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Search Results (1,596)

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Keywords = stochastic optimization methods

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31 pages, 2687 KB  
Article
Water Resource Allocation: A Learning-Based Optimization Framework for Sustainable Decision-Making Under Uncertainty
by Marwa Mallek, Boukthir Haddar, Mohamed Ali Elleuch, Francisco Silva Pinto and Tiago Cetrulo
Environments 2026, 13(2), 105; https://doi.org/10.3390/environments13020105 - 13 Feb 2026
Abstract
Water allocation remains a critical global challenge due to increasing scarcity, competing sectoral demands, and environmental pressures, requiring approaches that balance efficiency, equity, and ecosystem sustainability while facing the inherent contextual uncertainty. Recent developments in operations research and statistical learning have paved the [...] Read more.
Water allocation remains a critical global challenge due to increasing scarcity, competing sectoral demands, and environmental pressures, requiring approaches that balance efficiency, equity, and ecosystem sustainability while facing the inherent contextual uncertainty. Recent developments in operations research and statistical learning have paved the way for a new paradigm in nonlinear modeling under uncertainty, i.e., contextual optimization. This emerging framework seamlessly combines predictive analytics with robust optimization techniques to address sustainable decision-making problems in dynamic environments. In this study, we introduce a novel learning-enabled optimization method that extends the current domain of contextual stochastic optimization. Leveraging regression-based statistical learning techniques, our approach enhances predictive accuracy and reinforces decision robustness. Unlike traditional methods, which often struggle with parameter variability and unbounded solution spaces, our model establishes clear predictive bounds that reduce the uncertainty region, thereby minimizing deviations from optimality. We apply our methodology to water allocation in Tunisia’s coastal tourism sector (2010–2022), where resource availability is constrained and highly variable. While developed for this specific context, the framework is transferable to similar Mediterranean arid/semi-arid tourism regions subject to certain data and governance conditions. The proposed approach accurately predicts water demand and optimizes the allocation of diverse water sources, contributing to sustainable water resource management. This paper presents both theoretical foundations and practical applications of our method in complex, data-driven decision environments, demonstrating its relevance for achieving sustainable development goals. Full article
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53 pages, 3028 KB  
Review
Optimization and Machine Learning for Electric Vehicles Management in Distribution Networks: A Review
by Stefania Conti, Giovanni Aiello, Salvatore Coco, Antonino Laudani, Santi Agatino Rizzo, Nunzio Salerno, Giuseppe Marco Tina and Cristina Ventura
Energies 2026, 19(4), 986; https://doi.org/10.3390/en19040986 - 13 Feb 2026
Abstract
The growing penetration of Electric Vehicles (EVs) in power distribution networks presents both challenges and opportunities for grid operators and planners. This paper provides a comprehensive review of recent advances in optimization techniques and machine learning (ML) approaches for the efficient management of [...] Read more.
The growing penetration of Electric Vehicles (EVs) in power distribution networks presents both challenges and opportunities for grid operators and planners. This paper provides a comprehensive review of recent advances in optimization techniques and machine learning (ML) approaches for the efficient management of EV charging and integration in low- and medium-voltage distribution systems. Optimization methods are analyzed with reference to their objectives—such as load flattening, voltage regulation, loss minimization, and infrastructure cost reduction—and their capability to handle multi-objective, stochastic, and real-time constraints. Concurrently, the role of ML is explored in load forecasting, user behavior modeling, anomaly detection, and adaptive control strategies. Particular attention is given to hybrid approaches that combine optimization algorithms (e.g., MILP, heuristic methods) with data-driven models (e.g., neural networks, reinforcement learning), highlighting their effectiveness in enhancing grid flexibility and resilience. This review adopts a unified system-level perspective that links EV management objectives, optimization techniques, and machine learning-based solutions within distribution networks. In addition, particular attention is devoted to data availability, reproducibility, and practical deployment aspects, with the aim of identifying current limitations and providing actionable insights for future research and real-world applications. This study aims to support the development of intelligent energy management strategies for EVs, fostering a sustainable and reliable evolution of distribution networks. Full article
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18 pages, 6951 KB  
Article
Multi-Agent Proximal Policy Optimization for Coordinated Adaptive Control of Photovoltaic Inverter Clusters in Active Distribution Networks
by Gongrun Wang, Shumin Sun, Yan Cheng, Peng Yu, Shibo Wang and Xueshen Zhao
Energies 2026, 19(4), 978; https://doi.org/10.3390/en19040978 - 13 Feb 2026
Abstract
High penetration of distributed photovoltaic (PV) generation has transformed active distribution networks into inverter-dominated systems, where maintaining voltage stability, minimizing power losses, and maximizing renewable utilization under uncertainty remain significant challenges. Conventional centralized optimal power flow (OPF) and ADMM-based distributed optimization methods suffer [...] Read more.
High penetration of distributed photovoltaic (PV) generation has transformed active distribution networks into inverter-dominated systems, where maintaining voltage stability, minimizing power losses, and maximizing renewable utilization under uncertainty remain significant challenges. Conventional centralized optimal power flow (OPF) and ADMM-based distributed optimization methods suffer from scalability limitations, high computational latency, and reliance on accurate system models, while single-agent reinforcement learning approaches such as PPO struggle with non-stationarity and lack of coordination in multi-inverter settings. To address these limitations, this paper proposes a coordinated control framework based on Multi-Agent Proximal Policy Optimization (MAPPO) for photovoltaic inverter clusters. By adopting centralized training with decentralized execution, the proposed approach enables effective coordination among heterogeneous inverter agents while preserving real-time autonomy. The framework explicitly incorporates network-level objectives, inverter operational constraints, and stochastic irradiance and load uncertainties, allowing agents to learn adaptive and robust control strategies. Simulation studies on a modified IEEE 33-bus active distribution network demonstrate that the proposed MAPPO-based method reduces voltage deviations by more than 40%, decreases network losses by approximately 25%, and lowers photovoltaic curtailment ratios by nearly 50% compared with centralized optimization approaches. In addition, MAPPO achieves significantly faster and more stable convergence than independent PPO under highly variable operating conditions.b These results indicate that MAPPO provides a scalable and resilient alternative to conventional optimization and single-agent learning methods, offering a practical pathway to enhance hosting capacity, operational robustness, and renewable integration in future active distribution networks. Full article
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26 pages, 5703 KB  
Article
An Evolutionary Neural-Enhanced Intelligent Controller for Robotic Visual Servoing Under Non-Gaussian Noise
by Xiaolin Ren, Haobing Cui, Haoyu Yan and Yidi Liu
Mathematics 2026, 14(4), 653; https://doi.org/10.3390/math14040653 - 12 Feb 2026
Abstract
Accurate state estimation is essential for the performance of uncalibrated visual servoing systems, yet it is frequently undermined by non-Gaussian disturbances—such as impulse noise, motion blur, and occlusions—whose heavy-tailed statistical characteristics are not adequately represented by conventional Gaussian models. To address this issue, [...] Read more.
Accurate state estimation is essential for the performance of uncalibrated visual servoing systems, yet it is frequently undermined by non-Gaussian disturbances—such as impulse noise, motion blur, and occlusions—whose heavy-tailed statistical characteristics are not adequately represented by conventional Gaussian models. To address this issue, this paper presents an evolutionary neural-enhanced intelligent controller designed for robotic visual servoing under such noise conditions. The controller architecture incorporates a hybrid estimation core that integrates α-stable distribution modeling for principled noise characterization with an Interacting Multiple Model Kalman filter (IMM-KF) to address system dynamics and uncertainties. A multi-layer perceptron (MLP), optimized globally via the Stochastic Fractal Search (SFS) algorithm, is embedded to provide adaptive compensation for residual estimation errors. This integration of statistical modeling, adaptive filtering, and evolutionary optimization constitutes a coherent learning-based control framework. Simulations and physical experiments reveal that the proposed method enhances improvements in estimation accuracy and tracking performance relative to conventional approaches. The outcomes indicate that the framework offers a functional solution for vision-based robotic systems operating under realistic conditions where non-Gaussian sensor noise is present. Full article
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18 pages, 910 KB  
Article
Dynamic Modeling and Analysis of Channel Characterization for RIS-Aided V2V Wireless Communication Systems
by Lin Guo, Jiahao Ge, Biyang Tu, Chao Meng and Xuejun Zhang
Sensors 2026, 26(4), 1177; https://doi.org/10.3390/s26041177 - 11 Feb 2026
Viewed by 29
Abstract
Recently, wireless channel in vehicle-to-vehicle (V2V) communications is highly challenging due to rapid signal fluctuations, multi-path fading, and frequent obstructions. To mitigate these issues, this paper proposes a three-dimensional (3D) end-to-end channel model for reconfigurable intelligent surface (RIS)-assisted V2V wireless channels. The proposed [...] Read more.
Recently, wireless channel in vehicle-to-vehicle (V2V) communications is highly challenging due to rapid signal fluctuations, multi-path fading, and frequent obstructions. To mitigate these issues, this paper proposes a three-dimensional (3D) end-to-end channel model for reconfigurable intelligent surface (RIS)-assisted V2V wireless channels. The proposed channel model incorporates the motions of the mobile transmitter (MT), mobile receiver (MR), and a UAV-mounted RIS, capturing time-varying propagation characteristics. Key contributions include the derivation of exact analytical expressions for the level crossing rate (LCR) of the Rician fading envelope, along with efficient deterministic and stochastic simulation methods. Numerical results analyze the impact of RIS motion direction and scatterer distribution on the LCR, providing theoretical insights for optimizing RIS-assisted V2V systems in wireless communication environments. Full article
(This article belongs to the Section Sensor Networks)
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36 pages, 3689 KB  
Article
Bilevel Mixed-Integer Model and Efficient Algorithm for DER Aggregator Bidding: Accounting for EV Aggregation Uncertainty and Distribution Network Security
by Wentian Lu, Junwei Chen, Lefeng Cheng and Wenjie Liu
Mathematics 2026, 14(4), 631; https://doi.org/10.3390/math14040631 - 11 Feb 2026
Viewed by 32
Abstract
This paper proposes a robust bilevel mixed-integer profit maximization model for an independent distributed energy resource (DER) aggregator participating in the wholesale electricity market, considering the uncertain aggregation of electric vehicles (EVs) to the grid, as well as the discrete security check of [...] Read more.
This paper proposes a robust bilevel mixed-integer profit maximization model for an independent distributed energy resource (DER) aggregator participating in the wholesale electricity market, considering the uncertain aggregation of electric vehicles (EVs) to the grid, as well as the discrete security check of the distribution system conducted by the non-market-participating distribution company. Regarding the uncertainty in EV–grid connectivity caused by stochastic transportation behavior, we characterize the robust connectivity at the lower level to ensure that the energy required for their daily transportation can be met. Solving the proposed bilevel mixed-integer profit maximization model is challenging due to the integer variables involved in the lower-level security check and robust connectivity problem, which makes the traditional strong duality and KKT method inapplicable. Thus, we propose using the total unimodularity property, multi-value-function approach, and strong duality method to transform the original bilevel model into an equivalent single-level model. Moreover, a sampling-based accelerated optimization algorithm is proposed to solve the equivalent single-level model efficiently. Case studies on a real-world transmission–distribution system verify that: (1) the proposed robust model outperforms deterministic models in profit by accommodating EV aggregation uncertainty; (2) the algorithm significantly reduces computational time compared to stochastic modeling approaches, while ensuring compliance with distribution network discrete security constraints. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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29 pages, 11326 KB  
Article
Constrained Soft Actor–Critic for Joint Computation Offloading and Resource Allocation in UAV-Assisted Edge Computing
by Nawazish Muhammad Alvi, Waqas Muhammad Alvi, Xiaolong Zhou, Jun Li and Yifei Wei
Sensors 2026, 26(4), 1149; https://doi.org/10.3390/s26041149 - 10 Feb 2026
Viewed by 249
Abstract
Unmanned Aerial Vehicle (UAV)-assisted edge computing supports latency-sensitive applications by offloading computational tasks to ground-based servers. However, determining optimal resource allocation under strict latency constraints and stochastic channel conditions remains challenging. This paper addresses the joint computation partitioning and power allocation problem for [...] Read more.
Unmanned Aerial Vehicle (UAV)-assisted edge computing supports latency-sensitive applications by offloading computational tasks to ground-based servers. However, determining optimal resource allocation under strict latency constraints and stochastic channel conditions remains challenging. This paper addresses the joint computation partitioning and power allocation problem for UAV-assisted edge computing systems. We formulate the problem as a Constrained Markov Decision Process (CMDP) that explicitly models latency constraints, rather than relying on implicit reward shaping. To solve this CMDP, we propose Constrained Soft Actor–Critic (C-SAC), a deep reinforcement learning algorithm that combines maximum-entropy policy optimization with Lagrangian dual methods. C-SAC employs a dedicated constraint critic network to estimate long-term constraint violations and an adaptive Lagrange multiplier that automatically balances energy efficiency against latency satisfaction without manual tuning. Extensive experiments demonstrate that C-SAC achieves an 18.9% constraint violation rate. This represents a 60.6-percentage-point improvement compared to unconstrained Soft Actor–Critic, with 79.5%, and a 22.4-percentage-point improvement over deterministic TD3-Lagrangian, achieving 41.3%. The learned policies exhibit strong channel-adaptive behavior with a correlation coefficient of 0.894 between the local computation ratio and channel quality, despite the absence of explicit channel modeling in the reward function. Ablation studies confirm that both adaptive mechanisms are essential, while sensitivity analyses show that C-SAC maintains robust performance with violation rates varying by less than 2 percentage points even as channel variability triples. These results establish constrained reinforcement learning as an effective approach for reliable UAV edge computing under stringent quality-of-service requirements. Full article
(This article belongs to the Special Issue Communications and Networking Based on Artificial Intelligence)
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39 pages, 2558 KB  
Article
An Enhanced Projection-Iterative-Methods-Based Optimizer for Complex Constrained Engineering Design Problems
by Xuemei Zhu, Han Peng, Haoyu Cai, Yu Liu, Shirong Li and Wei Peng
Computation 2026, 14(2), 45; https://doi.org/10.3390/computation14020045 - 6 Feb 2026
Viewed by 135
Abstract
This paper proposes an Enhanced Projection-Iterative-Methods-based Optimizer (EPIMO) to overcome the limitations of its predecessor, the Projection-Iterative-Methods-based Optimizer (PIMO), including deterministic parameter decay, insufficient diversity maintenance, and static exploration–exploitation balance. The enhancements incorporate three core strategies: (1) an adaptive decay strategy that introduces [...] Read more.
This paper proposes an Enhanced Projection-Iterative-Methods-based Optimizer (EPIMO) to overcome the limitations of its predecessor, the Projection-Iterative-Methods-based Optimizer (PIMO), including deterministic parameter decay, insufficient diversity maintenance, and static exploration–exploitation balance. The enhancements incorporate three core strategies: (1) an adaptive decay strategy that introduces stochastic perturbations into the step-size evolution; (2) a mirror opposition-based learning strategy to actively inject structured population diversity; and (3) an adaptive adjustment mechanism for the Lévy flight parameter β to enable phase-sensitive optimization behavior. The effectiveness of EPIMO is validated through a multi-stage experimental framework. Systematic evaluations on the CEC 2017 and CEC 2022 benchmark suites, alongside four classical engineering optimization problems (Himmelblau function, step-cone pulley design, hydrostatic thrust bearing design, and three-bar truss design), demonstrate its comprehensive superiority. The Wilcoxon rank-sum test confirms statistically significant performance improvements over its predecessor (PIMO) and a range of state-of-the-art and classical algorithms. EPIMO exhibits exceptional performance in convergence accuracy, stability, robustness, and constraint-handling capability, establishing it as a highly reliable and efficient metaheuristic optimizer. This research contributes a systematic, adaptive enhancement framework for projection-based metaheuristics, which can be generalized to improve other swarm intelligence systems when facing complex, constrained, and high-dimensional engineering optimization tasks. Full article
(This article belongs to the Section Computational Engineering)
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54 pages, 5015 KB  
Article
Reliability in Robotics and Intelligent Systems: Mathematical Modeling and Algorithmic Innovations
by Madina Issametova, Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Elizaveta E. Kuleshova and Denis V. Valuev
Mathematics 2026, 14(3), 580; https://doi.org/10.3390/math14030580 - 6 Feb 2026
Viewed by 121
Abstract
The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the [...] Read more.
The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the probability of the end-effector falling into a given area of permissible poses. The proposed framework integrates a deterministic kinematic model, a stochastic representation of Denavit–Hartenberg parameters and control variables, analytical methods for estimating probabilities, and numerical modeling using the Monte Carlo method. The methodology has been tested on the widely used industrial robot FANUC LR Mate 200iD/7L. The results demonstrate a significant dependence of geometric reliability on the kinematic configuration of the manipulator, with maximum reliability in compact poses and a significant reduction in elongated configurations near singularities. Comprehensive validation was carried out, including numerical experiments on a planar prototype, high-precision physical measurements on a real robot and analysis of operational data, which confirmed the adequacy of the proposed model. The developed approach provides a powerful tool for designing, optimizing and predicting the reliability of robotic cells in high-precision automation environments. Full article
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22 pages, 1664 KB  
Article
KAN+Transformer: An Explainable and Efficient Approach for Electric Load Forecasting
by Long Ma, Changna Guo, Yangyang Wang, Yan Zhang and Bin Zhang
Sustainability 2026, 18(3), 1677; https://doi.org/10.3390/su18031677 - 6 Feb 2026
Viewed by 113
Abstract
Short-Term Residential Load Forecasting (STRLF) is a core task in smart grid dispatching and energy management, and its accuracy directly affects the economy and stability of power systems. Current mainstream methods still have limitations in addressing issues such as complex temporal patterns, strong [...] Read more.
Short-Term Residential Load Forecasting (STRLF) is a core task in smart grid dispatching and energy management, and its accuracy directly affects the economy and stability of power systems. Current mainstream methods still have limitations in addressing issues such as complex temporal patterns, strong stochasticity of load data, and insufficient model interpretability. To this end, this paper proposes an explainable and efficient forecasting framework named KAN+Transformer, which integrates Kolmogorov–Arnold Networks (KAN) with Transformers. The framework achieves performance breakthroughs through three innovative designs: constructing a Reversible Mixture of KAN Experts (RMoK) layer, which optimizes expert weight allocation using a load-balancing loss to enhance feature extraction capability while preserving model interpretability; designing an attention-guided cascading mechanism to dynamically fuse the local temporal patterns extracted by KAN with the global dependencies captured by the Transformer; and introducing a multi-objective loss function to explicitly model the periodicity and trend characteristics of load data. Experiments on four power benchmark datasets show that KAN+Transformer significantly outperforms advanced models such as Autoformer and Informer; ablation studies confirm that the KAN module and the specialized loss function bring accuracy improvements of 7.2% and 4.8%, respectively; visualization analysis further verifies the model’s decision-making interpretability through weight-feature correlation, providing a new paradigm for high-precision and explainable load forecasting in smart grids. Collectively, the results demonstrate our model’s superior capability in representing complex residential load dynamics and capturing both transient and stable consumption behaviors. By enabling more accurate, interpretable, and computationally efficient short-term load forecasting, the proposed KAN+Transformer framework provides effective support for demand-side management, renewable energy integration, and intelligent grid operation. As such, it contributes to improving energy utilization efficiency and enhancing the sustainability and resilience of modern power systems. Full article
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22 pages, 3477 KB  
Article
Monte Carlo Simulation-Based Robustness Analysis of High-Speed Railway Settlement Prediction Models for Non-Stationary Time Series
by Zhenyu Liu, Hu Zeng, Huiqin Guo, Taifeng Li, Zhonglin Zhu, Youming Zhao, Qianli Zhang and Tengfei Wang
Appl. Sci. 2026, 16(3), 1566; https://doi.org/10.3390/app16031566 - 4 Feb 2026
Viewed by 119
Abstract
Accurate prediction of post-construction settlement in high-speed railway (HSR) soft foundations is critical for operational safety yet challenging due to the non-equidistant and non-stationary nature of observation data. This study systematically evaluated the robustness and accuracy of settlement prediction models using a Monte [...] Read more.
Accurate prediction of post-construction settlement in high-speed railway (HSR) soft foundations is critical for operational safety yet challenging due to the non-equidistant and non-stationary nature of observation data. This study systematically evaluated the robustness and accuracy of settlement prediction models using a Monte Carlo simulation approach. A numerical model incorporating the permeability characteristics of soft foundations was established to simulate stochastic system responses. Furthermore, an innovative multi-metric evaluation framework was constructed using the entropy weight method, integrating goodness-of-fit, prediction accuracy (systematic error), and stability (random error). Four classical empirical models—Hyperbolic, Exponential Curve, Asaoka, and Hoshino—were assessed. The results indicate that: (1) The Hyperbolic Method significantly outperformed other models (p<0.01) in goodness-of-fit (mean correlation coefficient: 0.983 ± 0.006) and accuracy (systematic error: 3.2% ± 1.1%); (2) The Hoshino Method exhibited optimal stability, characterized by the lowest random error (3.8 ± 2.0 mm); and (3) Model performance showed a significant positive correlation with the permeability coefficient (R2>0.92). Validated by five distinct engineering cases, the comprehensive performance ranking was determined as: Hyperbolic > Hoshino > Exponential Curve > Asaoka. These findings provide a scientific strategy for model selection under non-stationary conditions and offer theoretical support for refining railway deformation monitoring standards. Full article
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21 pages, 2860 KB  
Article
Prediction of Photovoltaic Power Output at New Energy Bases in the Desert Region During Sandstorm Weather
by Shuhao Wang, Junhan Xu, Shi Chen, Jiangping Chen and Hongping Yan
Energies 2026, 19(3), 809; https://doi.org/10.3390/en19030809 - 4 Feb 2026
Viewed by 114
Abstract
To address the challenge of forecasting power output from large-scale photovoltaic (PV) bases in desert regions during sand and dust storms, this paper proposes a hybrid data-physics driven prediction method. This approach utilizes satellite remote sensing to obtain regional irradiance data, transforming the [...] Read more.
To address the challenge of forecasting power output from large-scale photovoltaic (PV) bases in desert regions during sand and dust storms, this paper proposes a hybrid data-physics driven prediction method. This approach utilizes satellite remote sensing to obtain regional irradiance data, transforming the traditional one-dimensional time-series forecasting into a two-dimensional spatiotemporal sequence prediction, thereby tracking the dynamic evolution of irradiance intensity under the influence of sand and dust. Firstly, a forecasting model based on a conditional variational autoencoder (CVAE) optimized with a recurrent state-space model (RSSM) is constructed to effectively capture both the deterministic trends and stochastic fluctuations in irradiance variation, providing a reliable input basis for power calculation. Secondly, at the physical modeling level, the model comprehensively considers the isotropic scattering characteristics and changes in sky clarity induced by sand and dust weather, establishing a physical mapping relationship from irradiance to PV output. This mitigates the constraint of scarce historical operational data in desert and sandy regions. This research provides a novel solution for regional-level PV power forecasting under extreme sand and dust weather, contributing to enhanced dispatchability and transmission stability of renewable energy bases during abrupt meteorological changes. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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17 pages, 8681 KB  
Article
Balanced Grey Wolf Optimizer Algorithm for Backpropagation Neural Networks
by Jiashuo Chen, Hao Zhu, Tanjile Shu, Chengkun Cao, Yuanwang Deng and Qing Cheng
Mathematics 2026, 14(3), 554; https://doi.org/10.3390/math14030554 - 3 Feb 2026
Viewed by 132
Abstract
Backpropagation Neural Networks (BPNNs) are widely used in fault diagnosis and parameter prediction due to their simple structure and strong universal approximation capabilities. However, BPNNs suffer from slow convergence and susceptibility to poor local minima under basic gradient descent settings. To address these [...] Read more.
Backpropagation Neural Networks (BPNNs) are widely used in fault diagnosis and parameter prediction due to their simple structure and strong universal approximation capabilities. However, BPNNs suffer from slow convergence and susceptibility to poor local minima under basic gradient descent settings. To address these issues, this paper proposes a Balanced Grey Wolf Optimizer (BGWO) as an alternative to gradient descent for training BPNNs. This paper proposes a novel stochastic position update formula and a novel nonlinear convergence factor to balance the local exploitation and global exploration of the traditional Grey Wolf Optimizer. After exploration, the optimal convergence coefficient is determined. The test results on the six benchmark functions demonstrate that BGWO achieves better objective function values under fixed iteration settings. Based on BGWO, this paper constructs a training method for BPNN. Finally, three public datasets are used to test the BPNN trained with BGWO (BGWO-BPNN), the BPNN trained with Levenberg–Marquardt, and the traditional BPNN. The relative error and mean absolute percentage error of BPNNs’ prediction results are used for comparison. The Wilcoxon test is also performed. The test results show that, under the experimental settings of this paper, BGWO-BPNN achieves superior predictive performance. This demonstrates certain advantages of BGWO-BPNN. Full article
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20 pages, 1672 KB  
Article
Robust Stochastic Power Allocation for Industrial IoT Federated Learning with Neurosymbolic AI
by Pratik Goswami, Adeel Iqbal and Kwonhue Choi
Mathematics 2026, 14(3), 547; https://doi.org/10.3390/math14030547 - 3 Feb 2026
Viewed by 152
Abstract
In this work, a robust optimization approach for energy-aware federated learning (FL) in industrial IoT networks is proposed that addresses uncertainties in harvested energy, device failures, and dynamic topologies. The proposed neurosymbolic reasoning approach combines graph neural networks (GNNs) for topology-aware power prediction [...] Read more.
In this work, a robust optimization approach for energy-aware federated learning (FL) in industrial IoT networks is proposed that addresses uncertainties in harvested energy, device failures, and dynamic topologies. The proposed neurosymbolic reasoning approach combines graph neural networks (GNNs) for topology-aware power prediction with symbolic rules to solve the stochastic power allocation problem, providing both optimality guarantees and explainable safety-critical decisions. The hierarchical Master-Coordination-Task Agent (MA-CoA-TA) architecture prioritizes critical industrial nodes while ensuring FL convergence under energy constraints. This work establishes approximation guarantees through theoretical analysis relative to the robust optimum and validates with rigorous simulations against existing methods. Experimental results demonstrate that proposed framework provides optimal balance for robust FL deployment in large-scale IIoT networks with real-world uncertainties by achieving 5.7% FL accuracy with 151 J remaining battery under the most challenging conditions (100 rounds, 200 devices), while baselines fail completely (0% accuracy, battery depletion). Ablation confirms component synergy—symbolic reasoning delivers 2.2 times accuracy over GNN-only, while GNN+harvesting preserves 30 times more battery than symbolic-only. Full article
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26 pages, 1825 KB  
Article
Safety-Oriented Motion Planning for a Wheeled Humanoid Robot Operating in Environments with Stochastically Moving Humans
by Jian Mi, Xianbo Zhang, Zhongjie Long, Jun Wang and Wei Xu
Appl. Sci. 2026, 16(3), 1500; https://doi.org/10.3390/app16031500 - 2 Feb 2026
Viewed by 205
Abstract
With the advancement of humanoid robotics, human–robot collaboration has emerged as a prominent research focus. Ensuring the safety of both humanoid robots and humans remains a critical challenge. In this paper, we address conflict resolutions at the planning level and propose a safety-oriented [...] Read more.
With the advancement of humanoid robotics, human–robot collaboration has emerged as a prominent research focus. Ensuring the safety of both humanoid robots and humans remains a critical challenge. In this paper, we address conflict resolutions at the planning level and propose a safety-oriented motion planning (SOMP) algorithm for a wheeled humanoid robot operating in environments with unknown human motions. In the proposed SOMP algorithm, we employ Monte Carlo simulations to predict trajectories of stochastically moving humans and formulate both hard and soft constraints. A dynamic-quadrant stochastic sampling policy, integrated with a rapidly exploring random tree method, is proposed to generate diverse initial paths. Building upon this, we develop a constraint-fusion mechanism that combines hard constraints for safety guarantees and soft constraints for path optimization, thereby effectively resolving potential conflicts between wheeled humanoid robots and stochastically moving humans. We evaluate the proposed algorithm under different configurations of conflict numbers, task success rates, and path rewards. The proposed method outperforms A*, RRT, and MDP in terms of conflict numbers (−77.8%, −76.6%, and −71.4%) and task success rates (+168.0%, +109.4%, and +91.4%). Our simulation results prove the efficiency and robustness of our algorithm in safe motion planning with stochastically moving humans. Full article
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