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32 pages, 5852 KB  
Article
Intelligent Solution for Switching Angles in Multi-Level SHEPWM: An Application of an Enhanced BKA Algorithm
by Yanxiu Yu, Jiawen Wang, Fanxing Meng and Dongman Cao
Electronics 2026, 15(7), 1350; https://doi.org/10.3390/electronics15071350 - 24 Mar 2026
Viewed by 104
Abstract
In recent years, industrial systems and power electronic equipment have imposed increasingly stringent requirements on power quality, and therefore, the realization of a high-quality power supply has garnered extensive research attention. Selective harmonic elimination pulse width modulation (SHEPWM) features superior harmonic suppression performance [...] Read more.
In recent years, industrial systems and power electronic equipment have imposed increasingly stringent requirements on power quality, and therefore, the realization of a high-quality power supply has garnered extensive research attention. Selective harmonic elimination pulse width modulation (SHEPWM) features superior harmonic suppression performance and can effectively attenuate specific sub-harmonics; however, solving the associated system of nonlinear transcendental equations remains a critical challenge, primarily due to its inherent computational complexity and the risk of convergence to local optima. To address these limitations, we propose a multi-strategy enhanced chaotic black-winged kite algorithm (CMBKA). The proposed CMBKA integrates three synergistic optimization strategies: logistic–tent chaotic mapping for uniform population initialization, golden sine strategy to balance global exploration and local exploitation, and Monte Carlo perturbation to avoid convergence to local optima. In contrast to BKA, the proposed CMBKA achieves markedly higher calculation accuracy for switching angles, which is systematically validated on a five-level modified packed U-cell (MPUC) inverter platform. Experimental results verify that the proposed CMBKA achieves a lower total harmonic distortion (THD) than does the BKA, while the targeted specific sub-order harmonics are effectively suppressed to below 0.05%, with a maximum voltage deviation of 2.3% between the simulation results and experimental hardware tests. This work provides a high-precision SHEPWM solution for multilevel inverters, offering significant potential for renewable energy systems requiring minimal harmonic pollution and high power density. Full article
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25 pages, 2445 KB  
Article
Reentry Trajectory Optimization of Hypersonic Vehicle Based on Multi-Strategy Improved WOA Optimized Attention-LSTM Network
by Encheng Dai, Guangbin Cai, Yonghua Fan, Hui Xu, Hao Wei and Xin Li
Aerospace 2026, 13(3), 283; https://doi.org/10.3390/aerospace13030283 - 17 Mar 2026
Viewed by 239
Abstract
Trajectory optimization of hypersonic vehicles face challenges from complex aerodynamic environments and multiple constraints, where traditional offline optimization methods struggle to meet real-time requirements. This study proposes a novel online trajectory optimization framework for hypersonic vehicles that integrates a multi-strategy improved whale optimization [...] Read more.
Trajectory optimization of hypersonic vehicles face challenges from complex aerodynamic environments and multiple constraints, where traditional offline optimization methods struggle to meet real-time requirements. This study proposes a novel online trajectory optimization framework for hypersonic vehicles that integrates a multi-strategy improved whale optimization algorithm (MWOA) with an attention-mechanism Long Short-Term Memory (AM-LSTM) network. First, an offline trajectory dataset under aerodynamic uncertainties is generated using sequential second-order cone programming (SOCP). Subsequently, a multi-head attention mechanism is incorporated into the LSTM network to effectively capture sequential dependencies within the trajectory data. To automate the hyperparameter tuning of the AM-LSTM architecture, a multi-strategy improved whale optimization algorithm is developed, which incorporates circle chaotic mapping for population initialization, a nonlinear convergence factor to balance global and local search, and a dynamic golden-sine mutation strategy to enhance optimization robustness. The trained MWOA-AM-LSTM hybrid model is then employed for real-time trajectory generation. Numerical simulation results demonstrate that the proposed framework achieves superior terminal accuracy under aerodynamic perturbations, validating its effectiveness and robustness for hypersonic vehicle reentry trajectory optimization. Full article
(This article belongs to the Section Aeronautics)
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31 pages, 22634 KB  
Article
A Novel Image Encryption Scheme Based on Two-Dimensional Chaotic Map Constructed from Ackley Function and DNA Operations
by Chao Jiang, Xiong Zhang and Xiaoqin Zhang
Entropy 2026, 28(3), 322; https://doi.org/10.3390/e28030322 - 13 Mar 2026
Viewed by 206
Abstract
In contemporary communication systems, digital images occupy an irreplaceable role; however, the privacy-related risks attendant to their prevalent application have grown increasingly salient. This paper presents an image encryption scheme integrating a novel two-dimensional Ackley-Sine chaotic map (2D-ASM) with dynamic DNA operations. First, [...] Read more.
In contemporary communication systems, digital images occupy an irreplaceable role; however, the privacy-related risks attendant to their prevalent application have grown increasingly salient. This paper presents an image encryption scheme integrating a novel two-dimensional Ackley-Sine chaotic map (2D-ASM) with dynamic DNA operations. First, a two-dimensional Ackley-Sine chaotic map, constructed based on the Ackley function and sine function, is designed and validated through a series of chaotic indicators. Results demonstrate that 2D-ASM exhibits superior chaotic properties compared to several existing state-of-the-art chaotic maps, with its maximum Lyapunov exponent (LE) exceeding 23, Permutation Entropy (PE) close to 1 in the full parameter range, and correlation dimension (CD) significantly higher than comparative chaotic systems. The proposed 2D-ASM-based image encryption scheme leverages the SHA-256 hash value of the plaintext image and four external keys to jointly generate the initial conditions and parameters of the 2D-ASM chaotic system, thereby ensuring a sufficiently large key space of 2256. Subsequently, chaotic sequences generated by 2D-ASM are employed to permute and diffuse the plaintext image, followed by dynamic DNA coding, operations, and decoding to obtain the encrypted image. Security analyses and comparisons with several existing representative algorithms confirm that the proposed encryption scheme achieves excellent encryption performance: the Number of Pixels Change Rate (NPCR) is above 99.6%, the Unified Average Changing Intensity (UACI) approaches 33.4%, and the information entropy of ciphertext images reaches 7.999 or higher. The scheme can effectively resist various potential attacks, including statistical and differential attacks, and outperforms representative algorithms in pixel correlation reduction and anti-interference performance. Full article
(This article belongs to the Section Signal and Data Analysis)
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27 pages, 3206 KB  
Article
Trajectory Planning of Spraying Robot Based on Multi Strategy Improved Beluga Optimization Algorithm
by Yifang Wen, Renzhong Wang and Ting Huang
Sensors 2026, 26(5), 1617; https://doi.org/10.3390/s26051617 - 4 Mar 2026
Viewed by 263
Abstract
In this paper, a trajectory planning method based on an improved beluga whale optimization algorithm is proposed for the trajectory planning of plasma-spraying robot with complex surfaces. Firstly, the system architecture, kinematics model and trajectory planning constraints of the 6-DOF mobile plasma robot [...] Read more.
In this paper, a trajectory planning method based on an improved beluga whale optimization algorithm is proposed for the trajectory planning of plasma-spraying robot with complex surfaces. Firstly, the system architecture, kinematics model and trajectory planning constraints of the 6-DOF mobile plasma robot are analyzed, including kinematics, dynamics and environmental constraints, and a constrained-objective optimization function with time optimization, energy consumption and smoothness as objectives is established. Secondly, aiming at the shortage of the balance between global search and local development of the original beluga optimization algorithm, the tent chaotic mapping strategy is introduced to enhance the population diversity, and the sine and cosine algorithm is integrated to optimize the search process, so as to improve the convergence accuracy and stability. The experimental part is verified by the standard test function and the special index of trajectory planning. The results show that the IBWO algorithm is significantly better than the original beluga optimization, particle swarm optimization and other comparative algorithms in convergence accuracy, stability and comprehensive performance. In addition, the trajectory planning example shows that the joint trajectory generated by improved beluga whale optimization is smooth and has high constraint satisfaction, which is suitable for complex surface spraying tasks. Full article
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36 pages, 997 KB  
Article
Genetic Algorithms for Pareto Optimization in Bayesian Cournot Games Under Incomplete Cost Information
by David Carfí, Alessia Donato and Emanuele Perrone
Mathematics 2026, 14(5), 762; https://doi.org/10.3390/math14050762 - 25 Feb 2026
Viewed by 363
Abstract
This paper develops a practical computational framework for the Bayesian Cournot model with bilateral incomplete cost information, where each player is uncertain about the opponent’s marginal cost, drawn from a continuous compact interval [c*, c*] with [...] Read more.
This paper develops a practical computational framework for the Bayesian Cournot model with bilateral incomplete cost information, where each player is uncertain about the opponent’s marginal cost, drawn from a continuous compact interval [c*, c*] with 0<c*<c*<. The infinite dimensionality of the functional strategy spaces (mappings from types to production quantities) renders analytical closed-form solutions infeasible in this continuous-type setting. To overcome this challenge, we restrict the strategy spaces to finite-dimensional differentiable sub-manifolds—specifically, one-parameter families of oscillatory functions (cosine, sine, and mixed forms). After suitable affine Q-rescaling to map the oscillatory range into the production interval [0, Q], and with parameter ranges satisfying α, β>(π/2)/c*, these curves ensure near-exhaustivity: the joint production map (α, β)(xα(s), yβ(t)) covers [0, Q]2 densely for every fixed cost pair (s, t), thereby recovering (up to density and closure) the full ex-post payoff space. We introduce the ex-post payoff mapping Φ(s, t, x, y)=(es(x, y)(t), ft(x, y)(s)), which collects every realizable payoff pair once nature draws the types and players select their strategies. The image of Φ defines the general payoff space of the game, and its non-dominated points constitute the general ex-post Pareto frontier—all efficient realized outcomes across type-strategy realizations, without dependence on private probability measures over types. Using multi-objective genetic algorithms, we numerically approximate this frontier (and selected collusive compromises) within the restricted but representative sub-manifolds. The resulting frontiers are computationally accessible, robust to parameter variations, and validated through hypervolume convergence, sensitivity analysis, and comparisons with NSGA-II, PSO and scalarization methods. The findings are significant because they provide decision-makers in oligopolistic markets (e.g., electric vehicles) with viable, implementable production policies that explore efficient trade-offs under genuine cost uncertainty, without requiring explicit forecasts of the opponent’s type distribution—a limitation of traditional expected-utility approaches. By focusing on ex-post efficiency, the method reveals belief-independent compromise solutions that may guide tacit coordination or collusive outcomes in real-world strategic settings. Full article
(This article belongs to the Special Issue AI in Game Theory: Theory and Applications)
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25 pages, 2562 KB  
Article
Research on the Assessment of Dairy Cow Dry Matter Intake Using ITSO-Optimized Stacking Ensemble Learning
by Shuairan Wang, Ting Long, Xiaoli Wei, Qinzu Guo, Hongrui Guo, Weizheng Shen and Zhixin Gu
Animals 2026, 16(4), 625; https://doi.org/10.3390/ani16040625 - 16 Feb 2026
Viewed by 279
Abstract
Dry matter intake (DMI) in dairy cows is a critical indicator of nutrient intake from feed, serving as the cornerstone of precision feeding practices, playing a critical role in improving production efficiency and enhancing the quality of dairy products. To address the high [...] Read more.
Dry matter intake (DMI) in dairy cows is a critical indicator of nutrient intake from feed, serving as the cornerstone of precision feeding practices, playing a critical role in improving production efficiency and enhancing the quality of dairy products. To address the high costs of traditional measurement methods and the structural complexity and large parameter counts of neural network models, this study proposes a Stacking ensemble learning model to assess DMI, with model parameters optimized using the Tuna Swarm Optimization (TSO) algorithm to enhance assessment accuracy, taking cow body weight, lying duration, lying times, rumination duration, foraging duration, walking steps, and the concentrate-to-roughage feed ratio as input variables. To further improve TSO’s search efficiency and spatial exploration, this study introduces Sine–Logistic chaotic mapping, Levy flight, and Gaussian random walk strategy to optimize the TSO algorithm, developing the improved Tuna Swarm Optimization (ITSO). ITSO-optimized Stacking model achieved superior performance in DMI assessment, with an accuracy of 95.84%, significantly outperforming SVR, RF, DT, GBR, ETR, and AdaBoost models. This study provides a robust tool for precision feeding, contributing to optimizing cow feeding strategies, improving farm efficiency, and supporting sustainable dairy farming practices. Full article
(This article belongs to the Section Cattle)
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32 pages, 27015 KB  
Article
ESDBO: A Multi-Strategy Enhanced Dung Beetle Optimization Algorithm for Urban Path Planning of UGV
by Chenhui Wei, Zhifang Wei, Yanlan Li, Jie Cui and Yanfei Su
Sensors 2026, 26(3), 930; https://doi.org/10.3390/s26030930 - 1 Feb 2026
Viewed by 289
Abstract
In the complex urban path planning of unmanned ground vehicles (UGVs), the dung beetle optimization (DBO) algorithm is widely used due to its simple structure and fast convergence speed. However, it still has the disadvantages of poor convergence accuracy and is easy to [...] Read more.
In the complex urban path planning of unmanned ground vehicles (UGVs), the dung beetle optimization (DBO) algorithm is widely used due to its simple structure and fast convergence speed. However, it still has the disadvantages of poor convergence accuracy and is easy to fall into a local optimum. To solve these problems, this paper proposes a multi-strategy enhanced DBO algorithm (ESDBO). Firstly, sine mapping is introduced in the population initialization stage to enhance solution diversity. Secondly, an adaptive information volatilization mutation strategy is proposed, which dynamically balances the convergence and global search ability. Finally, a multi-mechanism co-evolution strategy is designed, which significantly improves the local search ability and stability. Through ablation experiments and CEC2017 benchmark tests, the optimization ability of the proposed strategy and the convergence accuracy and stability of ESDBO are verified. Further path planning experiments are carried out on the public Random MAPF benchmark map. The results show that ESDBO can generate global optimal paths with short path length, few turns, and high safety margin on different obstacle densities and map scales. The algorithm provides an efficient and reliable solution for autonomous navigation in complex urban environments. Full article
(This article belongs to the Section Navigation and Positioning)
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24 pages, 393 KB  
Article
Global Transition of Energy Vectors in the Maritime Sector: Role of Liquefied Natural Gas, Green Hydrogen, and Ammonia in Achieving Net Zero by 2050
by Carmen Luisa Vásquez Stanescu, Rhonmer Pérez-Cedeño, Jesús C. Hernández and Teresa Batista
Energies 2026, 19(2), 568; https://doi.org/10.3390/en19020568 - 22 Jan 2026
Viewed by 595
Abstract
The global transition toward net-zero emissions by 2050, encompassing the International Energy Agency’s Roadmap for the energy sector, the IMO’s revised strategy for the maritime industry, and broader climate guidelines, necessitates a profound transformation of both global energy systems and the shipping sector. [...] Read more.
The global transition toward net-zero emissions by 2050, encompassing the International Energy Agency’s Roadmap for the energy sector, the IMO’s revised strategy for the maritime industry, and broader climate guidelines, necessitates a profound transformation of both global energy systems and the shipping sector. In this context, energy vectors such as Liquefied Natural Gas, Green Hydrogen, and Ammonia are emerging as key elements for this shift. This review article proposes a comprehensive analysis of these vectors, contrasting their roles: Liquefied Natural Gas as a transitional solution and Hydrogen and Ammonia as long-term pillars for decarbonization. The research moves beyond a simple comparative analysis, offering a detailed mapping and evaluation of the global port infrastructure required for their safe handling, cryogenic storage, and bunkering operations. We examine their technical specifications, decarbonization potential, and the challenges related to operational feasibility, costs, regulation, and sustainability. The objective is to provide a critical perspective on how the evolution of maritime ports into energy hubs is a sine qua non condition for the secure and efficient management of these vectors, thereby ensuring the sector effectively meets the Net Zero 2050 climate goals. Full article
31 pages, 9004 KB  
Article
Multi-Strategy Fusion Improved Walrus Optimization Algorithm for Coverage Optimization in Wireless Sensor Networks
by Ling Li, Youyi Ding, Xiancun Zhou, Xuemei Zhu, Zongling Wu, Wei Peng, Jingya Zhang and Chaochuan Jia
Biomimetics 2026, 11(1), 72; https://doi.org/10.3390/biomimetics11010072 - 15 Jan 2026
Viewed by 493
Abstract
The Walrus Optimization (WO) algorithm, a metaheuristic inspired by walrus behavior, is known for its competitive convergence speed and effectiveness in solving high-dimensional and practical engineering optimization problems. However, it suffers from a tendency to converge to local optima and exhibits instability during [...] Read more.
The Walrus Optimization (WO) algorithm, a metaheuristic inspired by walrus behavior, is known for its competitive convergence speed and effectiveness in solving high-dimensional and practical engineering optimization problems. However, it suffers from a tendency to converge to local optima and exhibits instability during the iterative process. To overcome these limitations, this study proposes an improved WO (IMWO) algorithm based on the integration of Differential Evolution/best/1 (DE/best/1) mutation, Logistics–Sine–Cosine (LSC) Mapping, and the Beta Opposition-Based Learning (Beta-OBL) strategy. These strategies work synergistically to enhance the algorithm’s global exploration capability, improve its search stability, and accelerate convergence with higher precision. The performance of the IMWO algorithm was comprehensively evaluated using the CEC2017 and CEC2022 benchmark test suites, where it was compared against the original WO algorithm and six other state-of-the-art metaheuristics. Experimental data revealed that the IMWO algorithm achieved average fitness rankings of 1.66 and 1.33 in the two test suites, ranking first among all compared algorithms. The WSN coverage optimization problem aims to maximize the monitored area while reducing perception blind spots under limited node resources and energy constraints, which is a typical complex optimization problem with multiple constraints. In a practical application addressing the coverage optimization problem in Wireless Sensor Networks (WSNs), the IMWO algorithm attained average coverage rates of 95.86% and 96.48% in two sets of coverage experiments, outperforming both the original WO and other compared algorithms. These results confirm the practical utility and robustness of the IMWO algorithm in solving complex real-world engineering problems. Full article
(This article belongs to the Section Biological Optimisation and Management)
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24 pages, 2901 KB  
Article
Performance Defect Identification in Switching Power Supplies Based on Multi-Strategy-Enhanced Dung Beetle Optimizer
by Zibo Yang, Jiale Guo, Rui Li, Guoqing An, Kai Zhang, Jiawei Liu and Long Zhang
Math. Comput. Appl. 2026, 31(1), 12; https://doi.org/10.3390/mca31010012 - 12 Jan 2026
Viewed by 359
Abstract
To address the limited defect-detection capability of existing performance testing methods for switching power supplies under varying operating conditions, this paper proposes a defect identification approach based on an enhanced Dung Beetle Optimizer. The algorithm integrates multi-strategy improvements—including piecewise chaotic mapping, Lévy flight [...] Read more.
To address the limited defect-detection capability of existing performance testing methods for switching power supplies under varying operating conditions, this paper proposes a defect identification approach based on an enhanced Dung Beetle Optimizer. The algorithm integrates multi-strategy improvements—including piecewise chaotic mapping, Lévy flight perturbation, hybrid sine–cosine updating, and an alert sparrow mechanism—to refine the initial population generation, position update rules, and late-stage exploration. These enhancements strengthen its spatial search ability and computational performance. The experimental results show that the method accurately identifies the predefined defect intervals with a precision of 94.79%, covering 91.3% of the operating conditions. Comparisons with existing mainstream methods confirm the superior performance, effectiveness, and feasibility of the proposed method. Full article
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14 pages, 2675 KB  
Article
A Discrete Map with a Hyperbolic Sine Function: Dynamics, Stabilization, and Synchronization
by Yanyun Xie and Xiaojun Liu
Symmetry 2026, 18(1), 115; https://doi.org/10.3390/sym18010115 - 7 Jan 2026
Viewed by 321
Abstract
In this paper, a fractional-order discrete map with a hyperbolic sine function has been proposed and studied. Firstly, the basic characteristics of the map in integer-order case are studied theoretically and numerically. Secondly, dynamics of the map are investigated via numerical simulations. Attractors [...] Read more.
In this paper, a fractional-order discrete map with a hyperbolic sine function has been proposed and studied. Firstly, the basic characteristics of the map in integer-order case are studied theoretically and numerically. Secondly, dynamics of the map are investigated via numerical simulations. Attractors and bifurcation diagram spectrums are given when a parameter is varied. Furthermore, the map with the Caputo fractional difference operator has been studied. The chaotic attractors in commensurate-order and incommensurate-order cases are shown. For the characteristics of hyperbolic sine function, the chaotic attractors with different structures for the map can be obtained. It can be concluded that the map has rich dynamics in integer-order and fractional-order cases. Finally, stabilization and adaptive synchronization of the fractional-order map are realized by designing suitable controllers, respectively. Numerical results are used to demonstrate the effectiveness of the controllers for the map. Full article
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30 pages, 6264 KB  
Article
An Efficient Image Encryption Scheme Based on DNA Mutations and Compression Sensing
by Jianhua Qiu, Shenli Zhu, Yu Liu, Xize Luo, Dongxin Liu, Hui Zhou, Congxu Zhu and Zheng Qin
Mathematics 2026, 14(1), 5; https://doi.org/10.3390/math14010005 - 19 Dec 2025
Viewed by 462
Abstract
In communication environments with limited computing resources, securely and efficiently transmitting image data has become a challenging problem. However, most existing image data protection schemes are based on high-dimensional chaotic systems as key generators, which suffer from issues such as high algorithmic complexity [...] Read more.
In communication environments with limited computing resources, securely and efficiently transmitting image data has become a challenging problem. However, most existing image data protection schemes are based on high-dimensional chaotic systems as key generators, which suffer from issues such as high algorithmic complexity and large computational overhead. To address this, this paper presents new designs for a 1D Sine Fractional Chaotic Map (1D-SFCM) as a random sequence generator and provides mathematical proofs related to the boundedness and fixed points of this model. Furthermore, this paper improves the traditional 2D compressive sensing (2DCS) algorithm by using the newly designed 1D-SFCM map to generate a chaotic measurement matrix, which can effectively enhance the quality of image recovery and reconstruction. Moreover, referring to the principle of gene mutation in biogenetics, this paper designs an image encryption algorithm based on DNA base substitution. Finally, the security of the proposed encryption scheme and the quality of image compression and reconstruction are verified through indicators such as key space, information entropy, and Number of Pixel Change Rate (NPCR). Full article
(This article belongs to the Special Issue Chaotic Systems and Their Applications, 2nd Edition)
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22 pages, 2732 KB  
Article
Coordinated Allocation of Channel-Tugboat-Berth Resources Under Tidal Constraints at Liquid Terminal
by Lingxin Kong, Hanbin Xiao, Yudong Wang, Keming Chen and Min Liu
Appl. Sci. 2025, 15(24), 13263; https://doi.org/10.3390/app152413263 - 18 Dec 2025
Viewed by 491
Abstract
Driven by the surging global demand for crude oil and its byproducts, liquid tanker vessels have undergone a marked shift toward ultra-large dimensions. This growth, while enhancing transport capacity, has also intensified congestion across many liquid terminals. As the Dead Weight Tonnage (DWT) [...] Read more.
Driven by the surging global demand for crude oil and its byproducts, liquid tanker vessels have undergone a marked shift toward ultra-large dimensions. This growth, while enhancing transport capacity, has also intensified congestion across many liquid terminals. As the Dead Weight Tonnage (DWT) of vessels rises, so does their draft, often requiring tide-dependent navigation for safe entry into ports. To address the resulting operational complexities, this study investigates the coordinated scheduling of three critical resources—channels, tugboats, and berths—at liquid terminals. A novel optimization framework, termed the Channel-Tugboat-Berth-Tide (CUBT) model, is proposed. The primary objective is to minimize the total operational cost over a planning horizon, accounting for anchorage waiting time, channel occupancy, tugboat utilization, and penalties from delayed departures. To solve this model efficiently, we adopt an enhanced variant of the Logistic-Hybrid-Adaptive Black Widow Optimization Algorithm (LHA-BWOA), incorporating Logistic-Sine-Cosine Chaotic Map (LSC-CM) initialization, hybrid reproduction mechanisms, and dynamic parameter adaptation. A series of case studies involving varying planning cycles are conducted to validate the model’s practical viability. Furthermore, sensitivity analyses are performed to evaluate the impact of channel choice, tugboat allocation, and vessel waiting time. Results indicate that tugboat operations account for the largest portion of the total costs. Notably, while two-way channels result in lower direct channel costs, they do not always yield the lowest overall expenditure. Among the service strategies evaluated, the First-In–First-Out (FIFO) rule is found to be the most cost-efficient. The results offer practical guidance for port improving the operational efficiency of liquid terminals under complex tidal and resource constraints. Full article
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17 pages, 6933 KB  
Article
Hot Deformation Behavior via Isothermal Compression and Constitutive Model of GH2132 Superalloy
by Yue Sun, Peng Cheng, Decheng Wang, Chenxi Shao and Lu Cheng
Materials 2025, 18(24), 5650; https://doi.org/10.3390/ma18245650 - 16 Dec 2025
Viewed by 440
Abstract
GH2132, an Ni–Cr–Fe-based superalloy for aero-engine components, exhibits hot workability that is highly sensitive to processing parameters. The hot deformation behavior of GH2132 alloy was investigated via isothermal compression (Gleeble-3500-GTC) over 850–1100 °C and 0.001–10 s−1, combined with optical microscopy and [...] Read more.
GH2132, an Ni–Cr–Fe-based superalloy for aero-engine components, exhibits hot workability that is highly sensitive to processing parameters. The hot deformation behavior of GH2132 alloy was investigated via isothermal compression (Gleeble-3500-GTC) over 850–1100 °C and 0.001–10 s−1, combined with optical microscopy and EBSD characterization. A strain-compensated Arrhenius-type hyperbolic-sine model was established, achieving high predictive accuracy (R2 = 0.9916; AARE = 3.86%) with an average activation energy Q = 446.2 kJ·mol−1. Flow stress decreases with increasing temperature and increases with strain rate, while microstructural softening transitions from dynamic recovery to complete dynamic recrystallization at higher temperatures and lower strain rates. Three-dimensional power-dissipation and hot-processing maps (Dynamic Materials Model) delineate safe domains and instability regions, identifying an optimal window of 1000–1100 °C at 0.001–0.01 s−1 and instability at 850–900 °C with 0.01–0.1 s−1. These results provide guidance for selecting parameters for hot deformation behavior during thermomechanical processing of GH2132. Full article
(This article belongs to the Section Metals and Alloys)
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25 pages, 2296 KB  
Article
A Novel Softsign Fractional-Order Controller Optimized by an Intelligent Nature-Inspired Algorithm for Magnetic Levitation Control
by Davut Izci, Serdar Ekinci, Mohd Zaidi Mohd Tumari and Mohd Ashraf Ahmad
Fractal Fract. 2025, 9(12), 801; https://doi.org/10.3390/fractalfract9120801 - 7 Dec 2025
Cited by 4 | Viewed by 750
Abstract
This study presents a novel softsign-function-based fractional-order proportional–integral–derivative (softsign-FOPID) controller optimized using the fungal growth optimizer (FGO) for the stabilization and precise position control of an unstable magnetic ball suspension system. The proposed controller introduces a smooth nonlinear softsign function into the conventional [...] Read more.
This study presents a novel softsign-function-based fractional-order proportional–integral–derivative (softsign-FOPID) controller optimized using the fungal growth optimizer (FGO) for the stabilization and precise position control of an unstable magnetic ball suspension system. The proposed controller introduces a smooth nonlinear softsign function into the conventional FOPID structure to limit abrupt control actions and improve transient smoothness while preserving the flexibility of fractional dynamics. The FGO, a recently developed bio-inspired metaheuristic, is employed to tune the seven controller parameters by minimizing a composite objective function that simultaneously penalizes overshoot and tracking error. This optimization ensures balanced transient and steady-state performance with enhanced convergence reliability. The performance of the proposed approach was extensively benchmarked against four modern metaheuristic algorithms (greater cane rat algorithm, catch fish optimization algorithm, RIME algorithm and artificial hummingbird algorithm) under identical conditions. Statistical analyses, including boxplot comparisons and the nonparametric Wilcoxon rank-sum test, demonstrated that the FGO consistently achieved the lowest objective function value with superior convergence stability and significantly better (p < 0.05) performance across multiple independent runs. In time-domain evaluations, the FGO-tuned softsign-FOPID exhibited the fastest rise time (0.0089 s), shortest settling time (0.0163 s), lowest overshoot (4.13%), and negligible steady-state error (0.0015%), surpassing the best-reported controllers in the literature, including the sine cosine algorithm-tuned PID, logarithmic spiral opposition-based learning augmented hunger games search algorithm-tuned FOPID, and manta ray foraging optimization-tuned real PIDD2. Robustness assessments under fluctuating reference trajectories, actuator saturation, sensor noise, external disturbances, and parametric uncertainties (±10% variation in resistance and inductance) further confirmed the controller’s adaptability and stability under practical non-idealities. The smooth nonlinearity of the softsign function effectively prevented control signal saturation, while the fractional-order dynamics enhanced disturbance rejection and memory-based adaptability. Overall, the proposed FGO-optimized softsign-FOPID controller establishes a new benchmark in nonlinear magnetic levitation control by integrating smooth nonlinear mapping, fractional calculus, and adaptive metaheuristic optimization. Full article
(This article belongs to the Section Engineering)
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