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Keywords = distributed constrained optimization

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18 pages, 4138 KB  
Article
A Lightweight Hybrid Mobile Groupcasting Protocol for Spatially Heterogeneous Sink Groups in WSNs
by Hyunseok Choi, Jeongcheol Lee and Euisin Lee
Electronics 2026, 15(13), 2973; https://doi.org/10.3390/electronics15132973 - 7 Jul 2026
Abstract
Efficient data dissemination to mobile sink groups with heterogeneous spatial distributions that are globally sparse but locally dense remains a critical challenge in wireless sensor networks (WSNs). To address severe energy inefficiencies in conventional single-strategy approaches, we propose an energy-efficient, strictly lightweight hybrid [...] Read more.
Efficient data dissemination to mobile sink groups with heterogeneous spatial distributions that are globally sparse but locally dense remains a critical challenge in wireless sensor networks (WSNs). To address severe energy inefficiencies in conventional single-strategy approaches, we propose an energy-efficient, strictly lightweight hybrid mobile groupcasting protocol that dynamically integrates unicasting and partial flooding. The proposed protocol eliminates in-network computational overhead by shifting the entire subgrouping burden exclusively to the data source. The source formulates data dissemination as an analytical cost minimization problem and executes a highly scalable heuristic subgrouping algorithm that operates in linear time, O(|M|), relative to the number of member sinks. By embedding this optimal configuration directly into the data packet header, resource-constrained intermediate sensor nodes are completely relieved from heavy clustering calculations and only need to execute simple, predefined geographic forwarding or localized flooding rules. The simulation results using the QualNet 4.0 platform validate that our source-delegated architecture significantly reduces redundant transmissions and unnecessary flooding regions. The proposed protocol achieves up to 24% and 44.5% reductions in communication energy consumption compared to conventional unicasting-based and flooding-based protocols, respectively, while maintaining reliable data delivery under realistic network dynamics. Full article
(This article belongs to the Section Networks)
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25 pages, 28716 KB  
Article
Poly(vinyl alcohol)-Controlled Spreading and Film Formation of Poly(3-hexylthiophene-2,5-diyl) at Liquid Interfaces: Influence of PVA Molecular Weight, Degree of Hydrolysis, and Concentration
by Ziyan Shi, Haibin Wang, Huibin Sun and Wei Huang
Polymers 2026, 18(13), 1674; https://doi.org/10.3390/polym18131674 - 7 Jul 2026
Abstract
The spreading and film formation of organic polymer solutions on liquid surfaces are key processes in coating, printing, and interfacial processing. However, the mechanisms by which aqueous polymers regulate spreading kinetics and film morphology are not yet fully understood. In this study, the [...] Read more.
The spreading and film formation of organic polymer solutions on liquid surfaces are key processes in coating, printing, and interfacial processing. However, the mechanisms by which aqueous polymers regulate spreading kinetics and film morphology are not yet fully understood. In this study, the free spreading of Poly(3-hexylthiophene-2,5-diyl) (P3HT)/chlorobenzene solution on poly(vinyl alcohol) (PVA) aqueous surface was employed as a model system to investigate how PVA concentration, molecular weight, degree of hydrolysis, and temperature collectively govern spreading behavior and film formation. Video recording was used to monitor the evolution of the spreading and front-edge morphology, while step-profilometry, UV–visible absorption spectroscopy, and atomic force microscopy were employed to characterize the resulting films in terms of thickness distribution, optical uniformity, and surface roughness. The results reveal that PVA can significantly regulate both the spreading kinetics of P3HT/chlorobenzene droplets and the final film morphology. PVA concentration exhibited a non-monotonic effect on spreading behavior, with intermediate concentrations favoring larger spreading areas and more continuous films. Increasing the PVA molecular weight altered the concentration-dependent spreading window and enhanced asymmetry at the spreading front, whereas reducing the degree of hydrolysis decreased interfacial tension and thereby increased the thermodynamic driving force for spreading, yet the actual spreading rate remained constrained by molecular diffusion, interfacial adsorption, and chain-segment rearrangement. Temperature and a saturated chlorobenzene vapor atmosphere further modulated the interplay among solvent evaporation, interfacial driving force, and viscous dissipation. Under optimized conditions, the resulting P3HT films displayed uniform thickness profiles, consistent optical absorption, and nanoscale surface roughness, and could be repeatedly transferred, assembled into well-defined multilayer structures, and printed onto flexible and curved substrates. These findings demonstrate that PVA aqueous subphase provides a tunable low-shear route for transferable P3HT thin-film fabrication and suggests its potential applicability to other polymer film-forming systems. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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14 pages, 2099 KB  
Article
Time-Series Modeling-Based Early Detection of DDoS Attacks in Drone Networks
by ChungMan Oh, JaePil Youn, WonHo Ryu and Jin Ho Park
Electronics 2026, 15(13), 2945; https://doi.org/10.3390/electronics15132945 (registering DOI) - 6 Jul 2026
Viewed by 38
Abstract
Drone (UAV)-based ad hoc networks are highly vulnerable to Distributed Denial of Service (DDoS) attacks due to their resource constraints and dynamic connectivity. To ensure the survivability of UAVs, ultra-low latency early threat detection is essential. This study proposes three novel time-series network [...] Read more.
Drone (UAV)-based ad hoc networks are highly vulnerable to Distributed Denial of Service (DDoS) attacks due to their resource constraints and dynamic connectivity. To ensure the survivability of UAVs, ultra-low latency early threat detection is essential. This study proposes three novel time-series network metrics—Packet Flood Rate (PFR), Link Jitter Index (LJI), and Network Congestion Factor (NCF)—optimized for capturing the dynamic characteristics of DDoS attacks in drone networks. To evaluate the effectiveness of the proposed metrics, we applied lightweight deep learning architectures, including 1D-CNN, GRU, and LSTM. The experimental results demonstrate that the 1D-CNN model, guided by the proposed metrics, achieved the highest accuracy with an F1 Score of 0.9669 and an ROC-AUC of 0.9971. Notably, in terms of Average Detection Delay, a critical factor for early defense, the metric-driven 1D-CNN recorded 0.364 steps, reducing the detection time by approximately 30% compared to GRU (0.527) and LSTM (0.522) with statistical significance (p < 0.001, d = 0.6). Furthermore, despite requiring significantly fewer parameters (20,097), the 1D-CNN achieved a per-window inference latency of 0.611 ms on a standard CPU, demonstrating computational efficiency suitable for edge deployment in resource-constrained UAV environments. These results quantitatively demonstrate that the proposed feature-engineering approach combined with lightweight deep learning is highly viable for real-time threat mitigation in resource-constrained UAV networks. Full article
(This article belongs to the Special Issue AI for Cybersecurity and Emerging Technologies for Secure Systems)
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24 pages, 4898 KB  
Article
Mode-Aware Constrained Inverse Optimization for Behind-the-Meter Energy Storage Power Estimation Under Time-of-Use Tariffs
by Hao Jiang, Wenle Ding, Chuan Qin and Yuhang Zhou
Appl. Sci. 2026, 16(13), 6739; https://doi.org/10.3390/app16136739 - 6 Jul 2026
Viewed by 38
Abstract
With the increasing penetration of behind-the-meter photovoltaic generation and distributed energy storage, distribution system operators usually observe only the net load at the point of common coupling, while the actual user load and energy storage charging/discharging power are difficult to measure directly. To [...] Read more.
With the increasing penetration of behind-the-meter photovoltaic generation and distributed energy storage, distribution system operators usually observe only the net load at the point of common coupling, while the actual user load and energy storage charging/discharging power are difficult to measure directly. To address this problem, this paper proposes a mode-aware constrained inverse optimization method for behind-the-meter distributed energy storage power estimation under fixed time-of-use tariffs. The proposed method uses net load, photovoltaic power, and tariff information as inputs and estimates the hidden user load, storage power, SOC trajectory, and dominant storage arbitrage mode. A mode-aware joint representation model is developed by introducing single-cycle and dual-cycle charge–discharge templates, daily action intensity factors, mode weights, and local correction terms. In addition, power limits, SOC dynamics, SOC bounds, daily energy balance constraints, tariff-response consistency, and mode selection penalty are incorporated into the inverse optimization framework to improve the physical feasibility and interpretability of the estimation results. Case studies are conducted using a 40-day hybrid dataset with a 1 h sampling interval and a 70%/30% training/testing split. The dataset is constructed from park-level user load and photovoltaic data, while the storage power profile is reconstructed according to typical time-of-use arbitrage operation. For the main dual-cycle testing case, the NRMSEs of storage power, user load, and net load are 14.75%, 3.90%, and 3.76%, respectively. The results show that the proposed method can recover the main variation trend of hidden storage power under the studied fixed time-of-use tariff scenario and provides a preliminary basis for park-level storage monitoring and flexible resource perception. Full article
(This article belongs to the Section Energy Science and Technology)
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21 pages, 1542 KB  
Article
Semantic Consistency and Uncertainty-Driven Small-Object Detection for Class Imbalance
by Nuo Chen, Peng Zhao and Shouquan Hou
Remote Sens. 2026, 18(13), 2208; https://doi.org/10.3390/rs18132208 - 5 Jul 2026
Viewed by 81
Abstract
In aerial image small-object detection, complex imaging perspectives, arbitrary object orientations, and long-tailed category distributions jointly exacerbate sample imbalance, which significantly degrades detection stability and leads to frequent misclassification of minority categories. To address these challenges, this paper proposes a novel training framework [...] Read more.
In aerial image small-object detection, complex imaging perspectives, arbitrary object orientations, and long-tailed category distributions jointly exacerbate sample imbalance, which significantly degrades detection stability and leads to frequent misclassification of minority categories. To address these challenges, this paper proposes a novel training framework termed SCUD. Specifically, in the label noise suppression strategy (LNSS), a contrastive learning mechanism based on semantic consistency is introduced to constrain the aggregation of similar samples in the feature space, thereby reducing the adverse impact of noisy samples on model optimization. In addition, a scale-aware resampling strategy (SARS) is designed to alleviate noise amplification and overfitting caused by excessive repetition of small objects during training. Furthermore, an adaptive instance selection mechanism (AISM) is developed by jointly modeling prediction uncertainty and global statistical priors, enabling the model to dynamically emphasize learning from informative samples. Extensive experiments are conducted on two publicly available unmanned aerial vehicle (UAV) aerial image datasets to validate the effectiveness of the proposed approach. The proposed method achieves an mAP50 of 70.7% on the DOTA-v1.0 dataset and 88.1% on the DIOR dataset. Notably, the detection accuracy of several rare categories is significantly improved, further demonstrating the effectiveness of the proposed method in addressing sample imbalance in aerial image small-object detection. Full article
25 pages, 35847 KB  
Article
Three-Dimensional Numerical Investigation of a Novel Vertical-Axis Wind Turbine Using Modern Turbulence Models
by Ismatulla Khujaev, Muzaffar Hamdamov, Olimjon Toirov, Javokhir Toshov, Bohong Wang, Yujie Chen, Rongsheng Lin and Yue Su
Energies 2026, 19(13), 3173; https://doi.org/10.3390/en19133173 - 3 Jul 2026
Viewed by 207
Abstract
This paper presents a comprehensive three-dimensional numerical investigation of a novel vertical-axis wind turbine (VAWT) characterised by a unique aerodynamic profile and a passive blade-pitch control mechanism. Unlike conventional fixed-geometry designs, the proposed turbine utilizes rectangular blades mounted on horizontal axes via articulated [...] Read more.
This paper presents a comprehensive three-dimensional numerical investigation of a novel vertical-axis wind turbine (VAWT) characterised by a unique aerodynamic profile and a passive blade-pitch control mechanism. Unlike conventional fixed-geometry designs, the proposed turbine utilizes rectangular blades mounted on horizontal axes via articulated bearings, allowing them to rotate freely up to 90 degrees, constrained by a vertical pin-and-belt system. This configuration ensures that blades on the power-stroke side hit the vertical stopper to capture maximum wind energy, while blades on the return-stroke side open up to 90 degrees to significantly reduce aerodynamic drag. This dynamic adjustment enables the turbine to operate efficiently in low-wind conditions (3–5 m/s) while maintaining enhanced torque stability. To ensure numerical reliability, a rigorous grid independence study was performed, and the computational domain was configured to eliminate wall interference effects. The aerodynamic performance was analyzed using COMSOL Multiphysics v6.2 by solving the Reynolds-averaged Navier–Stokes (RANS) equations. Four turbulence models—SST, kε, kω, and RNG—were evaluated, with the SST model demonstrating the highest fidelity in capturing flow separation and wake structures under adverse pressure gradients. This study establishes the turbine’s performance benchmarks, including the power coefficient (Cp) versus tip speed ratio (TSR) curves. The numerical results were validated against laboratory experimental data, with excellent agreement (relative error < 5%). The findings identify the optimal geometric parameters and tangential velocity distributions that distinguish this configuration (Patent FAP 20240465) from traditional VAWTs. Finally, the successful implementation of a 2 kW prototype confirms the model’s accuracy and highlights the turbine’s potential as a stable and efficient solution for sustainable urban energy harvesting. Full article
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32 pages, 3426 KB  
Article
A Hybrid Rank-Preserving and Evolutionary Algorithm for Multisite Daily Streamflow Simulation
by Stefan Pitulić, Dragana Radosavljević, Đurica Marković and Siniša Ilić
Algorithms 2026, 19(7), 541; https://doi.org/10.3390/a19070541 - 3 Jul 2026
Viewed by 163
Abstract
This paper presents a hybrid algorithmic framework for nonparametric multisite daily streamflow simulation, evaluated on 52 years of observed data from three hydrological stations. The method generates streamflow data of 1000 synthetic years while preserving marginal distributions, daily rank structures, inter-station consistency, annual-sum [...] Read more.
This paper presents a hybrid algorithmic framework for nonparametric multisite daily streamflow simulation, evaluated on 52 years of observed data from three hydrological stations. The method generates streamflow data of 1000 synthetic years while preserving marginal distributions, daily rank structures, inter-station consistency, annual-sum behavior, and dependence across consecutive years. The workflow integrates Monte Carlo sampling, Schaake-shuffle reordering, block-mosaic reconstruction with partial freezing, Hungarian assignment optimization, annual-sum matching, and an adaptive permutation genetic algorithm for year-order optimization. The results show that the proposed algorithm improves aggregate hydrological diagnostics, particularly annual-sum autocorrelation, hydrological indices, persistence, seasonality, and timing of extremes, while reducing runtime in the final optimization phase by 45.2% compared to the benchmark algorithm. The study therefore formulates daily streamflow simulation as a constrained time-series reconstruction and permutation-optimization problem, making the method suitable for further algorithmic development and other multisite environmental time-series applications. Full article
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27 pages, 3682 KB  
Article
Dynamic Soft Sensing of Stack NOx Concentration in Cement Kiln SNCR–SCR Denitrification Using a DAC-IVY-Optimized TCN-SE-LSTM Model
by Zheng Zhao, Si-Yuan Liu, Yu-Xin Zhang, Jia-Le Quan and Xin-Yu Tang
Processes 2026, 14(13), 2176; https://doi.org/10.3390/pr14132176 - 3 Jul 2026
Viewed by 176
Abstract
Accurate single-step prediction of stack NOx concentration is essential for emission monitoring and ammonia-injection control in cement kiln SNCR–SCR hybrid denitrification systems. However, this task is challenging because industrial kiln data are affected by nonstationary emission fluctuations, nonlinear multivariable coupling, process-dependent time [...] Read more.
Accurate single-step prediction of stack NOx concentration is essential for emission monitoring and ammonia-injection control in cement kiln SNCR–SCR hybrid denitrification systems. However, this task is challenging because industrial kiln data are affected by nonstationary emission fluctuations, nonlinear multivariable coupling, process-dependent time delays, and online deployment constraints. To address these process-specific challenges, this study develops a leakage-free dynamic soft-sensing framework for stack NOx concentration prediction. In the proposed framework, variational mode decomposition (VMD) is used to characterize the multi-scale nonstationarity of the stack NOx sequence under a sliding-window protocol. Trend-guided maximal information coefficient (MIC) analysis is then applied for nonlinear feature selection and delay compensation using only the training data, and the identified feature subset and delay parameters are fixed for validation and testing. A TCN-SE-LSTM model is constructed to extract temporal dependencies, recalibrate informative feature channels, and capture long-lag dynamic behavior. In addition, the Dual Adaptive Constrained Ivy Algorithm (DAC-IVY) is used only for offline hyperparameter optimization, so that the online stage requires only the trained prediction model. Experiments using 21,600 raw samples collected from an actual cement kiln Distributed Control System (DCS) show that the proposed framework achieves an RMSE of 0.2084 mg/Nm3 and an R2 of 0.9844 on the test set, outperforming conventional baseline models. These results indicate that the proposed framework can provide an effective soft-sensing basis for subsequent denitrification control and operational optimization. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
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32 pages, 13541 KB  
Article
Ivy Optimization Algorithm Combining Sine–Cosine Operator and Adaptive T-Distribution and Its Engineering Application
by Zhenkun Lu, Jianyong Zhu, Dingfeng Lu, Hongze Lv, Haolin Gan and Zicong An
Biomimetics 2026, 11(7), 468; https://doi.org/10.3390/biomimetics11070468 - 3 Jul 2026
Viewed by 201
Abstract
The Ivy Optimization Algorithm (IVY) is a novel swarm intelligence optimization algorithm that simulates the phototropic growth mechanism of plants. To comprehensively improve the overall optimization performance, this paper proposes an enhanced Ivy Optimization Algorithm (LSIVY) integrating improved Logistics chaotic mapping, sine–cosine operator, [...] Read more.
The Ivy Optimization Algorithm (IVY) is a novel swarm intelligence optimization algorithm that simulates the phototropic growth mechanism of plants. To comprehensively improve the overall optimization performance, this paper proposes an enhanced Ivy Optimization Algorithm (LSIVY) integrating improved Logistics chaotic mapping, sine–cosine operator, and adaptive t-distribution mutation strategy. Firstly, an improved cascaded Logistics chaotic mapping is used for population initialization. The double arcsine transformation improves the ergodicity and uniformity of chaotic sequences, so that initial solutions are distributed more evenly in the search space, population diversity is enhanced, and premature convergence is suppressed. Secondly, the sine–cosine operator is embedded into the position update mechanisms of IVY growth, climbing, and propagation evolution. Nonlinearly decreasing control parameters realize adaptive switching between global exploration and local exploitation and accelerate convergence. Thirdly, an adaptive t-distribution mutation strategy is designed to dynamically adjust mutation intensity according to the iteration cycle and implement directional perturbation at the optimal solution position. It combines the large-scale exploration advantage of the Cauchy distribution and the local fine search merit of the Gaussian distribution, which significantly improves the ability to escape from local optima. Comparative experiments with eight mainstream metaheuristics (DE, WOA, GWO, HHO, DBO, MBWO, AOO, native IVY) are conducted with 30 independent runs on 30-dimensional CEC 2014 (30 test functions) and CEC 2020 (10 composite functions). Quantitatively, LSIVY achieves 20~30 orders of magnitude higher optimization accuracy than standard IVY on unimodal functions, and its average standard deviation across all benchmarks drops by 4–6 orders of magnitude. LSIVY ranks first on all CEC 2020 composite functions, reducing over 30% of iterations compared with native IVY. Three classical constrained mechanical design problems (three-bar truss, cantilever beam, pressure vessel) are adopted for engineering verification. In the pressure vessel case, the average manufacturing cost of LSIVY is reduced by 9.2% against standard IVY, and the standard deviation of three engineering cases decreases by 2–3 orders on average, demonstrating remarkable robustness. The proposed algorithm not only improves the theoretical system of plant-inspired swarm intelligence algorithms but also has great application prospects in mechanical structure lightweight design, industrial equipment cost optimization, and other practical engineering fields. Full article
(This article belongs to the Special Issue Advances in Biological and Bio-Inspired Algorithms: 2nd Edition)
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26 pages, 11952 KB  
Article
A Stepwise Calibration Method for Microscopic Traffic Simulation in Continuous-Flow Tunnel Scenarios Based on Macro- and Mesoscopic Indicators
by Nale Zhao, Ruiche Liu, Jiahui Li and Siyuan Hao
Appl. Sci. 2026, 16(13), 6656; https://doi.org/10.3390/app16136656 - 3 Jul 2026
Viewed by 90
Abstract
Microscopic traffic simulation is widely used to evaluate traffic operations in continuous-flow tunnel scenarios. However, conventional calibration methods mainly rely on aggregate indicators such as average speed or traffic flow. Under constrained geometric conditions, stable lane-use patterns, and mixed passenger car and truck [...] Read more.
Microscopic traffic simulation is widely used to evaluate traffic operations in continuous-flow tunnel scenarios. However, conventional calibration methods mainly rely on aggregate indicators such as average speed or traffic flow. Under constrained geometric conditions, stable lane-use patterns, and mixed passenger car and truck operations, different parameter combinations may reproduce similar macroscopic traffic states while generating different car-following behaviors. Therefore, aggregate-indicator-based calibration alone cannot ensure behavioral realism. The principal contribution of this study is a stepwise macro- and mesoscopic calibration framework that first constrains car-following behavior using the Speed Gap Function (SGF) and then refines the macroscopic traffic state using the Speed Distribution Function (SDF). The SGF characterizes the relationship between vehicle speed and net spacing, thereby capturing longitudinal interactions often overlooked in conventional calibration, whereas SDF describes the cumulative speed distribution. Latin Hypercube Sampling and VISSIM batch simulations are used to generate a dataset for 19 driving behavior parameters, and multilayer perceptron surrogate models are trained to improve optimization efficiency. Single-objective, simultaneous multi-objective, and stepwise calibration schemes are compared. The SGF-priority stepwise scheme achieves the most balanced performance, with SGF and SDF MAPE values of 12.00% and 11.53%, respectively, corresponding to average relative discrepancies of approximately 12% in reproducing the two calibration curves. An independent capacity pressure test used for external validation yields a deviation of only −1.84%, indicating that the simulated capacity is within 2% of the reference value. Overall, the proposed framework improves behavioral consistency and engineering applicability under high-demand tunnel conditions. Full article
(This article belongs to the Section Transportation and Future Mobility)
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80 pages, 16230 KB  
Article
HALA: A Hybrid Dual-Population Optimizer Integrating an Enhanced Artificial Lemming Algorithm and SHADE
by Han Yang and Xingwang Huang
Biomimetics 2026, 11(7), 464; https://doi.org/10.3390/biomimetics11070464 - 2 Jul 2026
Viewed by 149
Abstract
The rapid development of intelligent systems has introduced increasingly sophisticated optimization problems across diverse domains. While contemporary metaheuristic algorithms, including the recent Artificial Lemming Algorithm (ALA), have shown considerable promise, they frequently encounter difficulties such as premature convergence, inadequate local refinement, and diminished [...] Read more.
The rapid development of intelligent systems has introduced increasingly sophisticated optimization problems across diverse domains. While contemporary metaheuristic algorithms, including the recent Artificial Lemming Algorithm (ALA), have shown considerable promise, they frequently encounter difficulties such as premature convergence, inadequate local refinement, and diminished performance in high-dimensional multimodal environments. To overcome these issues, this study presents HALA, a new hybrid dual-subpopulation optimizer that effectively integrates an enhanced ALA with the SHADE algorithm. HALA employs two interacting subpopulations: one leverages an improved ALA with hybrid t-distribution and Levy flight perturbations to promote persistent long-range exploration and diversity preservation; the other applies SHADE’s success-history adaptation and external archive for accurate local exploitation. Periodic bidirectional elite migration facilitates knowledge transfer between the subpopulations, reducing early stagnation in the enhanced ALA and strengthening SHADE’s global search capability. HALA is thoroughly benchmarked against 17 advanced metaheuristics, including ALA, LSHADE, LSHADE-SPACMA, AOOA, BAEO, BPBO, CCO, CEO, CQALA, DFL, DMOA, DHOA, FGO, KLA, PGA, SO, and SOO, using the IEEE CEC2017 suite in 10, 30, 50, and 100 dimensions and the IEEE CEC2022 suite in 10 dimensions. Comprehensive analyses involving qualitative visualization, convergence curves, boxplots, and statistical tests indicate that HALA achieves competitive or superior solution quality, comparable or faster convergence, and robust stability on a substantial proportion of the test instances. In particular, HALA obtains the most favorable Friedman average ranking values among the compared algorithms, which are 2.55, 2.38, 2.34, and 2.55 for the 10-, 30-, 50-, and 100-dimensional CEC2017 functions, respectively, and 2.58 for the 12 10-dimensional CEC2022 functions. Moreover, HALA is successfully applied to five well-known constrained engineering design problems—pressure vessel, rolling element bearing, tension/compression spring, cantilever beam, and gear train—where it reliably achieves optimal or near-optimal results that match or surpass the compared methods. These findings underscore HALA’s competitive strength and broad potential for practical engineering optimization. Full article
(This article belongs to the Section Biological Optimisation and Management)
25 pages, 7965 KB  
Article
Finite-Time Consensus Neurodynamic Optimization for Distributed Pseudoconvex Problems with Engineering Applications to Economic Dispatch
by Mantong Huang, Xin Yu and Rixin Lin
Algorithms 2026, 19(7), 537; https://doi.org/10.3390/a19070537 - 2 Jul 2026
Viewed by 89
Abstract
This paper proposes an adaptive single-layer distributed neurodynamic optimization approach with the penalty method to address a non-smooth pseudoconvex optimization problem with affine equality and inequality constraints in multi-agent systems, where the global objective function for the agents is pseudoconvex but not required [...] Read more.
This paper proposes an adaptive single-layer distributed neurodynamic optimization approach with the penalty method to address a non-smooth pseudoconvex optimization problem with affine equality and inequality constraints in multi-agent systems, where the global objective function for the agents is pseudoconvex but not required to be differentiable. The target of this approach is to optimize the global objective while ensuring compliance with various constraints. The approach avoids the use of additional auxiliary variables, thereby reducing communication bandwidth and computational complexity. Under mild assumptions, the solution of the designed model is bounded for any initial conditions, to enter their respective feasible domains in finite time, and remain within these domains indefinitely. To achieve finite-time consensus in undirected, connected networks for multi-agent systems, a novel consensus mechanism is introduced to ensure that all agents synchronize their states within finite time. By exploiting the unique pseudoconvexity of the global objective function, the solution trajectory converges to the optimal state of the original problem. Furthermore, the effectiveness of the proposed approach is verified through two simulation experiments, and comparisons with four existing algorithms are conducted to demonstrate its superiority in convergence performance. Finally, an economic dispatch problem in power systems is provided as an engineering application to illustrate the practical applicability of the proposed algorithm. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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45 pages, 2461 KB  
Article
Solving the 3D UAV Path Planning Problem Using an Improved Multi-Leader Multi-Objective Whale Optimization Algorithm
by Binbin Tu, Jiawei Bao, Haoyuan Zhou, Yan Huo, Xiaowei Han and Nanmu Hui
Biomimetics 2026, 11(7), 459; https://doi.org/10.3390/biomimetics11070459 - 1 Jul 2026
Viewed by 189
Abstract
UAV path planning in complex static 3D environments involves multiple conflicting objectives and intricate constraints. However, when applied to highly constrained path planning tasks, MOWOA often suffers from a low proportion of feasible solutions, convergence instability, single-leader search bias, and an uneven distribution [...] Read more.
UAV path planning in complex static 3D environments involves multiple conflicting objectives and intricate constraints. However, when applied to highly constrained path planning tasks, MOWOA often suffers from a low proportion of feasible solutions, convergence instability, single-leader search bias, and an uneven distribution of Pareto solutions. To address these issues, this study formulates the UAV path planning problem as a multi-objective optimization problem that simultaneously considers path length, threat cost, smoothness cost, and altitude cost, and proposes an improved multi-leader multi-objective whale optimization algorithm (IML-MOWOA). The proposed IML-MOWOA progressively improves three key stages of the optimization process: initial population construction, search guidance, and external archive maintenance. Specifically, an adaptive opposition-based learning initialization strategy is first introduced to improve the feasibility and spatial coverage of initial paths. Based on the resulting non-dominated solution set, a grid-based external archive update strategy is then used to regulate solution density and provide representative candidate leaders from sparse Pareto regions. Subsequently, a multi-leader dynamic weighted search mechanism with Softmax-based cosine annealing integrates these leaders into the WOA update process, thereby enhancing multi-directional path exploration and alleviating premature convergence. Comparative experiments conducted in three static 3D environments of varying complexity demonstrate that the proposed method achieves more robust convergence, better Pareto-front distribution, and more balanced task-level path quality than the benchmark algorithms. In the most challenging scenario, IML-MOWOA achieves the highest number of feasible paths, reduces the mean IGD by 25.04%, and decreases the mean path length, threat cost, smoothness cost, and altitude cost by 1.65%, 28.45%, 53.23%, and 29.88%, respectively, compared with the best-performing competing algorithm for each metric. These results indicate that the proposed algorithm is effective and robust for constrained multi-objective UAV path planning in complex static 3D environments. Full article
(This article belongs to the Section Biomimetic Design, Constructions and Devices)
27 pages, 3733 KB  
Article
Spatiotemporal Evolution Characteristics of GPP and Its Nonlinear Response Mechanisms to Climate Change Across China’s Three Major Forest Regions
by Hongji Zhu, Hao Li, Lunpeng Zeng, Haokai Wang, Chunhua Chen, Rui Yao, Pengcheng Wang and Yu Xia
Remote Sens. 2026, 18(13), 2125; https://doi.org/10.3390/rs18132125 - 1 Jul 2026
Viewed by 288
Abstract
Gross primary productivity (GPP) is central to terrestrial carbon cycling and forest carbon sink assessment. Using Google Earth Engine, MODIS GPP, ERA5-Land meteorological data, and forest extent masks, this study examined GPP dynamics and climatic controls in China’s northeast, southern, and southwest forest [...] Read more.
Gross primary productivity (GPP) is central to terrestrial carbon cycling and forest carbon sink assessment. Using Google Earth Engine, MODIS GPP, ERA5-Land meteorological data, and forest extent masks, this study examined GPP dynamics and climatic controls in China’s northeast, southern, and southwest forest regions from 2005 to 2025. GPP increased overall in all three regions, with higher values in the south and lower values in the north. Climatic drivers differed regionally: in the northeast, GPP responded positively to temperature, while VPD slightly exceeded temperature in the dominant-control area; in the southern region, temperature was the main driver but VPD remained important; in the southwest, temperature dominated larger areas, whereas moisture-related controls showed stronger spatial heterogeneity. Piecewise analysis identified temperature–VPD turning points of 11.74 °C, 10.43 °C, and 25.64 °C for the northeast, southwest, and southern regions, respectively. Two-dimensional temperature–VPD binning further revealed nonlinear GPP distributions and distinct optimal hydrothermal combinations across regions. These results show that warming effects on forest productivity are region-specific and constrained by atmospheric dryness, providing evidence for assessing China’s forest carbon sink responses to climate change. Full article
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26 pages, 1298 KB  
Article
A Unified Federated Learning Framework for Power Data Terminals Under Privacy and Resource Constraints
by Xu Dong, Chang Liu, Jiakai Hao, Yuting Li, Xianzhou Gao, Ruxia Yang and Yujia Zhai
Electronics 2026, 15(13), 2873; https://doi.org/10.3390/electronics15132873 - 1 Jul 2026
Viewed by 148
Abstract
Power data terminals deployed in smart-grid environments generate massive amounts of operational data, yet the sensitive nature of these data and the existence of cross-region silos make centralized model training difficult in practice. Federated learning offers a natural alternative by enabling collaborative model [...] Read more.
Power data terminals deployed in smart-grid environments generate massive amounts of operational data, yet the sensitive nature of these data and the existence of cross-region silos make centralized model training difficult in practice. Federated learning offers a natural alternative by enabling collaborative model optimization without transferring raw data, but its direct use in power terminal scenarios is still limited by four coupled challenges: update leakage, malicious or abnormal client behavior, constrained terminal-side resources, and severe Non-IID data heterogeneity. To address these issues, we develop SFL-PDT, a hierarchical federated learning framework tailored to power data terminals. The proposed method is built on a server–edge–terminal architecture. Within this architecture, edge nodes aggregate terminal updates from relatively homogeneous regional groups and perform local robustness screening, while the central server aggregates edge-level updates across heterogeneous regions and coordinates the privacy budget schedule for protected updates. It combines adaptive privacy-aware update perturbation, robust suppression of suspicious regional updates, terminal-oriented update compression, and similarity-guided aggregation for heterogeneous data distributions. Experiments on two representative power-system tasks, load forecasting and fault diagnosis, demonstrate that SFL-PDT achieves a superior overall balance among privacy protection, robustness, efficiency, and predictive performance. Compared with the evaluated baselines, the proposed method more effectively reduces reconstruction-related leakage under different privacy budgets, lowers leakage similarity under gradient inversion attacks, and maintains robust performance when malicious clients participate. It also converges faster and more stably under heterogeneous data partitions. In addition, SFL-PDT achieves the best overall predictive results, reaching an MAE of 0.021 for load forecasting and an accuracy of 88.2% for fault diagnosis, while reducing average terminal-side local training time from 4.3 s to 2.9 s and per-round upload volume from 4.2 MB to 1.5 MB relative to FedAvg. These results suggest that SFL-PDT is a practical solution for secure, efficient, and heterogeneity-aware collaborative learning in power data terminal environments. Full article
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