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Keywords = dynamic constrained multiobjective optimization

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51 pages, 3669 KB  
Review
Fractional-Order Control Strategies for Complex Non-Linear Systems: A Systematic Review of Methodological Progress, Implementation Challenges, and Hardware Real-Time Feasibility
by Morteza Farrokhnia, Abbas Karami, Mohammad Hossein Heydari and Masoud Sotoodeh Bahraini
Fractal Fract. 2026, 10(9), 658; https://doi.org/10.3390/fractalfract10090658 (registering DOI) - 21 Sep 2026
Abstract
Fractional-order control (FOC) represents memory-dependent, hereditary, and nonlocal dynamics by incorporating non-integer integration and differentiation operators into conventional control laws. However, the numerical realization of these operators increases the effective controller order and imposes additional computational and hardware requirements. This systematic literature review [...] Read more.
Fractional-order control (FOC) represents memory-dependent, hereditary, and nonlocal dynamics by incorporating non-integer integration and differentiation operators into conventional control laws. However, the numerical realization of these operators increases the effective controller order and imposes additional computational and hardware requirements. This systematic literature review synthesizes 136 peer-reviewed studies published between 2010 and 2025 and identified through six scholarly databases and search platforms. Five focal strategy families—Fractional-Order Proportional–Integral–Derivative Control (FOPID), Fractional-Order Sliding Mode Control (FOSMC), Fractional-Order Adaptive Control (FOAC), Fractional-Order Impedance Control (FOIC), and Fractional-Order Optimal Control (FOOC)—are compared across nonlinear mechanical, biological/physiological, and aerospace/vehicle systems. The comparative analysis reveals distinct operational trade-offs. FOPID extends the conventional PID structure from three to five tunable parameters and provides the highest real-time feasibility, but its enlarged tuning space increases design complexity. FOSMC offers strong robustness and disturbance rejection but requires demanding fractional-order stability analysis and does not fully eliminate switching-induced chattering. FOAC accommodates unknown and time-varying dynamics through online adaptation but increases computational load and validation complexity. FOIC effectively captures compliant and viscoelastic force–motion interactions but involves numerous coupled impedance parameters and interaction-stability constraints. FOOC provides a powerful framework for memory-dependent multi-objective optimization but imposes the highest numerical and theoretical burden, often making direct real-time deployment impractical. Across the five strategies, increasing the order of numerical approximations improves the representation of fractional dynamics over the selected frequency range but adds internal filter states, memory requirements, arithmetic operations, and execution latency. Therefore, performance scalability is fundamentally constrained by growth in the effective state dimension and the available embedded-hardware resources. Future research should prioritize reduced-order fractional approximations, standardized benchmarks and software libraries, stability-certified adaptive architectures, and experimentally validated real-time implementations. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Control for Nonlinear Systems)
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27 pages, 8995 KB  
Review
Review of Boiler Intelligence: From In-Furnace Sensing to Decision Optimization
by Rui Luo, Junbo Yu, Na Li, Qulan Zhou, Jingkao Tan and Zhaomin Lv
Appl. Sci. 2026, 16(18), 9313; https://doi.org/10.3390/app16189313 (registering DOI) - 19 Sep 2026
Abstract
Driven by global carbon neutrality targets, coal-fired power generation is undergoing substantial operational changes. Modern boilers must operate more flexibly while maintaining low emissions and reliable performance. This transition has increased the need for intelligent monitoring, operator-supervised optimization, and safety-constrained decision support. Using [...] Read more.
Driven by global carbon neutrality targets, coal-fired power generation is undergoing substantial operational changes. Modern boilers must operate more flexibly while maintaining low emissions and reliable performance. This transition has increased the need for intelligent monitoring, operator-supervised optimization, and safety-constrained decision support. Using a reproducible search and screening procedure, this review examines the development of boiler intelligence across four interconnected technological stages. At the sensing layer, data-driven soft sensors support rapid prediction of flue gas emissions, while graph-structured spatiotemporal models are used to characterize flame and combustion states. At the modeling layer, physics-informed neural networks (PINNs) and proper orthogonal decomposition reduced-order models (POD-ROMs) are reviewed as routes for accelerating physical-field reconstruction. Surrogate models coupling computational fluid dynamics (CFD) with artificial intelligence (AI) provide another route to rapid prediction and can incorporate physical constraints. These fast field models can also serve as components of boiler digital twins for online assessment and operational guidance. They may also support early warning when abnormal conditions emerge. At the decision layer, reinforcement learning, model predictive control, and multi-objective optimization are reviewed for combustion and selective catalytic reduction (SCR) control. Because these applications are safety-critical, autonomous control must remain within actuator limits and established operating margins. Emission requirements and ammonia-slip constraints must also be satisfied. Safe deployment further requires fallback mechanisms, cybersecurity protection, and human supervision. Industrial application is still limited by data scarcity and lifecycle concept drift, while limited interpretability and simulator-to-real transfer create additional challenges. Edge latency and insufficient validation under abnormal conditions remain important barriers. Finally, industrial foundation models and large language models are discussed mainly as knowledge interfaces and operator-assistance tools rather than direct safety-critical controllers. Full article
50 pages, 693 KB  
Review
A Review of Joint Unmanned Aerial Vehicle Trajectory and Camera Orientation Optimization
by Jakub Kůdela
Information 2026, 17(9), 911; https://doi.org/10.3390/info17090911 (registering DOI) - 17 Sep 2026
Viewed by 75
Abstract
Camera-equipped Unmanned Aerial Vehicle (UAV) planning couples vehicle motion, camera pose, and scene-dependent sensing utility. The relevant literature is distributed across aerial reconstruction, inspection, target tracking, active perception, cinematography, and coverage planning, with substantial differences in vehicle models, camera mechanisms, visibility assumptions, and [...] Read more.
Camera-equipped Unmanned Aerial Vehicle (UAV) planning couples vehicle motion, camera pose, and scene-dependent sensing utility. The relevant literature is distributed across aerial reconstruction, inspection, target tracking, active perception, cinematography, and coverage planning, with substantial differences in vehicle models, camera mechanisms, visibility assumptions, and evaluation practice. A common vehicle–camera formulation is used here to compare two physical camera-realization mechanisms—independent gimbal actuation and body-coupled orientation—while treating viewpoint-first camera-pose planning as a separate representation that may defer physical realization. Mixed-integer formulations are first examined in detail because coverage, visibility, sequencing, assignment, and discrete camera modes introduce a logical structure; a representative time-expanded MILP is then provided for joint motion–view selection. Evolutionary methods are reviewed from early genetic and differential-evolution UAV planners through information-driven, constrained multiobjective, and hybrid formulations; and cooperative, surrogate-assisted, and transferability-aware methods from adjacent problem classes are then examined as possible extensions. In the frozen coded corpus, 13 direct studies use a physically independently actuated camera/gimbal, but none uses an evolutionary method as the primary optimizer for joint vehicle–gimbal motion; direct evolutionary joint vehicle–gimbal optimization therefore remains sparse. Simulation-to-reality transfer is analyzed as mismatch in dynamics, tracking, gimbal response, calibration, image formation, scene geometry, perception, and timing, with corresponding discussion of randomization, adaptive models, HIL evaluation, robust optimization, and transferability-aware search. A structured reproducibility audit through 31 August 2026 freezes the evidence base at 124 coded sources (62 direct studies, 48 adjacent precedents, and 14 proposed-transfer sources) and confirms persistent fragmentation in scenes, sensors, metrics, and computational budgets. The remaining technical questions concern mechanism-aware camera realization, scalable visibility, multi-view sensing utility under feedback, solver decomposition for mixed discrete–continuous problems, and transfer-sensitive evaluation. By synthesizing these methodological differences, this review identifies persistent research gaps and formulates recommendations for algorithm design, hybrid optimization, benchmarking, and sim-to-real validation. Full article
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22 pages, 4411 KB  
Article
Lightweight Design and Static–Dynamic Analysis of a Gantry Crane Main Girder Based on Multi-Objective Topology Optimization
by Yu Chen and Jinyuan Tang
Appl. Sci. 2026, 16(18), 9064; https://doi.org/10.3390/app16189064 - 12 Sep 2026
Viewed by 129
Abstract
Existing lightweight optimization studies on gantry crane girders merely adopt static strength and stiffness constraints, ignoring fatigue damage induced by dynamic loads and welding fabrication, which results in impractical optimal designs. To address this limitation, a novel multi-objective topology optimization method incorporating static, [...] Read more.
Existing lightweight optimization studies on gantry crane girders merely adopt static strength and stiffness constraints, ignoring fatigue damage induced by dynamic loads and welding fabrication, which results in impractical optimal designs. To address this limitation, a novel multi-objective topology optimization method incorporating static, dynamic, fatigue and minimum weld thickness constraints is proposed in this work. With structural weight and compliance minimization and first-order natural frequency maximization as the optimization targets, the model is constrained by structural stress, displacement, vibration frequency and minimum weld thickness, and a modified genetic algorithm is utilized to acquire the Pareto optimal solution set. Finite element analysis is conducted to compare the static performance, modal characteristics and transient dynamic responses of the original and optimized girders under diverse working conditions. The results demonstrate that the optimized girder exhibits comprehensive performance improvements, with a 15.6% reduction in structural mass, 8.3% decrease in maximum equivalent stress, 10.9% reduction in mid-span deflection, 12.1% increase in first-order natural frequency, and 18.3% extension in fatigue life. The proposed method can effectively support the precise lightweight design of crane metal structures and provides a feasible technical solution for their high-efficiency lightweight optimization. Full article
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26 pages, 2307 KB  
Article
Acoustic-Aware BDA-QL: A Hybrid Binary Dragonfly and Q-Learning Framework for Adaptive Clustering in Underwater Wireless Sensor Networks
by Eduardo Vázquez, Aldo Méndez, Leopoldo A. Garza, Gerardo Romero, Marco A Panduro and Omar Elizarraras
Technologies 2026, 14(9), 573; https://doi.org/10.3390/technologies14090573 - 10 Sep 2026
Viewed by 201
Abstract
Underwater Wireless Sensor Networks (UWSNs) are constrained by limited energy resources, high acoustic propagation delay, and topology variations caused by underwater mobility. This paper proposes a hybrid clustering framework that integrates the Binary Dragonfly Algorithm with Q-learning (BDA-QL) for adaptive cluster-head selection in [...] Read more.
Underwater Wireless Sensor Networks (UWSNs) are constrained by limited energy resources, high acoustic propagation delay, and topology variations caused by underwater mobility. This paper proposes a hybrid clustering framework that integrates the Binary Dragonfly Algorithm with Q-learning (BDA-QL) for adaptive cluster-head selection in UWSNs. The proposed method formulates clustering as a binary multi-objective optimization problem considering acoustic-aware energy consumption, end-to-end latency, and cluster load balance. Q-learning is incorporated to dynamically adjust the Dragonfly algorithm coefficients during the optimization stage, while the selected clustering configuration is evaluated under a controlled semicircular mobility model. Simulations were conducted with 100 nodes deployed in a 500 m × 500 m area over 500 simulation rounds and compared against GA, LEACH, C-LEACH, SS-GSO, CDFO-UWSN, and BDA. The results show that BDA-QL preserved the highest number of alive nodes, retaining 59 nodes at the final round, achieved the lowest final latency with 25.43 s, and delivered the highest number of packets, reaching 45,339 packets. BDA-QL provided the strongest overall trade-off across network lifetime, latency, packet delivery, and energy preservation. These findings suggest that reinforcement-learning-based coefficient adaptation can improve the robustness of Dragonfly-based clustering under underwater mobility conditions. Full article
(This article belongs to the Section Information and Communication Technologies)
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59 pages, 10068 KB  
Review
Sustainable Polymer Aerogels: Multiscale Design from Biomass and Thermoset Networks to AI-Guided Materials Discovery
by Trung Chi Duong, Phan Minh Quoc Binh, Dam Thi Thanh Hai, Le Thanh Thanh, Truong Thanh Tuan, Nguyen Thi Phuong Nhung, Nguyen Van Kiet, Nga H. N. Do and Hai M. Duong
Gels 2026, 12(9), 824; https://doi.org/10.3390/gels12090824 - 8 Sep 2026
Viewed by 293
Abstract
Polymer aerogels have attracted increasing attention as lightweight porous materials for thermal insulation, separation, adsorption, remediation, and other environmental applications. Their low density and tunable surface chemistry also make them suitable for converting renewable, recycled, and waste-derived feedstocks into value-added materials. However, their [...] Read more.
Polymer aerogels have attracted increasing attention as lightweight porous materials for thermal insulation, separation, adsorption, remediation, and other environmental applications. Their low density and tunable surface chemistry also make them suitable for converting renewable, recycled, and waste-derived feedstocks into value-added materials. However, their overall sustainability remains difficult to assess because most studies focus on material properties, whereas solvent use, drying energy, processing yield, durability, regeneration, and end-of-life pathways are reported less consistently. This review examines sustainable polymer aerogels from the perspectives of cleaner production and waste valorization and focuses on two main features. First, a unified multiscale framework of structure, formation, and performance links network formation mechanisms, pore architecture, and macroscopic behavior across biomass-derived, thermoset, dynamic covalent, hybrid, and recycled polymer aerogels, which are compared in terms of feedstock origin, processing intensity, functional performance, durability, and circularity. Second, structure–property mapping is combined with sustainability-constrained, AI-guided design, with environmental descriptors treated as optimization objectives from the outset rather than as post hoc justifications. Particular attention is given to waste and secondary resources, including agricultural residues, textile waste, paper waste, recycled poly(ethylene terephthalate), and end-of-life tire fibers. The review also discusses how life-cycle assessment, service-based functional units, and minimum reporting standards can help assess whether sustainability claims are supported by measurable environmental benefits. Several recurring limitations emerge from the literature: sustainability is often discussed only qualitatively, processing data are insufficient to support robust life-cycle assessments, solvent exchange and drying remain major environmental hotspots, and circularity claims frequently conflate bio-based content, biodegradability, recyclability, and reusability. Finally, the review discusses how data-driven tools, including literature mining, machine learning, and multi-objective optimization, can support polymer-aerogel design when environmental descriptors are included from the beginning of materials development. The review also proposes a reporting and design roadmap for future work toward polymer aerogels that combine useful performance with lower resource intensity and credible end-of-life value retention. Full article
(This article belongs to the Special Issue Sustainable Advanced Materials in Aerogels and Hydrogels)
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58 pages, 20057 KB  
Article
A Sobol-Driven Multi-Objective Whale Migration Algorithm for Engineering Optimization
by Lizhen Du, Dahongnian Zhou, Xiaoshuang Xiong, Min Shen, Hongtao Tang, Lianqing Yu and Fei Fan
Biomimetics 2026, 11(9), 642; https://doi.org/10.3390/biomimetics11090642 - 7 Sep 2026
Viewed by 209
Abstract
Multi-objective optimization plays an important role in modern design and complex engineering applications. However, achieving an effective balance between the convergence and diversity of Pareto-optimal solutions remains challenging. This paper proposes a Sobol-driven Multi-objective Whale Migration Algorithm (SMOWMA), which extends the Whale Migration [...] Read more.
Multi-objective optimization plays an important role in modern design and complex engineering applications. However, achieving an effective balance between the convergence and diversity of Pareto-optimal solutions remains challenging. This paper proposes a Sobol-driven Multi-objective Whale Migration Algorithm (SMOWMA), which extends the Whale Migration Algorithm within a non-dominated sorting and elite-selection framework. A maximin scrambled Sobol initialization scheme is first employed to improve the distribution of the initial population. An archive-guided adaptive Student-t flight mechanism is then incorporated into the leader-whale position update to dynamically balance global exploration and local exploitation. In addition, archive crowding information and archive-entry success feedback are jointly used to adjust the search behavior according to both environmental diversity and recent search performance. SMOWMA is evaluated on five widely used multi-objective benchmark suites, namely ZDT, DTLZ, WFG, UF, and CF, using four performance indicators: generational distance (GD), inverted generational distance (IGD), spacing (SP), and hypervolume (HV). The results, together with Friedman tests and Holm-adjusted Wilcoxon tests, demonstrate that SMOWMA achieves competitive overall performance in terms of convergence, diversity, and objective-space coverage, although its relative advantage remains problem-dependent. The practical applicability of SMOWMA is further examined using multi-objective welded-beam design formulations, a bi-objective four-bar truss design problem, and a five-objective car side-impact design problem. The engineering results show that SMOWMA can obtain competitive and stable approximation sets for constrained design problems with different numbers of objectives, supporting its effectiveness and applicability in multi-objective engineering optimization. Full article
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39 pages, 18970 KB  
Article
A Quantum-Memetic Hybrid Framework for Combinatorial Optimization: Synergistic Integration of Superposition-Based Exploration with Adaptive Exploitation
by Raza Hasan, Vishal Dattana and Salman Mahmood
AI 2026, 7(9), 342; https://doi.org/10.3390/ai7090342 - 1 Sep 2026
Viewed by 610
Abstract
The effective resolution of non-deterministic polynomial time hard (NP-hard) combinatorial optimization problems requires a delicate balance between global exploration and local exploitation. While Quantum-Inspired Algorithms (QIAs) leverage principles of superposition to explore vast search spaces, they often lack the fine-grained exploitation capabilities of [...] Read more.
The effective resolution of non-deterministic polynomial time hard (NP-hard) combinatorial optimization problems requires a delicate balance between global exploration and local exploitation. While Quantum-Inspired Algorithms (QIAs) leverage principles of superposition to explore vast search spaces, they often lack the fine-grained exploitation capabilities of classical heuristics. To address this limitation, we propose the Quantum-Memetic Hybrid Algorithm (QMHA), a component-based framework that synergistically integrates qubit-based global search with adaptive classical refinement. The QMHA architecture explicitly coordinates five distinct algorithmic components: (1) quantum rotation gates for exploration, (2) a problem-aware memetic operator for immediate solution refinement, (3) an adaptive learning rate schedule, (4) periodic local search, and (5) a stagnation-based population reset for diversity management. We rigorously evaluate the framework against nine established metaheuristics, including Genetic Algorithms (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Ant Colony Optimization (ACO), MAX-MIN Ant System (MMAS), Memetic Algorithms (MA), Quantum Evolutionary Algorithm (QEA), and Harmony Search (HS), across a comprehensive benchmark suite comprising six NP-hard problem families: constrained combinatorial (Knapsack), graph-based (Max-Cut), permutation-based (TSP), constraint satisfaction (Graph Coloring), bin optimization (Bin Packing), and scheduling (Flow Shop Scheduling), as well as real-world machine learning (Feature Selection) problems and the continuous Congress on Evolutionary Computation (CEC) 2022 benchmark. Statistical analysis using Friedman tests and Nemenyi post hoc comparisons confirms that QMHA achieves a statistically significant performance advantage (p<0.004) and superior average rank (1.5) compared to component baselines and state-of-the-art competitors. Comprehensive analyses include computational complexity profiling, parameter sensitivity mapping, scalability testing up to D=2000, noise robustness evaluation, variable correlation degradation analysis, a six-component ablation study, exploration–exploitation dynamics tracking, integration mechanism comparison across five architectures, and a multi-objective extension feasibility study. The proposed framework offers a robust, verified approach to hybrid optimization without relying on biological metaphors. Full article
(This article belongs to the Special Issue Advances in Quantum Computing and Quantum Machine Learning)
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31 pages, 36883 KB  
Article
Stability Simulation and Angle Optimization for Open-Pit Rock Slopes Under Multi-Condition Coupling
by Daoyuan Sun, Ruosong Bu, Guohui Zhang, Quan Jiang, Xiao Li, Chenliang Hao and Jian Wang
Mathematics 2026, 14(17), 3123; https://doi.org/10.3390/math14173123 - 31 Aug 2026
Viewed by 284
Abstract
To achieve the optimal balance between structural safety and stripping economy for the rock slopes of a specific open-pit iron mine, a rigorous mathematical modeling and computational framework was established. In contrast to traditional simplified pseudo-static evaluations, authentic monitored seismic and blasting waveforms [...] Read more.
To achieve the optimal balance between structural safety and stripping economy for the rock slopes of a specific open-pit iron mine, a rigorous mathematical modeling and computational framework was established. In contrast to traditional simplified pseudo-static evaluations, authentic monitored seismic and blasting waveforms were integrated within an explicit dynamic strength reduction model to ensure that transient stress wave propagation and progressive failure paths of rock slopes were accurately captured. Furthermore, a constrained multi-objective optimization model was established so that the nonlinear trade-off between dynamic safety margins and stripping volumes could be quantitatively resolved. Based on the application to the studied open-pit slopes, it was revealed that severe deep plastic yielding and topological shear band coalescence were caused by transient dynamic stress waves when the slope angle was steepened to 45°. Consequently, the factor of safety (FS) was abruptly reduced to an unsafe range of 1.01 to 1.20. Through the effective exclusion of this high-risk 45° configuration, a global optimal mining slope angle of 42° was rigorously established. At this optimal angle, a robust factor of safety ranging from 1.45 to 1.98 was consistently maintained across all extreme multi-field coupled conditions. Ultimately, from an engineering perspective, dynamic shear failure paths were successfully interrupted, and the need for expensive structural reinforcement was eliminated. Economically, waste rock stripping volumes were significantly minimized, whereby the overall stripping ratio was optimized, and life-cycle excavation efficiency was maximized. Full article
(This article belongs to the Special Issue Mathematics Applied in Rock Mechanics and Mining Science)
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36 pages, 3068 KB  
Article
AI-Driven Assessment of Flexibility and Sustainability in Power Systems
by Shuai Zhang and Cangbao Du
Symmetry 2026, 18(9), 1463; https://doi.org/10.3390/sym18091463 - 31 Aug 2026
Viewed by 246
Abstract
New energy power systems with high penetration rates feature complex spatiotemporal coupling relationships among generation, transmission, load, and storage. The random fluctuations in wind and solar power output, combined with load uncertainty, exacerbate system operational risks. Traditional static modeling, single-metric evaluation, and centralized [...] Read more.
New energy power systems with high penetration rates feature complex spatiotemporal coupling relationships among generation, transmission, load, and storage. The random fluctuations in wind and solar power output, combined with load uncertainty, exacerbate system operational risks. Traditional static modeling, single-metric evaluation, and centralized analysis methods struggle to adapt to the dynamic, highly uncertain, and multi-constrained operational scenarios of new power systems. To address this, this paper proposes an Artificial Intelligence-based Comprehensive Evaluation Method for Power System Flexibility and Sustainability (AI-FSEA) under privacy and security constraints. This method first establishes an intelligent fusion module for multi-source, heterogeneous power data, which accurately extracts the system’s multidimensional dynamic features through adaptive wavelet denoising and a temporal self-attention mechanism. Second, it establishes a five-objective coupled evaluation model that balances technical, economic, low-carbon, and reliability considerations, with regulation margin loss, response delay, operating costs, carbon emissions, and power supply instability rate as the core optimization objectives, thereby achieving multi-objective trade-off optimization within the system’s feasible domain; furthermore, a Hierarchical Deep Q-Network-Assisted Multi-Objective Evolutionary Algorithm (HDQN-MOEA) is designed, which leverages the value iteration, composite reward mechanism, and feedback clustering screening mechanism of the deep Q-network to enhance the model’s solution accuracy and convergence efficiency. Results from multiple sets of comparative experiments, ablation studies, and uncertainty generalization experiments conducted using the IEEE standard node system and real-world power grid data from East China indicate that, compared with mainstream optimization algorithms such as NSGA-III and TS-NSGA-II, the proposed HDQN-MOEA algorithm achieves an average improvement of 10.2% in the hypervolume metric and an average reduction of 35.6% in the span metric; the results of the ablation experiments confirm that the absence of the multi-source data fusion module, the hierarchical strategy module, or the feedback clustering screening module would result in a 15.3% and 12.1% decrease in the model’s hypervolume metric, respectively, as well as a slight deterioration in population diversity; under three types of highly uncertain operating conditions—random fluctuations in renewable energy, sudden load spikes, and extreme weather—the algorithm proposed in this paper consistently maintains stable optimization performance, meeting convergence accuracy requirements in as few as 5000 iterations. Without increasing the complexity of existing algorithms, it achieves the synergistic optimization of data privacy and security, evaluation accuracy, and operational efficiency. The proposed method can accurately quantify the dynamic flexibility and long-term sustainability of the new power system, providing reliable intelligent technical support for the planning and dispatch of the new power system, the optimal allocation of resources, and low-carbon, sustainable operation. Full article
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37 pages, 5914 KB  
Article
Projection-Iterative-Method-Based Coordinated Power Control for Renewable-Rich Islanded Microgrids
by Yuemeng Wang and Qiming Sun
Processes 2026, 14(17), 2789; https://doi.org/10.3390/pr14172789 - 30 Aug 2026
Viewed by 313
Abstract
High renewable-energy penetration introduces rapid source-load variations and operating uncertainties into islanded microgrids, challenging conventional droop control in terms of dynamic frequency/voltage regulation and proportional power sharing. This paper proposes a coordinated control strategy integrating adaptive droop control, dynamic virtual impedance, and a [...] Read more.
High renewable-energy penetration introduces rapid source-load variations and operating uncertainties into islanded microgrids, challenging conventional droop control in terms of dynamic frequency/voltage regulation and proportional power sharing. This paper proposes a coordinated control strategy integrating adaptive droop control, dynamic virtual impedance, and a Projection-Iterative-Method-Based Optimizer (PIMO). A constrained multi-objective formulation coordinates active- and reactive-power-sharing errors, frequency and voltage deviations, virtual-impedance regularization, and parameter variation, while stability is enforced through Lyapunov- and eigenvalue-based feasibility criteria. PIMO periodically coordinates the droop coefficients and virtual-impedance parameters within prescribed feasible bounds. The proposed strategy is evaluated in MATLAB/Simulink under five-stage load transitions and renewable-rich scenarios covering PV penetration levels from 30% to 90%, irradiance and temperature variations, simultaneous source-load disturbances, and operating constraints. Compared with adaptive droop control, the proposed strategy reduces the full-window frequency and voltage RMSE by 9.4% and 26.6%, respectively. The active- and reactive-power-sharing errors decrease to 1.73% and 2.08%, while the worst-case settling time is reduced to 220 ms. In addition, PIMO achieves a mean execution time of 28.4 s within the adopted 60 s supervisory update interval. These results demonstrate improved dynamic regulation, proportional power sharing, and feasible supervisory optimization under renewable-rich operating conditions. Full article
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42 pages, 6840 KB  
Article
A Hybrid Particle Swarm Optimization and Differential Evolution Algorithm with Adaptive Population and Dynamic Parameter Allocation
by Yaopei Wang, Yufeng Wang and Ke Liu
Algorithms 2026, 19(9), 710; https://doi.org/10.3390/a19090710 - 24 Aug 2026
Viewed by 223
Abstract
Traditional particle swarm optimization (PSO) easily falls into premature convergence, while differential evolution (DE) is highly sensitive to fixed control parameters. Existing PSO-DE hybrid frameworks suffer from static population sizes and insufficient cross-population information exchange. This paper proposes PSO-DE-ADP, a hybrid optimizer with [...] Read more.
Traditional particle swarm optimization (PSO) easily falls into premature convergence, while differential evolution (DE) is highly sensitive to fixed control parameters. Existing PSO-DE hybrid frameworks suffer from static population sizes and insufficient cross-population information exchange. This paper proposes PSO-DE-ADP, a hybrid optimizer with sinusoidal adaptive parameters, elite-guided mutation, ring neighborhood-weighted PSO and fitness-driven dynamic dual-population allocation. Four complementary mechanisms are integrated: (i) sine-wave perturbation superimposed on linear decay adaptively adjusts PSO inertia weight, acceleration factors and DE scaling/crossover coefficients to balance search stages; (ii) global elite individuals are embedded into DE mutation to reduce blind random search; (iii) ring topology with weighted learning realizes bidirectional information interaction between PSO and DE subpopulations; (iv) the proportion of PSO/DE individuals is dynamically adjusted according to elite ratio to allocate computing resources. Experiments adopt the CEC2017 30-dimensional benchmark with 30 test functions covering unimodal, multimodal, hybrid and composite landscapes. Compared with 8 state-of-the-art metaheuristics, PSO-DE-ADP achieves the lowest Friedman rank (1.08 vs. 2.23–4.90 for PSO variants; 1.53 vs. 2.07–5.00 for non-PSO algorithms). Ablation tests prove each component significantly boosts accuracy; The algorithm only costs 0.172 s average runtime, superior to all competitors. Statistical Wilcoxon and Friedman tests verify its significant superiority. Future work extends this method to multi-objective, constrained and real engineering optimization tasks. Full article
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24 pages, 2258 KB  
Article
Economic Emission Dispatch of Power Systems Using an Improved Multi-Objective Grey Wolf Optimizer
by Weichao Huang and Ruyin Wu
Electricity 2026, 7(3), 90; https://doi.org/10.3390/electricity7030090 - 23 Aug 2026
Viewed by 190
Abstract
With the increasing conflict between economic and environmental objectives in power systems, the economic emission dispatch (EED) problem has become a highly constrained, nonlinear, and strongly non-convex multi-objective optimization problem due to valve-point effects and nonlinear constraints such as network losses. To address [...] Read more.
With the increasing conflict between economic and environmental objectives in power systems, the economic emission dispatch (EED) problem has become a highly constrained, nonlinear, and strongly non-convex multi-objective optimization problem due to valve-point effects and nonlinear constraints such as network losses. To address this challenge, this paper proposes an improved multi-objective Grey Wolf Optimizer (IMOGWO). The proposed method enhances search performance through four strategies: a hybrid initialization scheme combining circle chaotic mapping and Latin hypercube sampling to improve population diversity, a dream-inspired group perturbation mechanism to strengthen global exploration, a nonlinearly decreasing convergence factor to dynamically balance exploration and exploitation, and a hybrid update strategy incorporating Lévy flight to avoid local optima. Experimental results demonstrate that IMOGWO can effectively balance the trade-off between generation cost and pollutant emissions while exhibiting competitive performance in terms of convergence behavior, solution quality, and stability. Full article
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25 pages, 25785 KB  
Article
Pareto-Active-Region-Guided Sequential Surrogate Modeling for CFD-Based Multi-Objective Optimization of Liquid-Cooled Battery Thermal Management Systems
by Zhanming Luo, Lei Wang and Deyong Song
Processes 2026, 14(16), 2675; https://doi.org/10.3390/pr14162675 - 21 Aug 2026
Viewed by 432
Abstract
Computational fluid dynamics (CFD)-driven optimization of engineering systems is often constrained by high computational cost, particularly when surrogate models must be constructed from limited simulation samples. Although surrogate-assisted multi-objective optimization can substantially reduce CFD evaluations, local prediction errors in decision-sensitive Pareto regions may [...] Read more.
Computational fluid dynamics (CFD)-driven optimization of engineering systems is often constrained by high computational cost, particularly when surrogate models must be constructed from limited simulation samples. Although surrogate-assisted multi-objective optimization can substantially reduce CFD evaluations, local prediction errors in decision-sensitive Pareto regions may alter feasibility classification and engineering recommendations near active constraints. To address this issue, this study proposes a Pareto-active-region-guided sequential surrogate modeling framework (PAR-SSM) for multi-objective optimization of liquid-cooled battery thermal management systems. Starting from 15 face-centered central composite design (FCCD) samples, the framework selectively introduces additional high-fidelity CFD evaluations into Pareto-active and constraint-sensitive regions, yielding a 21-sample refined surrogate model. Rather than uniformly improving global prediction accuracy, PAR-SSM directs the limited CFD budget toward regions where surrogate errors can directly influence engineering decisions. After model freezing, three independent Fluent cases were used exclusively for validation, yielding mean absolute deviations of 0.098 °C for maximum temperature and 0.341 °C for temperature difference, while also revealing residual feasibility risk near active constraint boundaries. Application to an autonomous underwater vehicle (AUV) battery module showed that the N = 3 configuration dominated the nominally constrained Pareto set and provided a favorable thermal–hydraulic trade-off under low auxiliary energy consumption. Overall, PAR-SSM provides a decision-oriented strategy for balancing computational cost and optimization credibility in CFD-intensive, constrained multi-objective design. Full article
(This article belongs to the Section Energy Systems)
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34 pages, 5406 KB  
Review
A Review of Coordinated Torque Allocation for Energy Efficiency and Stability in Distributed-Drive Electric Vehicles
by Bin Huang, Shuai Zhao, Jinyu Wei, Guochao Zhang and Xiaoxu Wei
World Electr. Veh. J. 2026, 17(8), 431; https://doi.org/10.3390/wevj17080431 - 20 Aug 2026
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Abstract
Distributed-drive electric vehicles (DDEVs) enable independent wheel-torque control, providing flexibility to improve energy efficiency and vehicle stability. However, tire–road adhesion, motor and battery capabilities, and actuator availability constrain these objectives, which may conflict under low-adhesion conditions, high-power acceleration, emergency braking, and combined longitudinal–lateral [...] Read more.
Distributed-drive electric vehicles (DDEVs) enable independent wheel-torque control, providing flexibility to improve energy efficiency and vehicle stability. However, tire–road adhesion, motor and battery capabilities, and actuator availability constrain these objectives, which may conflict under low-adhesion conditions, high-power acceleration, emergency braking, and combined longitudinal–lateral maneuvers. This paper provides a structured review of coordinated torque-allocation strategies for balancing energy efficiency and stability in DDEVs. Existing research is examined in terms of regenerative braking, tire-slip energy-loss reduction, and stability control under longitudinal, yaw, and combined conditions. Control approaches are classified as rule-based, stability-region-based, mode-switching, multi-objective optimization and predictive control, state-adaptive dynamic-priority coordination, and learning-based safety-hybrid methods. These approaches differ in real-time performance, constraint handling, adaptability, interpretability, and engineering maturity. A hierarchical hybrid architecture integrating rule-based supervision, state assessment, constraint-aware optimization, and learning-based enhancement appears more suitable for practical deployment than a single algorithm or fixed-weighting scheme. Key challenges include dynamic stability-boundary estimation, safety-assured coordination, multi-actuator fault tolerance, real-time implementation, and standardized vehicle-level validation. This review provides guidance for coordinated control-system development and future research on DDEVs. Full article
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