy is introduced to balance exploration and exploitation, and Levy flight is adopted to improve the ability to escape local optima. The optimized solution obtained by NSL-GWO is then used as the initial guess for hpRPM to achieve high-precision local refinement. Simulation results show that the proposed NSL-GWO-hpRPM achieves a feasible range of 71,211.514 m, improving the range by 4.53% over hpRPM and 1.48% over GWO-hpRPM. Statistical results from 35 independent runs further demonstrate that the proposed method obtains the best mean range, Friedman mean rank, and significant Wilcoxon test results with p<0.001. The optimized trajectory reaches a maximum range of approximately 71.2 km with an optimal launch angle of 62.4 while satisfying all flight constraints, indicating that the proposed framework is effective for complex constrained glide trajectory optimization. Full article
(This article belongs to the Special Issue Advanced Navigation, Guidance, and Control for Aerospace Vehicles)
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29 pages, 4574 KB  
Article
A Novel Vibration Centroid-Based Approach for Fault Diagnosis of Transformer Winding
by Bo Ren, Peidong Gao, Fenghua Wang, Linzhi Zhang, Teng Yi and Chengxiang Liu
Energies 2026, 19(14), 3329; https://doi.org/10.3390/en19143329 - 14 Jul 2026
Viewed by 180
Abstract
Tank vibrations of a power transformer, originating primarily from winding vibration and core vibration through mechanical coupling and fluid–structure interaction, are regarded as essential carrier signals for assessing the integrity of the winding. To improve the diagnostic accuracy of winding condition, this paper [...] Read more.
Tank vibrations of a power transformer, originating primarily from winding vibration and core vibration through mechanical coupling and fluid–structure interaction, are regarded as essential carrier signals for assessing the integrity of the winding. To improve the diagnostic accuracy of winding condition, this paper presents a vibration centroid-based diagnostic model that integrates feature fusion from vibration signals. According to the frequency spectrum of vibration signals obtained using Zoom-FFT, a set of new spatial vibration feature vectors—namely vibration centroid coordinates and Boyce-Clark shape index—were defined. This approach converts spatially distributed vibration signals into compact and discriminate indicators. A diagnostic model was subsequently constructed by integrating the grey wolf optimization (GWO) algorithm with the least squares support vector machine (LSSVM), ensuring that optimal classification performance was achieved. No-load, short-circuit, and load tests were made on a 35 kV-rated oil-immersed transformer. During the experiments, the transformer winding was divided into four categories: healthy condition, winding looseness, axial deformation, and radial deformation. The proposed GWO-LSSVM-based classifier was trained and tested using the defined vibration feature vectors. The results indicate that the proposed method achieves superior performance, with a recognition rate of 98.44%, and offers high efficiency. Full article
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25 pages, 10859 KB  
Article
Optimal Design of Non-Linear Fuzzy Inference Controllers via Black-Backed Jackal Optimization: A New Robust Bio-Inspired Framework for Industrial and Autonomous Systems
by Omar Bahou, Karim El Moutaouakil and Savin Treanţă
Algorithms 2026, 19(7), 566; https://doi.org/10.3390/a19070566 - 10 Jul 2026
Viewed by 200
Abstract
This study introduces the ’Black-Backed Jackal Optimization’ (BBJO), a nature-inspired meta-heuristic algorithm designed for complex, non-linear, and high-dimensional search spaces. The fundamental mathematical model of BBJO relies on the opportunistic hunting behavior and survivability strategies of the black-backed jackal (Lupulella mesomelas). [...] Read more.
This study introduces the ’Black-Backed Jackal Optimization’ (BBJO), a nature-inspired meta-heuristic algorithm designed for complex, non-linear, and high-dimensional search spaces. The fundamental mathematical model of BBJO relies on the opportunistic hunting behavior and survivability strategies of the black-backed jackal (Lupulella mesomelas). We use non-linear energy decrease and adaptive Lévy flight to maintain the equilibrium of the search. This allows the algorithm to scan large areas first, then zoom in with a high degree of precision once it has identified a suitable location. This configuration prevents the algorithm from getting stuck on a suboptimal local solution, which is a frequent danger during searches in complex spaces. BBJO has been validated against 23 standard benchmark functions, demonstrating significantly greater accuracy than Particle Swarm Optimization (PSO) on complex and large-scale search spaces. On fixed-size domains (F21F23), the BBJO algorithm achieved a 100% success rate with zero standard deviation, surpassing the Grey Wolf Optimizer (GWO) and Differential Evolution (DE), which frequently suffered from structural stagnation. Visual convergence study shows that BBJO efficiently identifies optimal search regions early in the iteration budget, saving time compared to traditional linear decay models. BBJO optimizes fuzzy inference systems (FISs) for two practical applications: autonomous car speed control and industrial furnace regulation. Experimental results indicate that BBJO significantly decreased cumulative penalties and improved steady-state error reduction compared to baseline configurations and established meta-heuristic methods. The results show that BBJO is a reliable and useful technique for engineering optimization. Full article
(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)
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28 pages, 2895 KB  
Article
Tunnel Water Inflow Prediction Using CatBoost and Comparative Hyperparameter Optimization Strategies
by Weibin Wu, Wenrui Guo, Wenrui Wang, Jinbo Chen, Zongqing Zhou, Huaqing Ma and Songsong Bai
Appl. Sci. 2026, 16(14), 6882; https://doi.org/10.3390/app16146882 - 9 Jul 2026
Viewed by 230
Abstract
Accurate prediction of tunnel water inflow in water-rich fault zones is important for groundwater control design and construction risk prevention. In this study, a per-linear-meter tunnel water inflow database containing 425 valid samples was established through orthogonal numerical simulations based on a three-dimensional [...] Read more.
Accurate prediction of tunnel water inflow in water-rich fault zones is important for groundwater control design and construction risk prevention. In this study, a per-linear-meter tunnel water inflow database containing 425 valid samples was established through orthogonal numerical simulations based on a three-dimensional steady-state seepage model with a grouting ring. The input variables included four hydraulic and grouting parameters and two excavation-position descriptors, namely the excavation-position distance and excavation-position category, thereby reflecting both the water-blocking effect of grouting reinforcement and the spatial variation in water inflow as the excavation face approached the fault zone. Considering that the samples were generated from 25 orthogonal simulation cases at different excavation positions, grouped validation was adopted to reduce information leakage at the simulation-case level. Four baseline machine learning models, including SVM, RF, XGBoost, and CatBoost, were evaluated using ten repeated grouped hold-out validations. CatBoost achieved the best overall baseline generalization performance, with an average test R2 of 0.6209 ± 0.0405, MAE of 0.1084 ± 0.0079, and RMSE of 0.1555 ± 0.0085. CatBoost was therefore selected for further hyperparameter optimization. Subsequently, random search, Bayesian optimization, the Osprey Optimization Algorithm, and the Grey Wolf Optimizer were compared under the same search space and computational budget. Hyperparameter optimization was conducted only within the training set using grouped cross-validation, and the independent grouped test set was used only for final evaluation. The results showed that the unoptimized CatBoost model achieved the best overall balance between prediction accuracy, stability, and computational efficiency. Although RS-CatBoost slightly improved MAE and MAPE among the optimized models, none of the optimization strategies consistently outperformed the unoptimized CatBoost baseline, indicating that the choice of hyperparameter optimization algorithm played a secondary role under the current dataset and grouped-validation framework. The proposed framework is intended as a preliminary modeling reference under controlled numerical simulation conditions, and its practical engineering reliability requires further validation using field monitoring data or independent benchmark cases. Full article
(This article belongs to the Section Civil Engineering)
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27 pages, 2302 KB  
Article
Adaptive Ensemble Clustering Using Meta-Heuristics-Algorithms for Global Navigation Satellite System (GNSS) Line of Sight (LOS)/Non Line of Sight (NLOS) Classification
by Gianmarco Baldini and Fausto Bonavitacola
Algorithms 2026, 19(7), 554; https://doi.org/10.3390/a19070554 - 7 Jul 2026
Viewed by 252
Abstract
Global Navigation Satellites Systems (GNSSs) have become a predominant feature in the digital life of citizens, and they provide positioning services in various applications including pedestrian and vehicular navigation. In urban environments with the presence of buildings and another obstacles, GNSS positioning may [...] Read more.
Global Navigation Satellites Systems (GNSSs) have become a predominant feature in the digital life of citizens, and they provide positioning services in various applications including pedestrian and vehicular navigation. In urban environments with the presence of buildings and another obstacles, GNSS positioning may be unreliable because of non-line-of-sight (NLOS) conditions, and the classification of observed satellite visibility between LOS and NLOS may improve GNSS receivers to improve their performance to provide the positioning services. In this context, machine learning algorithms using features like signal noise ratio, pseudorange, elevation angle, and others have been applied to this problem both in supervised and unsupervised mode. Because the ground truth information on LOS/NLOS conditions may not always be available, unclustering algorithms have been applied for unsupervised classification, but the classification performance is still limited. This paper proposes an ensemble approach where different clustering algorithms, both historical and recently introduced in the literature, are combined to improve the LOS/NLOS classification accuracy. Even if the ensemble approach manages to achieve a significant improvement, a novel and more sophisticated approach is proposed in this paper, where the contributions of each clustering algorithm are weighted. The optimal values of the weights are estimated using various Meta-Heuristics Algorithms (MHA) on a subset of GNSS data where the ground-truth information is available (i.e., labeled data set). In a subsequent step, the performance of the optimal weighted clustering ensemble is evaluated. The approach is applied to a recent public data set with 57 satellites, where it is shown to outperform the specific clustering approaches by a large margin (more than 7%). The Meta Heuristics Algorithm (MHA)s have similar performance, with the Dynamic Opposition Grey Wolf Optimization (DOLGWO) having a minor advantage against the other MHAs. Full article
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26 pages, 4295 KB  
Article
A Reinforcement-Learning-Driven Multi-Strategy Spherical-Vector Grey Wolf Optimizer for UAV 3D Path Planning
by Anna Li and Yanqiang Yang
Biomimetics 2026, 11(7), 470; https://doi.org/10.3390/biomimetics11070470 - 5 Jul 2026
Viewed by 281
Abstract
Unmanned aerial vehicles (UAVs) have been widely used in surveying and mapping, inspection, emergency rescue, and environmental monitoring. However, effective path planning remains a key challenge in complex three-dimensional terrain, where UAVs must simultaneously cope with terrain undulations, no-fly zones, safety-clearance requirements, and [...] Read more.
Unmanned aerial vehicles (UAVs) have been widely used in surveying and mapping, inspection, emergency rescue, and environmental monitoring. However, effective path planning remains a key challenge in complex three-dimensional terrain, where UAVs must simultaneously cope with terrain undulations, no-fly zones, safety-clearance requirements, and trajectory-smoothness constraints. In addition, conventional intelligent optimization algorithms often suffer from search instability and premature convergence. To address these challenges, this study proposes a reinforcement-learning-driven multi-strategy spherical-vector grey wolf optimizer, termed TLQ-SGWO, where TLQ denotes the combined use of Tent–Logistic hybrid initialization and Q-learning search-strategy scheduling. In the proposed method, candidate trajectories are encoded using spherical-vector increments; Tent–Logistic hybrid initialization is introduced to enhance population diversity; and Q-learning is incorporated to adaptively select search strategies, thereby dynamically balancing exploration and exploitation. A comprehensive cost function integrating path length, threat avoidance, terrain clearance, and trajectory smoothness is further constructed to improve the feasibility and safety of the planned trajectories. Experiments are conducted on the CEC2017 benchmark functions and artificially generated complex mountainous terrain scenarios. On the CEC2017 benchmark suite, TLQ-SGWO achieves the best average rankings in both mean error and standard deviation among the seven compared algorithms, indicating a stronger balance between optimization accuracy and robustness. In artificial mountainous scenarios, TLQ-SGWO obtains the lowest mean path cost in three of the four scenarios and remains statistically comparable to the strongest hybrid baseline in the remaining scenario, while maintaining stable feasible 3D trajectories under increasing no-fly-zone complexity. Full article
(This article belongs to the Section Biological Optimisation and Management)
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21 pages, 9193 KB  
Article
Improved Langevin Surrogate-Assisted Process-Parameter Optimization for Candidate Recipe Generation in Czochralski Silicon Single Crystal Growth
by Yin Wan, Yanlong Ma, Chi Zhang, Ding Liu and Junchao Ren
Crystals 2026, 16(7), 422; https://doi.org/10.3390/cryst16070422 - 29 Jun 2026
Viewed by 215
Abstract
To support offline process-parameter screening for Czochralski (CZ) silicon single crystal growth, this paper proposes a surrogate-assisted optimization framework based on an improved Langevin evolutionary algorithm. First, a multi-variable constrained optimization model is established, with the LSA-Transformer-predicted solid–liquid interface deformation used as the [...] Read more.
To support offline process-parameter screening for Czochralski (CZ) silicon single crystal growth, this paper proposes a surrogate-assisted optimization framework based on an improved Langevin evolutionary algorithm. First, a multi-variable constrained optimization model is established, with the LSA-Transformer-predicted solid–liquid interface deformation used as the objective evaluation and with process-smoothness and physical-feasibility constraints considered. Six key process parameters–heater power, pulling rate, argon flow rate, crystal rotation speed, crucible rotation speed, and magnetic field strength–are selected as decision variables. Second, building on the classical Langevin algorithm, an adaptive inertia weight mechanism, a diversity promoter (DP) operator, and a local escaping operator (LEO) are introduced to improve global exploration and local optima escape in complex search spaces. Verification on 23 classical benchmark functions indicates that the ILEE algorithm shows competitive overall performance and achieves better or comparable results on many functions when compared with particle swarm optimization (PSO), grey wolf optimization (GWO), the original Langevin evolutionary algorithm (LEE), and other baseline algorithms. The proposed framework is then used for offline candidate recipe generation during the crystal equal-diameter growth stage (200 mm, 400 mm, 600 mm, 800 mm, and 1000 mm). The optimized candidate parameter combinations yield lower surrogate-predicted interface deformation under the given LSA-Transformer model and physical constraints. Because these values are not independent CFD or experimental measurements, the results should be interpreted as process-parameter guidance for future physical validation. This work provides a feasible surrogate-assisted offline screening framework for CZ silicon single crystal growth. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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40 pages, 5102 KB  
Article
Algorithm-Driven Demand Optimization as an Enabler of Industrial Prosumers in Renewable Energy Communities: A Techno-Economic Assessment of a Flat Glass Processing SME
by Ateeq Ur Rehman, Dario Atzori, Sandra Corasaniti, Paolo Coppa, Muhammad Mazhar Rathore and Gianluigi Bovesecchi
Processes 2026, 14(13), 2053; https://doi.org/10.3390/pr14132053 - 24 Jun 2026
Viewed by 202
Abstract
This study addresses the multi-objective optimization of characterizing a flat glass processing plant. To assess the operational conditions required for a flat glass processing small and medium-sized enterprise (SME) to become a prosumer compatible with renewable energy community (REC) participation. This work is [...] Read more.
This study addresses the multi-objective optimization of characterizing a flat glass processing plant. To assess the operational conditions required for a flat glass processing small and medium-sized enterprise (SME) to become a prosumer compatible with renewable energy community (REC) participation. This work is motivated by the presence of more than 300 SMEs in Italy, like this, where RECs represent one of the few viable strategies for achieving the European Union’s 2050 decarbonization targets. The research is carried out in two scenarios; Scenario-I includes Stage-i and Stage-ii with the mutual goal of forecasting and optimizing. Forecasting is used in Stage-i to optimize the factory load, and in Stage-ii to shift and curtail energy loads based on the forecast, considering the Italian national energy price and the regional price bands (“fasce orarie”) F1, F2, and F3. Forecasting and the indicators of environmental and social performance are the means to ensure the best energy utilization and management, as they prove that the reduction in CO2 emissions and benefits on the community level can be both obtainable. Subsequently, the techno-economic analysis and evaluation of prosumer-readiness conditions are carried out through the optimization of industrial energy demand: three optimization objectives are assessed in this study (i) energy cost, (ii) carbon emission, and (iii) load curtailment. Four algorithms are put into effect to solve the tri-objective optimization: multi-objective particle swarm optimization (MOPSO), multi-objective ant nesting algorithm (MOANA), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective grey wolf optimization (MOGWO). The algorithms are validated in Stage-ii to find the desired optimum in the cost of energy, reduce peak formation, and carbon emissions. To achieve this goal, a stochastic approach based on Monte Carlo simulations and VIKOR is used to optimally select the results. The findings show that the NSGA-II, MOPSO, and MOANA are more effective in solving the problem, while the MOGWO algorithm more quickly finds the optimal solution. Based on the defined objectives, a new configuration for the energy community is introduced, together with a community well-being index and an evaluation of the resulting benefits for the factory. In Scenario-II, the PV plants’ installation on the factory is sized, and the excess energy shared with the grid is evaluated. The Scenario-II results show that 497.184 MWh (33.9%) of energy is shared with the grid. Both results suggest how optimized industrial demand profiles improve SME participation in future RECs. Full article
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21 pages, 13902 KB  
Article
A Hybrid Method of Binary Grey Wolf Optimization and Equilibrium Optimization for Feature Selection in Diagnosing Bearing Faults
by Chun-Yao Lee, Kuan-Yu Huang, Truong-An Le, Guang-Lin Zhuo, Mu-Ze Li and Chung-Hao Huang
Mathematics 2026, 14(13), 2244; https://doi.org/10.3390/math14132244 - 23 Jun 2026
Viewed by 246
Abstract
Diagnosing bearing faults remains a crucial challenge, particularly in effectively extracting fault information and achieving high diagnostic accuracy. To address this issue, this study presents a model for diagnosing bearing faults, which comprises three primary stages: feature extraction, feature selection, and classification. In [...] Read more.
Diagnosing bearing faults remains a crucial challenge, particularly in effectively extracting fault information and achieving high diagnostic accuracy. To address this issue, this study presents a model for diagnosing bearing faults, which comprises three primary stages: feature extraction, feature selection, and classification. In the feature extraction stage, features are extracted from raw motor signals using empirical mode decomposition (EMD) and fast Fourier transform (FFT). In the feature selection stage, an effective method based on binary grey wolf optimization (BGWO) and the equilibrium optimizer (EO) is developed to remove redundant and irrelevant features. Finally, k-nearest neighbours (KNNs) and support vector machine (SVM) classifiers are used to identify bearing fault conditions. The proposed model is evaluated using four datasets: the University of California, Irvine (UCI) benchmark datasets, a motor bearing fault current-signal dataset, the Case Western Reserve University (CWRU) benchmark dataset, and the Machinery Failure Prevention Technology (MFPT) benchmark dataset. The experimental results show that the proposed method improves bearing fault diagnosis accuracy and demonstrates strong robustness compared with conventional methods. Full article
(This article belongs to the Special Issue Mathematical Models for Fault Detection and Diagnosis)
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