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Search Results (612)

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25 pages, 1039 KiB  
Article
CEEMDAN-IHO-SVM: A Machine Learning Research Model for Valve Leak Diagnosis
by Ruixue Wang and Ning Zhao
Algorithms 2025, 18(3), 148; https://doi.org/10.3390/a18030148 - 5 Mar 2025
Abstract
Due to the complex operating environment of valves, when a fault occurs inside a valve, the vibration signal generated by the fault is easily affected by the environmental noise, making the extraction of fault features difficult. To address this problem, this paper proposes [...] Read more.
Due to the complex operating environment of valves, when a fault occurs inside a valve, the vibration signal generated by the fault is easily affected by the environmental noise, making the extraction of fault features difficult. To address this problem, this paper proposes a feature extraction method based on the combination of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Fuzzy Entropy (FN). Due to the slow convergence speed and the tendency to fall into local optimal solutions of the Hippopotamus Optimization Algorithm (HO), an improved Hippopotamus Optimization (IHO) algorithm-optimized Support Vector Machine (SVM) model for valve leakage diagnosis is introduced to further enhance the accuracy of valve leakage diagnosis. The improved Hippopotamus Optimization algorithm initializes the hippopotamus population with Tent chaotic mapping, designs an adaptive weight factor, and incorporates adaptive variation perturbation. Moreover, the performance of IHO was proven to be optimal compared to HO, Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), and Sparrow Search Algorithm (SSA) by calculating twelve test functions. Subsequently, the IHO-SVM classification model was established and applied to valve leakage diagnosis. The prediction effects of the seven models, IHO-SVM. HO-SVM, PSO-SVM, GWO-SVM, WOA-SVM, SSA-SVM, and SVM were compared and analyzed with actual data. As a result, the comparison indicated that IHO-SVM has desirable robustness and generalization, which successfully improves the classification efficiency and the recognition rate in fault diagnosis. Full article
(This article belongs to the Section Evolutionary Algorithms and Machine Learning)
38 pages, 10567 KiB  
Article
A Bionic-Based Multi-Objective Optimization for a Compact HVAC System with Integrated Air Conditioning, Purification, and Humidification
by He Li, Bozhi Yang, Xinyu Gu, Wen Xu and Xuan Liu
Biomimetics 2025, 10(3), 159; https://doi.org/10.3390/biomimetics10030159 - 3 Mar 2025
Viewed by 203
Abstract
This study is dedicated to the development of a multifunctional device that integrates air conditioning, humidification, and air purification functions, aimed at meeting the demands for energy efficiency, space-saving, and comfortable indoor environments in modern residential and commercial settings. The research focuses on [...] Read more.
This study is dedicated to the development of a multifunctional device that integrates air conditioning, humidification, and air purification functions, aimed at meeting the demands for energy efficiency, space-saving, and comfortable indoor environments in modern residential and commercial settings. The research focuses on achieving a balance between performance, energy consumption, and noise levels by combining bionic design principles with advanced optimization algorithms to propose innovative design and optimization methods. Specific methods include the establishment and optimization of mathematical models for air conditioning, air purification, and humidification functions. The air conditioning module employs a nonlinear programming model optimized through the Parrot Optimizer (PO) Algorithm to achieve uniform temperature distribution and minimal energy consumption. The air purification function is based on a bionic model and optimized using the Deep ACO Algorithm to ensure high efficiency and low noise levels. The humidification function utilizes a mist diffusion model optimized through the Slime Mold Algorithm (SMA) to enhance performance. Ultimately, a multi-objective optimization model is constructed using the Beluga Whale Optimization (BWO), successfully integrating the three main functions and designing a compact segmented cylindrical device that achieves a balance of high efficiency and multifunctionality. The optimization results indicate that the device exhibits superior performance, with a Clean Air Delivery Rate (CADR) of 400 m3/h, a humidification rate of 1.2 kg/h, a temperature uniformity index of 0.08, and a total power consumption controlled within 1600 W. This study demonstrates the significant potential of bionic design and optimization technology in the development of multifunctional indoor environment control devices, enhancing not only the overall performance of the device but also the comfort and sustainability of the indoor environment. Future work will focus on system scalability, experimental validation, and further optimization of bionic characteristics to expand the device’s applicability and enhance its environmental adaptability. Full article
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<p>Flowchart of the PO algorithm.</p>
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<p>Flowchart of the DeepACO algorithm.</p>
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<p>Flowchart of the Slime Mold Algorithm.</p>
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<p>Flowchart of the BWO algorithm.</p>
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<p>Convergence of the PO algorithm.</p>
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<p>Impact of outlet parameters on air conditioning efficiency.</p>
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<p>Indoor temperature dynamics: summer vs. winter simulation.</p>
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<p>Impact of air conditioning dimensions on temperature distribution.</p>
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<p>Sensitivity analysis for air conditioning partial modeling.</p>
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<p>DeepACO model iteration process.</p>
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<p>Air purifier design drawing.</p>
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<p>Sensitivity analysis for air purifier partial modeling.</p>
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<p>SMA iteration process.</p>
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<p>Air humidifier visualization.</p>
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<p>Room humidity distribution and dynamics.</p>
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<p>Sensitivity analysis for humidifier partial modeling.</p>
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<p>BWO algorithm iteration process.</p>
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<p>The design of an all-in-one device.</p>
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<p>The effect visualization of the all-in-one device.</p>
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<p>Sensitivity analysis for tri-unit air conditioner modeling.</p>
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25 pages, 1706 KiB  
Article
Field Strength Prediction in High-Speed Train Carriages Using a Multi-Neural Network Ensemble Model with Optimized Output Weights
by Zhou Fang, Hengkai Zhao, Yichen Feng, Yating Wu, Yanqiong Sun, Qi Yang and Guoxin Zheng
Appl. Sci. 2025, 15(5), 2709; https://doi.org/10.3390/app15052709 - 3 Mar 2025
Viewed by 223
Abstract
Accurate path loss prediction within train carriages is crucial for deploying base stations along high-speed railway lines. The field strength at receiving points inside carriages is influenced by outdoor signal transmission, penetration through window glass, and multiple reflections within the carriage, making it [...] Read more.
Accurate path loss prediction within train carriages is crucial for deploying base stations along high-speed railway lines. The field strength at receiving points inside carriages is influenced by outdoor signal transmission, penetration through window glass, and multiple reflections within the carriage, making it challenging for traditional models to predict the field strength distribution accurately. To address this issue, this paper proposes a machine learning-based path loss prediction method that incorporates ensemble techniques of multiple neural networks to enhance prediction stability and accuracy. The Whale Optimization Algorithm (WOA) is used to optimize the output weight configuration of each neural network in the ensemble model, thereby significantly improving the overall model performance. Specifically, on the test set, the WOA-optimized ensemble model reduces RMSE by 1.47 dB for CI, 0.47 dB for CNN, 0.93 dB for RNN, 1.38 dB for GNN, 0.1 dB for Transformer, 0.09 dB for AutoML, 0.33 dB for the GA-optimized ensemble model, and 0.18 dB for the PSO-optimized ensemble model. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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<p>The communication scenario between the base station and the terminal in HSR.</p>
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<p>Schematic diagram of the base station-train two-path communication scenario.</p>
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<p>Channel measurement campaigns in the HSR scenario.</p>
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<p>RT simulation scenario.</p>
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<p>Comparison of Received Power: Theoretical (Based on Two-path Model in <a href="#sec2dot2-applsci-15-02709" class="html-sec">Section 2.2</a>, see Equation (<a href="#FD1-applsci-15-02709" class="html-disp-formula">1</a>)), Measurement (<a href="#sec2dot3-applsci-15-02709" class="html-sec">Section 2.3</a>), and Simulation (Ray tracing with parameters adjusted in <a href="#sec2dot4-applsci-15-02709" class="html-sec">Section 2.4</a>).</p>
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<p>Seat layout inside the carriage: (<b>a</b>) Cross-section view of the seat arrangement; (<b>b</b>) Top view of the carriage seating layout.</p>
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<p>Field strength prediction method for HSR carriages.</p>
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<p>Flowchart of the WOA-optimized ensemble model method.</p>
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<p>MAPE performance of 144 models with varying hidden layer neuron counts.</p>
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<p>MAPE curve versus number of ensemble networks.</p>
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<p>WOA iterative optimization curve.</p>
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<p>Comparison of prediction results for Height III and Position E.</p>
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<p>Path loss distribution at height III in the first carriage: (<b>a</b>) WI simulation, (<b>b</b>) The method in this paper, and (<b>c</b>) Interpolation distribution based on the method in this paper.</p>
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23 pages, 3631 KiB  
Article
Optimization and Reliability Analysis of the Combined Application of Multiple Air Tanks Under Extreme Accident Conditions Based on the Multi-Objective Whale Optimization Algorithm
by Ran Li, Yanqiang Gao, Yihong Guan, Mou Lv and Hang Li
Sustainability 2025, 17(5), 2172; https://doi.org/10.3390/su17052172 - 3 Mar 2025
Viewed by 260
Abstract
The operational condition of fire water supply aims to ensure the continuous and reliable supply of high-pressure water in emergency situations. Assuming a fire breaks out in a mountain village located far from the city center, due to the significantly higher flow rate [...] Read more.
The operational condition of fire water supply aims to ensure the continuous and reliable supply of high-pressure water in emergency situations. Assuming a fire breaks out in a mountain village located far from the city center, due to the significantly higher flow rate and velocity of the water supply pipeline compared to normal operating conditions, any malfunction or shutdown of the pump caused by improper operation could result in catastrophic damage to the pipeline system. In response to the call for sustainable development, addressing this urgent academic challenge means finding a way to safely and economically maintain a continuous water supply to the target water demand point, even under extreme accident conditions. In this paper, drawing on engineering examples, we considered air tanks with varying process parameters installed at multiple locations within a water conveyance system to prevent water hammer and ensure water supply safety. To ensure that air tanks are of high quality and cost-effective after procurement and use, a multi-objective optimization design model comprising fitting, optimization, and evaluation plates was constructed, aimed at selecting certain process parameters. In the multi-objective optimization design model, Latin hypercube sampling improved by simulated annealing (LHS-SA), stepwise regression analysis (SRA), the Multi-Objective Whale Optimization Algorithm (MOWOA), and the Multi-Criteria Decision Analysis (MCDA) method with various weight biases are used to ensure the rationality of the optimization process. By comparing the optimization results obtained using these different MCDA methods, it is evident that the results output after AHP-EWM evaluation tend to be economic indicators, whereas the results output after FN-MABAC evaluation tend to be safety indicators. In addition, according to the sensitivity analysis of weight distribution, it can be inferred that the changes in maximum transient pressure head caused by water hammer have the most significant impact on final decision-making. Full article
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<p>Geographic information display of engineering examples.</p>
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<p>Multi-objective optimization design model.</p>
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<p>Stepwise regression fitting line graph: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">H</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">L</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>The fitting results of the functional relationship between <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mi mathvariant="normal">T</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">W</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi mathvariant="normal">W</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi mathvariant="normal">W</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>The location and details of the theoretical optimal solution in the Pareto frontier scatter plot.</p>
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25 pages, 1443 KiB  
Article
Enhancing Multi-Objective Optimization: A Decomposition-Based Approach Using the Whale Optimization Algorithm
by Jorge Ramos-Frutos, Angel Casas-Ordaz, Saúl Zapotecas-Martínez, Diego Oliva, Arturo Valdivia-González, Abel García-Nájera and Marco Pérez-Cisneros
Mathematics 2025, 13(5), 767; https://doi.org/10.3390/math13050767 - 26 Feb 2025
Viewed by 180
Abstract
Optimization techniques aim to identify optimal solutions for a given problem. In single-objective optimization, the best solution corresponds to the one that maximizes or minimizes the objective function. However, when dealing with multi-objective optimization, particularly when the objectives are conflicting, identifying the best [...] Read more.
Optimization techniques aim to identify optimal solutions for a given problem. In single-objective optimization, the best solution corresponds to the one that maximizes or minimizes the objective function. However, when dealing with multi-objective optimization, particularly when the objectives are conflicting, identifying the best solution becomes significantly more complex. In such cases, exact or analytical methods are often impractical, leading to the widespread use of heuristic and metaheuristic approaches to identify optimal or near-optimal solutions. Recent advancements have led to the development of various nature-inspired metaheuristics designed to address these challenges. Among these, the Whale Optimization Algorithm (WOA) has garnered significant attention. An adapted version of the WOA has been proposed to handle multi-objective optimization problems. This work extends the WOA to tackle multi-objective optimization by incorporating a decomposition-based approach with a cooperative mechanism to approximate Pareto-optimal solutions. The multi-objective problem is decomposed into a series of scalarized subproblems, each with a well-defined neighborhood relationship. Comparative experiments with seven state-of-the-art bio-inspired optimization methods demonstrate that the proposed decomposition-based multi-objective WOA consistently outperforms its counterparts in both real-world applications and widely used benchmark test problems. Full article
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<p>A performance assessment of the MOWOA/D with varying values of parameters <span class="html-italic">T</span> and <math display="inline"><semantics> <mi>δ</mi> </semantics></math>. The plots show (<b>a</b>) the <math display="inline"><semantics> <msup> <mi mathvariant="script">IGD</mi> <mo>+</mo> </msup> </semantics></math> indicator and (<b>b</b>) the <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mi>n</mi> </msub> </semantics></math> indicator. For clarity, the values are normalized for each test problem.</p>
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<p>Pareto front approximations obtained by MOWOA/D on UF test suite.</p>
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<p>Parallel coordinate plots of the LSID problem for (<b>a</b>) the reference Pareto and (<b>b</b>) the non-dominated solutions obtained by the MOWOA/D.</p>
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<p>Parallel coordinate plots of the UWAD problem for (<b>a</b>) the reference Pareto and (<b>b</b>) the non-dominated solutions obtained by the MOWOA/D.</p>
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23 pages, 1972 KiB  
Article
Multi-Scale Fusion MaxViT for Medical Image Classification with Hyperparameter Optimization Using Super Beluga Whale Optimization
by Jiaqi Zhao, Tiannuo Liu and Lin Sun
Electronics 2025, 14(5), 912; https://doi.org/10.3390/electronics14050912 - 25 Feb 2025
Viewed by 204
Abstract
This study presents an enhanced deep learning model, Multi-Scale Fusion MaxViT (MSF-MaxViT), designed for medical image classification. The aim is to improve both the accuracy and robustness of the image classification task. MSF-MaxViT incorporates a Parallel Attention mechanism for fusing local and global [...] Read more.
This study presents an enhanced deep learning model, Multi-Scale Fusion MaxViT (MSF-MaxViT), designed for medical image classification. The aim is to improve both the accuracy and robustness of the image classification task. MSF-MaxViT incorporates a Parallel Attention mechanism for fusing local and global features, inspired by the MaxViT Block and Multihead Dynamic Attention, to improve feature representation. It also combines lightweight components such as the novel Multi-Scale Fusion Attention (MSFA) block, Feature Boosting (FB) Block, Coord Attention, and Edge Attention to enhance spatial and channel feature learning. To optimize the hyperparameters in the network model, the Super Beluga Whale Optimization (SBWO) algorithm is used, which combines bi-interpolation and adaptive parameter tuning, and experiments have shown that it has a relatively excellent convergence performance. The network model, combined with the improved SBWO algorithm, has an image classification accuracy of 92.87% on the HAM10000 dataset, which is 1.85% higher than that of MaxViT, proving the practicality and effectiveness of the model. Full article
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<p>MSF-MaxViT.</p>
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<p>Parallel attention.</p>
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<p>Multi-Scale Fusion Attention.</p>
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<p>HAM10000 Image: (<b>a</b>) ISIC_0027419: bkl; (<b>b</b>) ISIC_0033603: mel; (<b>c</b>) ISIC_0031263: bcc; (<b>d</b>) ISIC_0029624: nv; (<b>e</b>) ISIC_0031228: akiec; (<b>f</b>) ISIC_0033749: vasc.</p>
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<p>Algorithm comparison curve.</p>
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<p>Convergence curve.</p>
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<p>(<b>a</b>) Accuracy images; (<b>b</b>) confusion matrix.</p>
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26 pages, 10136 KiB  
Article
3D Deployment Optimization of Wireless Sensor Networks for Heterogeneous Functional Nodes
by Zean Lu, Chengqun Wang, Peng Wang and Weiqiang Xu
Sensors 2025, 25(5), 1366; https://doi.org/10.3390/s25051366 - 23 Feb 2025
Viewed by 143
Abstract
The optimization of wireless sensor network (WSN) deployment is a current research hotspot, particularly significant in industrial applications. While some existing optimization methods focus more on balancing network coverage, connectivity, and deployment costs, aligning them with practical needs compared to single-performance optimization schemes, [...] Read more.
The optimization of wireless sensor network (WSN) deployment is a current research hotspot, particularly significant in industrial applications. While some existing optimization methods focus more on balancing network coverage, connectivity, and deployment costs, aligning them with practical needs compared to single-performance optimization schemes, they still tend to be overly idealized. In practical applications, networks often face monitoring requirements for different data types, and some single-function sensors can be integrated into multifunctional sensors capable of monitoring multiple types of data. When encountering diverse data detection needs in a target area, this integration can be further considered to reduce deployment costs. Therefore, this paper designs a new multi-objective optimization problem aimed at optimizing heterogeneous-function wireless sensor networks, balancing coverage, connectivity, and cost, while introducing an additional cost dimension to meet the monitoring needs of different functional sensors in specific areas. This problem is a typical non-convex, multimodal, NP-hard problem. To address this, an improved Secretary Bird Optimization Algorithm (ISBOA) is proposed, incorporating Gaussian Cuckoo Mutation and a smooth exploitation mechanism. The algorithm is compared with the original SBOA, Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), and Northern Goshawk Optimization (NGO). Simulation results demonstrate that ISBOA exhibits a faster convergence speed and higher accuracy in both the 23 benchmark functions and the newly designed multi-objective optimization problem, significantly overcoming the shortcomings of the compared algorithms. Finally, for large-scale optimization problems, a minimum spanning tree domain reduction strategy is proposed, which significantly improves solving efficiency with a moderate sacrifice in accuracy. Full article
(This article belongs to the Section Sensor Networks)
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<p>Monitoring scenario.</p>
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<p>Coverage radius and communication radius of the sensor node. (<b>a</b>) Sensor coverage and communication radii. (<b>b</b>) Uncertainty in sensor coverage. (<b>c</b>) Uncertainty in sensor communication.</p>
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<p>ISBOA flowchart.</p>
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<p>Position changes of movable network nodes in a closed space. (<b>a</b>) Initial deployment. (<b>b</b>) Optimized deployment.</p>
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<p>Potential deployment positions of sensor nodes.</p>
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<p>Potential Performance of ISBOA and comparison algorithms on 23 benchmark functions.</p>
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<p>Performance Comparison of the ISBOA with other algorithms.</p>
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<p>Sensor node positions before and after optimization using the ISBOA algorithm. (<b>a</b>) Initial positions of sensor nodes. (<b>b</b>) Optimized positions of sensor nodes.</p>
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<p><math display="inline"><semantics> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </semantics></math> cross-section of the optimized heterogeneous wireless sensor network.</p>
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<p><math display="inline"><semantics> <mrow> <mi>X</mi> <mi>Z</mi> </mrow> </semantics></math> cross-section of the optimized heterogeneous wireless sensor network.</p>
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<p><math display="inline"><semantics> <mrow> <mi>Y</mi> <mi>Z</mi> </mrow> </semantics></math> cross-section of the optimized heterogeneous wireless sensor network.</p>
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<p>The performance of ISBOA compared to other algorithms in multi-objective optimization problems.</p>
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24 pages, 2820 KiB  
Article
An Enhanced Misinformation Detection Model Based on an Improved Beluga Whale Optimization Algorithm and Cross-Modal Feature Fusion
by Guangyu Mu, Xiaoqing Ju, Hongduo Yan, Jiaxue Li, He Gao and Xiurong Li
Biomimetics 2025, 10(3), 128; https://doi.org/10.3390/biomimetics10030128 - 20 Feb 2025
Viewed by 266
Abstract
The proliferation of multimodal misinformation on social media has become a critical concern. Although detection methods have advanced, feature representation and cross-modal semantic alignment challenges continue to hinder the effective use of multimodal data. Therefore, this paper proposes an IBWO-CASC detection model that [...] Read more.
The proliferation of multimodal misinformation on social media has become a critical concern. Although detection methods have advanced, feature representation and cross-modal semantic alignment challenges continue to hinder the effective use of multimodal data. Therefore, this paper proposes an IBWO-CASC detection model that integrates an improved Beluga Whale Optimization algorithm with cross-modal attention feature fusion. Firstly, the Beluga Whale Optimization algorithm is enhanced by combining adaptive search mechanisms with batch parallel strategies in the feature space. Secondly, a feature alignment method is designed based on supervised contrastive learning to establish semantic consistency. Then, the model incorporates a Cross-modal Attention Promotion mechanism and global–local interaction learning pattern. Finally, a multi-task learning framework is built based on classification and contrastive objectives. The empirical analysis shows that the proposed IBWO-CASC model achieves a detection accuracy of 97.41% on our self-constructed multimodal misinformation dataset. Compared with the average accuracy of the existing six baseline models, the accuracy of this model is improved by 4.09%. Additionally, it demonstrates enhanced robustness in handling complex multimodal scenarios. Full article
(This article belongs to the Special Issue Nature-Inspired Metaheuristic Optimization Algorithms 2025)
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<p>The architecture of the IBWO-CASC model.</p>
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<p>(<b>a</b>) Self-attention mechanism; (<b>b</b>) cross-attention mechanism.</p>
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<p>Comparison of Models’ Parameters.</p>
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<p>Comparison of Models’ FLOPS.</p>
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<p>Loss function convergence curves.</p>
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<p>Multi-layer attention feature heatmaps.</p>
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23 pages, 1983 KiB  
Article
Using Optimization Algorithms for Effective Missing-Data Imputation: A Case Study of Tabular Data Derived from Video Surveillance
by Mahmoud M. Eid, Kamal ElDahshan, Abdelatif H. Abouali and Alaa Tharwat
Algorithms 2025, 18(3), 119; https://doi.org/10.3390/a18030119 - 20 Feb 2025
Viewed by 265
Abstract
Data are crucial components of machine learning and deep learning in real-world applications. However, when collecting data from actual systems, we often encounter issues with missing information, which can harm accuracy and lead to biased results. In the context of video surveillance, missing [...] Read more.
Data are crucial components of machine learning and deep learning in real-world applications. However, when collecting data from actual systems, we often encounter issues with missing information, which can harm accuracy and lead to biased results. In the context of video surveillance, missing data may arise due to obstructions, varying camera angles, or technical issues, resulting in incomplete information about the observed scene. This paper introduces a method for handling missing data in tabular formats, specifically focusing on video surveillance. The core idea is to fill in the missing values for a specific feature using values from other related features rather than relying on all available features, which we refer to as the imputation approach based on informative features. The paper presents three sets of experiments. The first set uses synthetic datasets to compare four optimization algorithms—Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), and the Sine–Cosine Algorithm (SCA)—to determine which one best identifies features related to the target feature. The second set works with real-world datasets, while the third focuses on video-surveillance datasets. Each experiment compares the proposed method, utilizing the best optimizer from the first set, against leading imputation methods. The experiments evaluate different types of data and various missing-data rates, ensuring that randomness does not introduce bias. In the first experiment, using only synthetic data, the results indicate that the WOA-based approach outperforms PSO, GWO, and SCA optimization algorithms. The second experiment used real datasets, while the third used tabular data extracted from a video-surveillance system. Both experiments show that our WOA-based imputation method produces promising results, outperforming other state-of-the-art imputation methods. Full article
(This article belongs to the Special Issue Algorithms for Feature Selection (3rd Edition))
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<p>Illustrative figure comparing the parameters of four optimization algorithms: PSO, GWO, WOA, and SCA. The shaded regions indicate shared parameters among the optimizers, highlighting the similarities in their configurations. Notably, GWO and WOA have closely aligned parameters, with WOA incorporating an additional parameter <span class="html-italic">b</span>, which distinguishes it from GWO.</p>
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<p>Flowchart of the proposed imputation method.</p>
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<p>Visualization of the iterative search phase in the proposed feature selection-based imputation method.</p>
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<p>Visualization of the convergence curves of the PSO, GWO, WOA, and SCA algorithms using a synthetic dataset.</p>
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48 pages, 16863 KiB  
Article
Multi-Strategy Hybrid Whale Optimization Algorithm Improvement
by Xie Xie, Yulin Yang and Huan Zhou
Appl. Sci. 2025, 15(4), 2224; https://doi.org/10.3390/app15042224 - 19 Feb 2025
Viewed by 278
Abstract
The whale optimization algorithm (WOA) is a swarm intelligence optimization algorithm developed by Mirjalili and Lewis in 2016 based on the foraging behavior of whales. Because of its simplicity and high efficiency, scholars have adopted this algorithm to address various problems in different [...] Read more.
The whale optimization algorithm (WOA) is a swarm intelligence optimization algorithm developed by Mirjalili and Lewis in 2016 based on the foraging behavior of whales. Because of its simplicity and high efficiency, scholars have adopted this algorithm to address various problems in different disciplines. However, standard WOA has the problems of slow convergence speed, insufficient search accuracy, and limited ability to solve complex problems. In order to solve these problems, this paper proposes a multi-strategy hybrid whale algorithm (MHWOA). Firstly, the calculation speed is accelerated by modifying the parameters; then, the accuracy of the algorithm is improved by incorporating the scatter search strategy; finally, the simulated annealing algorithm is integrated to improve its ability to solve complex problems. The performance differences between MHWOA, the baseline algorithm, and the improved WOA algorithm are compared using the CEC2017 test suite and three real-world engineering problems. In the comparison of processing results of various problems, the calculation accuracy of MHWOA is improved by no less than 1.96%, the calculation error is reduced by no less than 1.83%, and the execution time is improved by no less than 5.6%. In the CNN-MHWOA-based time series electricity load forecasting problem, MHWOA shows the advantages of reduced error and improved fitting degree with the true value compared with the standard WOA. Full article
(This article belongs to the Special Issue Evolutionary Algorithms and Their Real-World Applications)
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<p>WOA improvement types [<a href="#B15-applsci-15-02224" class="html-bibr">15</a>,<a href="#B16-applsci-15-02224" class="html-bibr">16</a>,<a href="#B17-applsci-15-02224" class="html-bibr">17</a>,<a href="#B18-applsci-15-02224" class="html-bibr">18</a>,<a href="#B19-applsci-15-02224" class="html-bibr">19</a>,<a href="#B20-applsci-15-02224" class="html-bibr">20</a>,<a href="#B21-applsci-15-02224" class="html-bibr">21</a>,<a href="#B22-applsci-15-02224" class="html-bibr">22</a>,<a href="#B23-applsci-15-02224" class="html-bibr">23</a>,<a href="#B24-applsci-15-02224" class="html-bibr">24</a>,<a href="#B25-applsci-15-02224" class="html-bibr">25</a>,<a href="#B26-applsci-15-02224" class="html-bibr">26</a>,<a href="#B27-applsci-15-02224" class="html-bibr">27</a>,<a href="#B28-applsci-15-02224" class="html-bibr">28</a>,<a href="#B29-applsci-15-02224" class="html-bibr">29</a>,<a href="#B30-applsci-15-02224" class="html-bibr">30</a>,<a href="#B31-applsci-15-02224" class="html-bibr">31</a>,<a href="#B32-applsci-15-02224" class="html-bibr">32</a>,<a href="#B33-applsci-15-02224" class="html-bibr">33</a>,<a href="#B34-applsci-15-02224" class="html-bibr">34</a>,<a href="#B35-applsci-15-02224" class="html-bibr">35</a>,<a href="#B36-applsci-15-02224" class="html-bibr">36</a>,<a href="#B37-applsci-15-02224" class="html-bibr">37</a>].</p>
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<p>Position deflection diagram.</p>
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<p>A diagram of the simulated annealing algorithm solution.</p>
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<p>Visual views of the comparison of MHWOA and standard swarm intelligence algorithms convergence cases.</p>
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<p>Visual views of the comparison of MHWOA and standard swarm intelligence algorithms convergence cases.</p>
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<p>Visual views of the comparison of convergence cases.</p>
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<p>Visual views of the comparison of convergence cases.</p>
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<p>Visual views of the comparison of convergence cases.</p>
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<p>The stability of the box can be compared with that of the standard algorithm.</p>
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<p>The stability of the box can be compared with that of the standard algorithm.</p>
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<p>The stability of the box can be compared with that of the standard algorithm.</p>
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<p>Box line visual views of the stability comparison.</p>
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<p>Box line visual views of the stability comparison.</p>
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<p>Convergence comparison for CEC2022 with dimension 10.</p>
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<p>Convergence comparison for CEC2022 with dimension 10.</p>
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<p>Convergence comparison for CEC2022 with dimension 20.</p>
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<p>Convergence comparison for CEC2022 with dimension 20.</p>
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<p>An illustration of the pressure vessel design.</p>
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<p>Convergence visibility of the pressure vessel design.</p>
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<p>A schematic diagram of the welded beam design problem.</p>
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<p>Convergence visibility of the welded beam design.</p>
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<p>A schematic diagram of weight minimization of a speed reducer problem.</p>
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<p>Convergence visibility of weight minimization of a speed reducer design.</p>
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<p>The convolutional neural network architecture.</p>
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<p>Standard long short-term memory network architecture.</p>
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<p>A schematic of the parallel multi-head attention.</p>
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<p>A diagram of the CNN structure applied by MHWOA.</p>
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<p>Specific visual data.</p>
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<p>MHWOA evolution curve.</p>
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<p>The fit curve between predicted and true values.</p>
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<p>Visual comparison of MAE and RMSE.</p>
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<p>Visual comparison between R2 and MAE.</p>
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<p>Visual comparison between MAE and MAPE.</p>
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<p>The contrast factor radar chart.</p>
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19 pages, 6079 KiB  
Article
A Method for Enhancing the Traffic Situation Awareness of Vessel Traffic Service Operators by Identifying High Risk Ships in Complex Navigation Conditions
by Lei Zhang, Jiahao Ge, Floris Goerlandt, Lei Du, Tuowei Chen, Tingting Gu, Langxiong Gan and Xiaobin Li
J. Mar. Sci. Eng. 2025, 13(2), 379; https://doi.org/10.3390/jmse13020379 - 19 Feb 2025
Viewed by 253
Abstract
As ship traffic volumes increase and navigable waters become more complex, vessel traffic service operators (VTSOs) face growing challenges to effectively monitor marine traffic. To address the heavy reliance on human expertise in current ship supervision, we propose a method for quickly identifying [...] Read more.
As ship traffic volumes increase and navigable waters become more complex, vessel traffic service operators (VTSOs) face growing challenges to effectively monitor marine traffic. To address the heavy reliance on human expertise in current ship supervision, we propose a method for quickly identifying high risk ships to enhance the situational awareness of VTSOs in complex waters. First, the K-means clustering algorithm is improved using the Whale Optimization Algorithm (WOA) to adaptively cluster ships within a waterway, segmenting the traffic in the area into multiple ship clusters. Second, a ship cluster collision risk assessment model is developed to quantify the degree of collision risk for each ship cluster. Finally, a weighted directed complex network is constructed to identify high risk ships within each ship cluster. Experimental simulations show that the proposed WOA–K-means clustering algorithm outperforms other adaptive clustering algorithms in terms of computation speed and accuracy. The developed ship cluster collision risk assessment model can identify high risk ship clusters that require VTSO attention, and the weighted directed complex network model accurately identifies high risk ships. This approach can assist VTSOs in executing a comprehensive and targeted monitoring process encompassing macro, meso, and micro aspects, thus boosting the efficacy of ship oversight, and mitigating traffic hazards. Full article
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<p>Overview of the methodology in this paper.</p>
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<p>Flowchart of the algorithm in this document.</p>
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<p>(<b>a</b>) SDOI &gt; 1, no risk of collision between ships; (<b>b</b>) SDOI = 1, risk of collision; (<b>c</b>) SDOI &lt; 1, risk of collision. Where R1 and R2 represent the distance from the center of the ship’s field to the ship’s field boundary of the two ships, respectively, and the longer dashed line represents the straight-line distance between the fields of the two ships.</p>
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<p>(<b>a</b>) Ship position and heading; (<b>b</b>) directed composite network considering ship collision risk; (<b>c</b>) multi-weighted directed network, where node sizes represent type weights, and the thickness of connected edges represent speed weights.</p>
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<p>(<b>a</b>) The best K value obtained by the WOA–K-means algorithm; (<b>b</b>) the ship cluster division based on the WOA–K-means algorithm.</p>
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<p>A directed complex network of cluster 1. Where the number represents the ship number in Cluster 1, and the red circle represents that the ship is the ship with the highest complexity in the cluster.</p>
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<p>Comparison results between GA-K-means algorithm and WOA-K-means algorithm. (<b>a</b>) is the simulated experimental scene, (<b>b</b>) is the comparison graph of the two types of algorithms to find the best K value, (<b>c</b>) is the GA-K-means optimization search iteration graph, and (<b>d</b>) is the WOA-K-means optimization search iteration graph.</p>
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<p>Dividing water bodies using a thermal map. where the numbers represent the ship cluster numbers and the red circles represent the boundaries of each ship cluster.</p>
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<p>Network efficiency change curve after different node deletion.</p>
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18 pages, 3749 KiB  
Article
Machine Learning-Driven Prediction of Vitamin D Deficiency Severity with Hybrid Optimization
by Usharani Bhimavarapu, Gopi Battineni and Nalini Chintalapudi
Bioengineering 2025, 12(2), 200; https://doi.org/10.3390/bioengineering12020200 - 18 Feb 2025
Viewed by 395
Abstract
There is a growing need to predict the severity of vitamin D deficiency (VDD) through non-invasive methods due to its significant global health concerns. For vitamin D-level assessments, the 25-hydroxy vitamin D (25-OH-D) blood test is the standard, but it is often not [...] Read more.
There is a growing need to predict the severity of vitamin D deficiency (VDD) through non-invasive methods due to its significant global health concerns. For vitamin D-level assessments, the 25-hydroxy vitamin D (25-OH-D) blood test is the standard, but it is often not a practical test. This study is focused on developing a machine learning (ML) model that is clinically acceptable for accurately detecting vitamin D status and eliminates the need for 25-OH-D determination while addressing overfitting. To enhance the capacity of the classification system to predict multiple classes, preprocessing procedures such as data reduction, cleaning, and transformation were used on the raw vitamin D dataset. The improved whale optimization (IWOA) algorithm was used for feature selection, which optimized weight functions to improve prediction accuracy. To gauge the effectiveness of the proposed IWOA algorithm, evaluation metrics like precision, accuracy, recall, and F1-score were used. The results showed a 99.4% accuracy, demonstrating that the proposed method outperformed the others. A comparative analysis demonstrated that the stacking classifier was the superior choice over the other classifiers, highlighting its effectiveness and robustness in detecting deficiencies. Incorporating advanced optimization techniques, the proposed method’s promise for generating accurate predictions is highlighted in the study. Full article
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Graphical abstract

Graphical abstract
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<p>Score-based feature importance.</p>
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<p>Feature correlation matrix (* |corr| &gt; 0.25).</p>
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<p>Confusion matrix outcomes of adopted models.</p>
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<p>Seasonal variation.</p>
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<p>Frequency of participants within each level of severity.</p>
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28 pages, 9558 KiB  
Article
Economy Optimization by Multi-Strategy Improved Whale Optimization Algorithm Based on User Driving Cycle Construction for Hybrid Electric Vehicles
by Jie Ma, Mingzhang Pan, Wei Guan, Zhiqing Zhang, Jingcheng Zhou, Nianye Ye, Haifeng Qin, Lulu Li and Xingjia Man
Machines 2025, 13(2), 158; https://doi.org/10.3390/machines13020158 - 17 Feb 2025
Viewed by 218
Abstract
Nowadays, there is an increasing focus on enhancing the economy of hybrid electric vehicles (HEVs). This study builds a framework model for the parameter optimization of hybrid powertrains in user driving cycles. Unlike the optimization under standard driving cycles, the applied user driving [...] Read more.
Nowadays, there is an increasing focus on enhancing the economy of hybrid electric vehicles (HEVs). This study builds a framework model for the parameter optimization of hybrid powertrains in user driving cycles. Unlike the optimization under standard driving cycles, the applied user driving cycle incarnates realistic driving situations, and the optimization results are more realistic. Firstly, the user driving cycle with high accuracy is constructed based on actual driving data, which provides a basis for the performance analysis of HEV. Secondly, the HEV model with good power and economy is constructed under user driving cycles. Finally, a multi-strategy improved whale optimization algorithm (MIWOA) is proposed, which can guarantee better economy of HEV compared with the original whale optimization algorithm (WOA). The economy optimization of HEV is completed by MIWOA under user driving cycles, and the hybrid vehicle economy parameters that are more in line with the user’s actual driving conditions are obtained. After optimization, the 100 km equivalent fuel consumption (EFC) of HEV is reduced by 5.20%, which effectively improves the vehicle’s economy. This study demonstrates the effectiveness of the MIWOA method in improving economy and contributes a fresh thought and method for the economic optimization of the hybrid powertrain. Full article
(This article belongs to the Section Vehicle Engineering)
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<p>Hybrid powertrain parameters optimization model based on user driving cycle.</p>
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<p>Schematic diagram of Internet of Vehicles data acquisition.</p>
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<p>Kinematic segments and motion states.</p>
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<p>Contribution and cumulative contribution of each principal component.</p>
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<p>Clustering bias for different N values.</p>
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<p>Flowchart of SAGAFCM algorithm.</p>
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<p>Scatter plot of clustering results of first three principal components.</p>
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<p>Representative driving cycle of users’ real vehicles.</p>
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<p>Characterization indicators and their relative errors.</p>
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<p>Topology of powertrain system.</p>
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<p>Motor (<b>a</b>) external characteristic curve and (<b>b</b>) efficiency map.</p>
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<p>Velocity following and real-time deviation under (<b>a</b>) user driving cycle, (<b>b</b>) WLTC, (<b>c</b>) NEDC, (<b>d</b>) FTP-75.</p>
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<p>Motor torque and battery current under (<b>a</b>) user driving cycle, (<b>b</b>) WLTC, (<b>c</b>) NEDC, (<b>d</b>) FTP-75.</p>
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<p>Battery SOC under four driving cycles.</p>
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<p>The 100 km equivalent fuel consumption under four driving cycles.</p>
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<p>Gear shift schedule.</p>
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<p>Flowchart of whale optimization algorithm.</p>
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<p>Flowchart of multi-strategy improved whale optimization algorithm.</p>
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<p>Optimization results of GA, WOA, and MIWOA.</p>
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<p>Velocity following and instantaneous deviations under (<b>a</b>) user driving cycle, (<b>b</b>) WLTC, (<b>c</b>) NEDC, (<b>d</b>) FTP-75 after optimization.</p>
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<p>Shift schedule before and after optimization.</p>
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<p>Comparison of 100 km EFC before and after optimization under (<b>a</b>) user driving cycle, (<b>b</b>) WLTC, (<b>c</b>) NEDC, (<b>d</b>) FTP-75.</p>
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<p>Comparison of SOC curves before and after optimization under (<b>a</b>) user driving cycle, (<b>b</b>) WLTC, (<b>c</b>) NEDC, (<b>d</b>) FTP-75.</p>
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<p>Comparison of SOC curves before and after optimization under (<b>a</b>) user driving cycle, (<b>b</b>) WLTC, (<b>c</b>) NEDC, (<b>d</b>) FTP-75.</p>
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17 pages, 2478 KiB  
Article
A Flexible Interconnected Distribution Network Power Supply Restoration Method Based on E-SOP
by Lin Jiang, Canbin Wang, Wei Qiu, Hui Xiao and Wenshan Hu
Energies 2025, 18(4), 954; https://doi.org/10.3390/en18040954 - 17 Feb 2025
Viewed by 315
Abstract
To enhance the self-healing control capability of soft open points with energy storage (E-SOPs) and optimize the fault recovery performance in flexible interconnected distribution networks, this paper proposes a novel power supply restoration method based on E-SOP. The methodology begins with a comprehensive [...] Read more.
To enhance the self-healing control capability of soft open points with energy storage (E-SOPs) and optimize the fault recovery performance in flexible interconnected distribution networks, this paper proposes a novel power supply restoration method based on E-SOP. The methodology begins with a comprehensive analysis of the E-SOP’s fundamental architecture and loss model. Subsequently, a dual-objective optimization function is formulated to maximize the sum of nodal active load restoration while minimizing network losses. The optimization problem is transformed into a second-order cone programming formulation under comprehensive operational constraints. To solve this complex optimization model, an innovative hybrid approach combining the Improved Whale Optimization Algorithm (IWOA) with second-order cone programming is developed. The proposed methodology is extensively validated using the IEEE 33-node test system. The experimental results demonstrate that this approach significantly enhances the power supply restoration capability of distribution networks while maintaining practical feasibility. Full article
(This article belongs to the Special Issue Measurement Systems for Electric Machines and Motor Drives)
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<p>Basic structure of E-SOP.</p>
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<p>Optimization results of different algorithms on Test Function 1.</p>
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<p>Optimization results of different algorithms on Test Function 2.</p>
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<p>Optimization results of different algorithms on Test Function 3.</p>
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<p>Flowchart of power supply restoration process based on E-SOP.</p>
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<p>Topology of IEEE 33-node test system.</p>
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<p>Modified test system topology with E-SOP.</p>
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<p>Network configuration diagram of Case 2.</p>
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<p>Node voltage distribution under different scenarios.</p>
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<p>Modified test system topology with DG integration.</p>
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<p>Node voltage distribution under different scenarios with DG integration.</p>
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26 pages, 2233 KiB  
Article
Exploring the Impact of Local Operator Configurations in the Multi-Demand Multidimensional Knapsack Problem
by José García, Ivo Cattarinich, Paola Moraga and Hernan Pinto
Appl. Sci. 2025, 15(4), 2059; https://doi.org/10.3390/app15042059 - 16 Feb 2025
Viewed by 218
Abstract
The Multi-demand Multidimensional Knapsack Problem (MDMKP) is a challenging combinatorial task due to its capacity and demand constraints. Local search operators play a key role in metaheuristics when navigating such complex solution spaces, yet their impact on MDMKP performance has received limited attention. [...] Read more.
The Multi-demand Multidimensional Knapsack Problem (MDMKP) is a challenging combinatorial task due to its capacity and demand constraints. Local search operators play a key role in metaheuristics when navigating such complex solution spaces, yet their impact on MDMKP performance has received limited attention. In this work, we investigate four local operator configurations—Add, Drop, Swap, and All Operator—within the Whale Optimization Algorithm framework. Our approach integrates these operators to broaden search coverage and refine candidate solutions. This design aims to enhance solution quality by balancing exploration and exploitation across multiple dimensions of the MDMKP. Experimental results on benchmark instances with different sizes (n=100,250, and 500) show that the All Operator configuration consistently achieves better maximum and average values. In large-scale instances (n = 500), the “All Operator” configuration achieves an average maximum value of 107,967, which is approximately 1.4% higher than the 106,490 achieved by the “Add Operator” and about 0.2% higher than the 107,771 obtained by the “Swap Operator”, while significantly outperforming the “Drop Operator” (average maximum of 99,164). Statistical tests confirm its advantage over the other configurations, suggesting that combining multiple local operators can significantly strengthen performance in high-dimensional and constraint-heavy settings like the MDMKP. Full article
(This article belongs to the Special Issue Novel Research and Applications on Optimization Algorithms)
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<p>The Developed Swarm Intelligence-Based Machine Learning Algorithm.</p>
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<p>Violin plots (<b>top row</b>) show the distribution of %GAP values for averages and maximums across configurations. Scatter plots (<b>bottom row</b>) compare %GAP values relative to the best-known solution for averages (<b>left</b>) and maximums (<b>right</b>) for small-sized instances (<math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>).</p>
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<p>Comparison of %GAP across different operators for average and maximum values relative to the best-known solution. The left panel shows the scatter plots of %GAP for averages, while the right panel displays %GAP for maximums. The violin and scatter plots below illustrate the distribution of %GAP for averages and maximums, emphasizing the variability and performance of each operator.</p>
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<p>Comparison of %GAP across different operators for <span class="html-italic">n</span> = 500 when evaluating average and maximum values relative to the best-known solution. The left panel presents scatter plots of %GAP for average results, and the right panel shows %GAP for maximum outcomes. Below these, the violin and scatter plots illustrate the distribution of %GAP, emphasizing the performance and variability among the operators.</p>
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<p>Sensitivity analysis results for the parameter <span class="html-italic">L</span>. (<b>a</b>) %GAP of maximum value. (<b>b</b>) %GAP of average maximum value.</p>
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