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Search Results (2,474)

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18 pages, 5863 KiB  
Article
Dung Beetle Optimization Algorithm Based on Improved Multi-Strategy Fusion
by Rencheng Fang, Tao Zhou, Baohua Yu, Zhigang Li, Long Ma and Yongcai Zhang
Electronics 2025, 14(1), 197; https://doi.org/10.3390/electronics14010197 (registering DOI) - 5 Jan 2025
Abstract
The Dung Beetle Optimization Algorithm (DBO) is characterized by its great convergence accuracy and quick convergence speed. However, like other swarm intelligent optimization algorithms, it also has the disadvantages of having an unbalanced ability to explore the world and to use local resources, [...] Read more.
The Dung Beetle Optimization Algorithm (DBO) is characterized by its great convergence accuracy and quick convergence speed. However, like other swarm intelligent optimization algorithms, it also has the disadvantages of having an unbalanced ability to explore the world and to use local resources, as well as being prone to settling into local optimal search in the latter stages of optimization. In order to address these issues, this research suggests a multi-strategy fusion dung beetle optimization method (MSFDBO). To enhance the quality of the first solution, the refractive reverse learning technique expands the algorithm search space in the first stage. The algorithm’s accuracy is increased by adding an adaptive curve to control the dung beetle population size and prevent it from reaching a local optimum. In order to improve and balance local exploitation and global exploration, respectively, a triangle wandering strategy and a fusion subtractive averaging optimizer were later added to Rolling Dung Beetle and Breeding Dung Beetle. Individual beetles will congregate at the current optimal position, which is near the optimal value, during the last optimization stage of the MSFDBO; however, the current optimal value could not be the global optimal value. Thus, to variationally perturb the global optimal solution (so that it leaps out of the local optimal solution in the final optimization stage of the MSFDBO) and to enhance algorithmic performance (generally and specifically, in the effect of optimizing the search), an adaptive Gaussian–Cauchy hybrid variational perturbation factor is introduced. Using the CEC2017 benchmark function, the MSFDBO’s performance is verified by comparing it to seven different intelligence optimization algorithms. The MSFDBO ranks first in terms of average performance. The MSFDBO can lower the labor and production expenses associated with welding beam and reducer design after testing two engineering application challenges. When it comes to lowering manufacturing costs and overall weight, the MSFDBO outperforms other swarm intelligence optimization methods. Full article
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<p>Refractive inverse learning schematics.</p>
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<p>MSFDBO algorithm flowchart.</p>
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<p>CEC2017 50 dimension average degree levels.</p>
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<p>CEC2017 100 dimension average degree levels.</p>
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<p>Average convergence curves of CEC2017 50-dimensional benchmarking functions.</p>
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<p>Average convergence curves of CEC2017 50-dimensional benchmarking functions.</p>
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<p>Schematic of the welded beam (Above: Engineering drawing, Below: 3D).</p>
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<p>Schematic of the reducer design (<b>Right</b>: Engineering drawing, <b>Left</b>: 3D).</p>
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21 pages, 1416 KiB  
Article
Multi-Agent Reinforcement Learning for Efficient Resource Allocation in Internet of Vehicles
by Jun-Han Wang, He He, Jaesang Cha, Incheol Jeong and Chang-Jun Ahn
Electronics 2025, 14(1), 192; https://doi.org/10.3390/electronics14010192 (registering DOI) - 5 Jan 2025
Abstract
The Internet of Vehicles (IoV), a burgeoning technology, merges advancements in the internet, vehicle electronics, and wireless communications to foster intelligent vehicle interactions, thereby enhancing the efficiency and safety of transportation systems. Nonetheless, the continual and high-frequency communications among vehicles, coupled with regional [...] Read more.
The Internet of Vehicles (IoV), a burgeoning technology, merges advancements in the internet, vehicle electronics, and wireless communications to foster intelligent vehicle interactions, thereby enhancing the efficiency and safety of transportation systems. Nonetheless, the continual and high-frequency communications among vehicles, coupled with regional limitations in system capacity, precipitate significant challenges in allocating wireless resources for vehicular networks. In addressing these challenges, this study formulates the resource allocation issue as a multi-agent deep reinforcement learning scenario and introduces a novel multi-agent actor-critic framework. This framework incorporates a prioritized experience replay mechanism focused on distributed execution, which facilitates decentralized computing by structuring the training processes and defining specific reward functions, thus optimizing resource allocation. Furthermore, the framework prioritizes empirical data during the training phase based on the temporal difference error (TD error), selectively updating the network with high-priority data at each sampling point. This strategy not only accelerates model convergence but also enhances the learning efficacy. The empirical validations confirm that our algorithm augments the total capacity of vehicle-to-infrastructure (V2I) links by 9.36% and the success rate of vehicle-to-vehicle (V2V) transmissions by 6.74% compared with a benchmark algorithm. Full article
22 pages, 2254 KiB  
Article
LSN-GTDA: Learning Symmetrical Network via Global Thermal Diffusion Analysis for Pedestrian Trajectory Prediction in Unmanned Aerial Vehicle Scenarios
by Ling Mei, Mingyu Fu, Bingjie Wang, Lvxiang Jia, Mingyu Yu, Yu Zhang and Lijun Zhang
Remote Sens. 2025, 17(1), 154; https://doi.org/10.3390/rs17010154 (registering DOI) - 4 Jan 2025
Viewed by 424
Abstract
The integration of pedestrian movement analysis with Unmanned Aerial Vehicle (UAV)-based remote sensing enables comprehensive monitoring and a deeper understanding of human dynamics within urban environments, thereby facilitating the optimization of urban planning and public safety strategies. However, human behavior inherently involves uncertainty, [...] Read more.
The integration of pedestrian movement analysis with Unmanned Aerial Vehicle (UAV)-based remote sensing enables comprehensive monitoring and a deeper understanding of human dynamics within urban environments, thereby facilitating the optimization of urban planning and public safety strategies. However, human behavior inherently involves uncertainty, particularly in the prediction of pedestrian trajectories. A major challenge lies in modeling the multimodal nature of these trajectories, including varying paths and targets. Current methods often lack a theoretical framework capable of fully addressing the multimodal uncertainty inherent in trajectory predictions. To tackle this, we propose a novel approach that models uncertainty from two distinct perspectives: (1) the behavioral factor, which reflects historical motion patterns of pedestrians, and (2) the stochastic factor, which accounts for the inherent randomness in future trajectories. To this end, we introduce a global framework named LSN-GTDA, which consists of a pair of symmetrical U-Net networks. This framework symmetrically distributes the semantic segmentation and trajectory prediction modules, enhancing the overall functionality of the network. Additionally, we propose a novel thermal diffusion process, based on signal and system theory, which manages uncertainty by utilizing the full response and providing interpretability to the network. Experimental results demonstrate that the LSN-GTDA method outperforms state-of-the-art approaches on benchmark datasets such as SDD and ETH-UCY, validating its effectiveness in addressing the multimodal uncertainty of pedestrian trajectory prediction. Full article
(This article belongs to the Section Remote Sensing Image Processing)
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<p>Illustration of the research process for pedestrian trajectory prediction from a UAV perspective. (<b>a</b>) Multi-modality of the trajectory prediction; (<b>b</b>) the behavioral factor in the prediction over the target nodes of the zero-input response; (<b>c</b>) the stochastic factor over the path nodes of the zero-state response; (<b>d</b>) the thermal distribution in the prediction; (<b>e</b>) each color indicates predicted trajectories for different target modality. The pentacle and triangle symbols mean the targets and nodes in a trajectory, respectively.</p>
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<p>The framework of the proposed LSN-GTDA pedestrian trajectory prediction method. LSN-GTDA comprises a scene segmentation module and a trajectory heatmap module, which constitutes symmetrical U-Net architectures including both target and trajectory branches. The decoding output uses the global thermal diffusion process including zero-input and zero-state response to predict the future trajectory, and TMSS and PNMSS are used to handle the target and path diversity of multimodality, respectively.</p>
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<p>Visualization of the proposed LSN-GTDA pedestrian trajectory prediction method on SDD. (<b>a</b>) Historical path nodes and the motion target marked as a yellow star; (<b>b</b>) diverse waypoint distribution; (<b>c</b>) resulting waypoint distribution; (<b>d</b>) the predicted trajectory result to the goal.</p>
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<p>A structural diagram of the TMSS and PNMSS strategy in the proposed global thermal diffusion process. Different colors and lines denote diverse prediction modalities.</p>
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<p>Visualization of predicted trajectories compared with the state-of-the-art on the ETH-UCY dataset.</p>
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<p>Benchmarking performance against time horizons.</p>
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<p>Evolution performance of two multimodal uncertainty parameters for the proposed LSN-GTDA on the SDD long-term benchmark. We fix the amount of the target modality (<math display="inline"><semantics> <msub> <mi>M</mi> <mi>b</mi> </msub> </semantics></math>) to observe the effect of the multi-modality path.</p>
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25 pages, 1035 KiB  
Article
AdaMoR-DDMOEA: Adaptive Model Selection with a Reliable Individual-Based Model Management Framework for Offline Data-Driven Multi-Objective Optimization
by Subhadip Pramanik, Abdalla Alameen, Hitesh Mohapatra, Debanjan Pathak and Adrijit Goswami
Mathematics 2025, 13(1), 158; https://doi.org/10.3390/math13010158 - 3 Jan 2025
Viewed by 444
Abstract
Many real-world expensive industrial and engineering multi-objective optimization problems (MOPs) are driven by historical, experimental, or simulation data. In such scenarios, due to the expensive cost and time required, we are only left with a small amount of labeled data to perform the [...] Read more.
Many real-world expensive industrial and engineering multi-objective optimization problems (MOPs) are driven by historical, experimental, or simulation data. In such scenarios, due to the expensive cost and time required, we are only left with a small amount of labeled data to perform the optimization. These offline data-driven MOPs are usually solved by multi-objective evolutionary algorithms (MOEAs) with the help of surrogate models constructed from offline historical data. The key challenge in developing these data-driven MOEAs is that they have to replace multiple conflicting fitness functions by approximating these objective functions, which may produce cumulative approximation errors and misguide the search. In order to build a reliable surrogate model from a small amount of multi-output offline data and solve the DDMOPs, we have proposed an adaptive model selection method with a reliable individual-based model management-driven MOEA. The proposed algorithm dynamically selects between DNN and XGBoost by comparing their k-fold cross-validation MAE error, which can capture the true generalization ability of the surrogates on unseen data. Then, the selected surrogate is updated with a reliable individual selection strategy, where the individual who is closest, both in the decision and objective space, to the most preferred solution among labeled offline data is chosen. As a result, these two strategies guide the underlying MOEA to the Pareto optimal solutions. The empirical results of the ZDT and DTLZ benchmark test suite validate the use of the three state-of-the-art offline DDMOEAs, showing that our algorithm is able to achieve highly competitive results in terms of convergence and diversity for 2–3 objectives. Finally, our algorithm is applied to an offline data-driven multi-objective problem—transonic airfoil (RAE 2822) shape optimization— to validate its efficiency on real-world DDMOPs. Full article
22 pages, 6880 KiB  
Article
MonoSeg: An Infrared UAV Perspective Vehicle Instance Segmentation Model with Strong Adaptability and Integrity
by Peng Huang, Yan Yin, Kaifeng Hu and Weidong Yang
Sensors 2025, 25(1), 225; https://doi.org/10.3390/s25010225 - 3 Jan 2025
Viewed by 202
Abstract
Despite rapid progress in UAV-based infrared vehicle detection, achieving reliable target recognition remains challenging due to dynamic viewpoint variations and platform instability. The inherent limitations of infrared imaging, particularly low contrast ratios and thermal crossover effects, significantly compromise detection accuracy. Moreover, the computational [...] Read more.
Despite rapid progress in UAV-based infrared vehicle detection, achieving reliable target recognition remains challenging due to dynamic viewpoint variations and platform instability. The inherent limitations of infrared imaging, particularly low contrast ratios and thermal crossover effects, significantly compromise detection accuracy. Moreover, the computational constraints of edge computing platforms pose a fundamental challenge in balancing real-time processing requirements with detection performance. Here, we present MonoSeg, a novel instance segmentation framework optimized for UAV perspective infrared vehicle detection. Our approach introduces three key innovations: (1) the Ghost Feature Bottle Cross module (GFBC), which enhances backbone feature extraction efficiency while significantly reducing computational over-head; (2) the Scale Feature Recombination module (SFR), which optimizes feature selection in the Neck stage through adaptive multi-scale fusion; and (3) Comprehensive Loss function that enforces precise instance boundary delineation. Extensive experimental evaluation on bench-mark datasets demonstrates that MonoSeg achieves state-of-the-art performance across standard metrics, including Box mAP and Mask mAP, while maintaining substantially lower computational requirements compared to existing methods. Full article
(This article belongs to the Section Sensing and Imaging)
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<p>Examples from the four image datasets: (<b>a</b>–<b>c</b>) publicly available datasets and (<b>d</b>) data we gathered ourselves.</p>
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<p>Illustration of SAM large model-assisted annotation [<a href="#B10-sensors-25-00225" class="html-bibr">10</a>].</p>
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<p>DIVIS dataset statistical properties. (<b>a</b>) The histogram of the area distribution of all instances. (<b>b</b>) The histogram of the ratio of the sum of contour areas to the image area. (<b>c</b>) A scatter plot of the aspect ratio of instance bounding boxes versus the ratio of instance contour area. (<b>d</b>) A scatter plot of the ratio of instance contour area to instance bounding box area against the instance area.</p>
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<p>Architecture diagram of the MonoSeg model.</p>
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<p>Architecture diagram of the Ghost Feature Bottle Cross module (GFBC) structure.</p>
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<p>Architecture diagram of the Scale Feature Recombination module (SFR) structure.</p>
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<p>Scatter plot of model inference frame rate vs. Mask0.5 mAP.</p>
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<p>Bar chart comparing Box and Mask mAP across multiple thresholds.</p>
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<p>Two classes of target Box and Mask P–R curves.</p>
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<p>Two classes of target Box and Mask P–R curves.</p>
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<p>Visualization examples of comparative experimental results. (<b>1</b>) and (<b>2</b>) represent the segmentation results of the two images respectively, (<b>a</b>–<b>h</b>) represents each method, and (<b>i</b>) represents GT. Red indicates a small vehicle and green indicates a large vehicle.</p>
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<p>Visualization examples of comparative experimental results. (<b>1</b>) and (<b>2</b>) represent the segmentation results of the two images respectively, (<b>a</b>–<b>h</b>) represents each method, and (<b>i</b>) represents GT. Red indicates a small vehicle and green indicates a large vehicle.</p>
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<p>Visualization comparison of heatmaps between baseline and MonoSeg algorithms. (<b>1</b>–<b>3</b>) represents the segmentation results of the three images respectively; (<b>a</b>,<b>b</b>) represent the heatmap of YOLOv8 and MonoSeg respectively; (<b>c</b>) represents GT. Red indicates a small vehicle and green indicates a large vehicle.</p>
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16 pages, 1558 KiB  
Article
One-Pot Combined Hydrodistillation of Industrial Orange Peel Waste for Essential Oils and Pectin Recovery: A Multi-Objective Optimization Study
by Jacopo Paini, Giusi Midolo, Francesca Valenti and Gianluca Ottolina
Sustainability 2025, 17(1), 293; https://doi.org/10.3390/su17010293 - 3 Jan 2025
Viewed by 365
Abstract
Sustainable waste management for orange peel waste is a global concern that presents a concomitant opportunity. In this study, a combined process was developed to optimize the simultaneous recovery of pectin, essential oils, and sugars from industrial orange peel waste. The sequential recovery [...] Read more.
Sustainable waste management for orange peel waste is a global concern that presents a concomitant opportunity. In this study, a combined process was developed to optimize the simultaneous recovery of pectin, essential oils, and sugars from industrial orange peel waste. The sequential recovery process was used as a benchmark, while a one-pot combined process was optimized through the design of the experiments. A multi-objective desirability function was computed to maximize process performance while balancing opposing optimal conditions. The aim was to find a model able to confidently predict yields while reducing the process environmental footprint, potentially giving the necessary multi-product flexibility in modern biorefining. As a result, the combined process under optimal conditions, liquid-to-solid ratio of 2.5, pH value of 3.7, and residence time of 130 min, yielded 0.52% of essential oils and 11% of pectin on a dry basis. The environmental factor 18 is relevant to the fine chemicals industry, which is the target sector of this study. Finally, the process mass balance was calculated, demonstrating the opportunity to further enhance process environmental sustainability and efficiency by upgrading the resulting solid fraction. Full article
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<p>Simplified scheme of the sequential and combined processes for the integrated recovery of limonene and pectin from OPW.</p>
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<p>Response surface plots of selected responses from the models described in <a href="#sustainability-17-00293-t002" class="html-table">Table 2</a> at the optimal RT of 130 min: (<b>A</b>) Essential oil mass (EO) against the effect of LSR and pH, 3D surface, and contour plot; (<b>B</b>) limonene purity (LP) against the effect of LSR and pH, 3D surface, and contour plot; (<b>C</b>) pectin mass (PM) against the effect of LSR and pH, 3D surface, and contour plot; (<b>D</b>) electric consumption (EC) against the effect of RT and the combined effect of LSR and pH; (<b>E</b>) desirability plot with the resulting optimal point at fixed residence time.</p>
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<p>Mass balance flowchart of the combined hydrodistillation process performed at the optimal conditions.</p>
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12 pages, 543 KiB  
Article
PaleAle 6.0: Prediction of Protein Relative Solvent Accessibility by Leveraging Pre-Trained Language Models (PLMs)
by Wafa Alanazi, Di Meng and Gianluca Pollastri
Biomolecules 2025, 15(1), 49; https://doi.org/10.3390/biom15010049 - 2 Jan 2025
Viewed by 332
Abstract
Predicting the relative solvent accessibility (RSA) of a protein is critical to understanding its 3D structure and biological function. RSA prediction, especially when homology transfer cannot provide information about a protein’s structure, is a significant step toward addressing the protein structure prediction challenge. [...] Read more.
Predicting the relative solvent accessibility (RSA) of a protein is critical to understanding its 3D structure and biological function. RSA prediction, especially when homology transfer cannot provide information about a protein’s structure, is a significant step toward addressing the protein structure prediction challenge. Today, deep learning is arguably the most powerful method for predicting RSA and other structural features of proteins. In particular, recent breakthroughs in deep learning—driven by the integration of natural language processing (NLP) algorithms—have significantly advanced the field of protein research. Inspired by the remarkable success of NLP techniques, this study leverages pre-trained language models (PLMs) to enhance RSA prediction. We present a deep neural network architecture based on a combination of bidirectional recurrent neural networks and convolutional layers that can analyze long-range interactions within protein sequences and predict protein RSA using ESM-2 encoding. The final predictor, PaleAle 6.0, predicts RSA in real values as well as two-state (exposure threshold of 25%) and four-state (exposure thresholds of 4%, 25%, and 50%) discrete classifications. On the 2022 test set dataset, PaleAle 6.0 achieved over 82% accuracy for two-state RSA (RSA_2C) and 59.75% accuracy for four-state RSA (RSA_4C), with a Pearson correlation coefficient (PCC) of 77.88 for real-value RSA prediction. When evaluated on the more challenging 2024 test set, PaleAle 6.0 maintained a strong performance, achieving 79.74% accuracy in the two-state prediction and 55.30% accuracy in the four-state prediction, with a PCC of 73.08 for real-value predictions, outperforming all previously benchmarked predictors. Full article
(This article belongs to the Section Bioinformatics and Systems Biology)
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<p>CBRNN structure for RSA prediction where N is the total number of convolutional layers, and <span class="html-italic">i</span> is the <span class="html-italic">i</span>th convolutional layer.</p>
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51 pages, 7469 KiB  
Review
Machine-Learning-Powered Information Systems: A Systematic Literature Review for Developing Multi-Objective Healthcare Management
by Maryam Bagheri, Mohsen Bagheritabar, Sohila Alizadeh, Mohammad (Sam) Salemizadeh Parizi, Parisa Matoufinia and Yang Luo
Appl. Sci. 2025, 15(1), 296; https://doi.org/10.3390/app15010296 - 31 Dec 2024
Viewed by 476
Abstract
The incorporation of machine learning (ML) into healthcare information systems (IS) has transformed multi-objective healthcare management by improving patient monitoring, diagnostic accuracy, and treatment optimization. Notwithstanding its revolutionizing capacity, the area lacks a systematic understanding of how these models are divided and analyzed, [...] Read more.
The incorporation of machine learning (ML) into healthcare information systems (IS) has transformed multi-objective healthcare management by improving patient monitoring, diagnostic accuracy, and treatment optimization. Notwithstanding its revolutionizing capacity, the area lacks a systematic understanding of how these models are divided and analyzed, leaving gaps in normalization and benchmarking. The present research usually overlooks holistic models for comparing ML-enabled ISs, significantly considering pivotal function criteria like accuracy, precision, sensitivity, and specificity. To address these gaps, we conducted a broad exploration of 306 state-of-the-art papers to present a novel taxonomy of ML-enabled IS for multi-objective healthcare management. We categorized these studies into six key areas, namely diagnostic systems, treatment-planning systems, patient monitoring systems, resource allocation systems, preventive healthcare systems, and hybrid systems. Each category was analyzed depending on significant variables, uncovering that adaptability is the most effective parameter throughout all models. In addition, the majority of papers were published in 2022 and 2023, with MDPI as the leading publisher and Python as the most prevalent programming language. This extensive synthesis not only bridges the present gaps but also proposes actionable insights for improving ML-powered IS in healthcare management. Full article
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<p>Process of selecting papers.</p>
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<p>The first phase of paper selection.</p>
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<p>The second phase of paper selection.</p>
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<p>The third phase of paper selection.</p>
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<p>Fourth phase of paper selection.</p>
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<p>Distribution of publishers of studied articles in the fifth phase.</p>
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<p>Taxonomy of various HISs using AI-driven multi-objective decision-making.</p>
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<p>Frequency of programming languages used for simulating the proposed methods of the investigated papers.</p>
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<p>Main categories of healthcare systems based on their function.</p>
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<p>Dynamic system of intelligent healthcare management.</p>
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<p>Various information systems for multi-objective healthcare management.</p>
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<p>The average accuracy of the studied paper.</p>
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<p>The average precision of the studied paper.</p>
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<p>The average F1 score of the studied paper.</p>
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<p>The average sensitivity of the studied paper.</p>
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<p>The average specificity of the studied paper.</p>
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<p>The average computational efficiency of the studied paper.</p>
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<p>The average AUC-ROC of the studied paper.</p>
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<p>Procedure of function of treatment-planning systems for multi-objective healthcare management.</p>
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<p>The procedure of preventive healthcare systems for multi-objective healthcare management.</p>
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<p>Comparison of healthcare systems types.</p>
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<p>Parameters considered in evaluating studied papers.</p>
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18 pages, 1805 KiB  
Article
DPSTCN: Dynamic Pattern-Aware Spatio-Temporal Convolutional Networks for Traffic Flow Forecasting
by Zeping Dou and Danhuai Guo
ISPRS Int. J. Geo-Inf. 2025, 14(1), 10; https://doi.org/10.3390/ijgi14010010 - 31 Dec 2024
Viewed by 280
Abstract
Accurate forecasting of multivariate traffic flow poses formidable challenges, primarily due to the ever-evolving spatio-temporal dynamics and intricate spatial heterogeneity, where the heterogeneity signifies that the correlations among locations are not just related to distance. However, few of the existing models are designed [...] Read more.
Accurate forecasting of multivariate traffic flow poses formidable challenges, primarily due to the ever-evolving spatio-temporal dynamics and intricate spatial heterogeneity, where the heterogeneity signifies that the correlations among locations are not just related to distance. However, few of the existing models are designed to fully and effectively integrate the above-mentioned features. To address these complexities head-on, this paper introduces a novel solution in the form of Dynamic Pattern-aware Spatio-Temporal Convolutional Networks (DPSTCN). Temporally, the model introduces a novel temporal module, containing a temporal convolutional network (TCN) enriched with an enhanced pattern-aware self-attention mechanism, adept at capturing temporal patterns, including local/global dependencies, dynamics, and periodicity. Spatially, the model constructs static and dynamic pattern-aware convolutions, leveraging geographical and area-functional information to effectively capture intricate spatial patterns, including dynamics and heterogeneity. Evaluations across four distinct traffic benchmark datasets consistently demonstrate the state-of-the-art capacity of our model compared to the existing eleven approaches, especially great improvements in RMSE (Root Mean Squared Error) value. Full article
(This article belongs to the Topic Spatial Decision Support Systems for Urban Sustainability)
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<p>Distribution of sensors and consequential traffic flow.</p>
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<p>The overall framework of DPSTCN. DPSTCN stacks multiple ST-Conv layers. Each layer contains three parts: spatial module, temporal module, and gated fusion module.</p>
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<p>Pattern-aware self-attention.</p>
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<p>Temporal convolution network. (<b>a</b>) A dilated casual convolution with dilation factors {1, 2, 4} and kernel 3. (<b>b</b>) Residual connection with a convolution for cross-layer information transmission.</p>
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<p>The forecasting results at different time steps on PEMS04 and PEMS08.</p>
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<p>Feature visualization.</p>
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<p>Ablation experiments.</p>
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57 pages, 5329 KiB  
Article
Development of a New Rubber Buckling-Restrained Brace System for Structures
by Nima Ostovar and Farzad Hejazi
Appl. Sci. 2025, 15(1), 276; https://doi.org/10.3390/app15010276 - 30 Dec 2024
Viewed by 458
Abstract
Buckling-Restrained Braces (BRBs) are widely utilized in structures as an anti-seismic system to enhance performance against lateral excitations. While BRBs are designed to yield symmetrically under both tension and compression without significant buckling, their effectiveness is often limited to moderate seismic events. During [...] Read more.
Buckling-Restrained Braces (BRBs) are widely utilized in structures as an anti-seismic system to enhance performance against lateral excitations. While BRBs are designed to yield symmetrically under both tension and compression without significant buckling, their effectiveness is often limited to moderate seismic events. During high-intensity earthquakes, repetitive yielding can lead to core failure, resulting in the loss of BRB functionality and potentially causing structural collapse. This study proposes an innovative design for BRBs to improve energy dissipation capacity under severe seismic activity. The new design incorporates Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC) filler and hyper-elastic rubber components as primary load-bearing elements. Through extensive testing and simulation, the proposed Rubber Buckling-Restrained Brace (RBRB) was developed and manufactured by integrating hyper-elastic rubber between the concrete and core to enhance the device’s strength. Additionally, a prototype of the conventional BRB device was fabricated to serve as a benchmark for evaluating the performance of the RBRB. Experimental testing of both the conventional BRB and the proposed RBRB prototypes was conducted using a heavy-duty dynamic actuator to assess the RBRB’s performance under applied loads. Based on the experimental results, an analytical model of the proposed RBRB was formulated for use in finite element modeling and analysis. Furthermore, a specialized seismic design procedure for structures equipped with the RBRB was developed, according to the performance-based design method. This procedure was applied to the design of a seven-story steel structure, and the impact of the RBRB on the seismic response of the structure was investigated through finite element simulations. The analysis results demonstrated that the RBRB significantly improves the loading capacity and energy dissipation capabilities of structures, thereby enhancing their overall performance against earthquake excitations. Full article
53 pages, 21334 KiB  
Article
An Improved Grey Wolf Optimizer Based on Attention Mechanism for Solving Engineering Design Problems
by Yuming Zhang, Yuelin Gao, Liming Huang and Xiaofeng Xie
Symmetry 2025, 17(1), 50; https://doi.org/10.3390/sym17010050 - 30 Dec 2024
Viewed by 269
Abstract
The grey wolf optimization (GWO) algorithm is a simple and effective meta-heuristic algorithm that mimics the leadership of grey wolves and the social behavior of wolves in nature. However, the updating of GWO population positions only relies on the guidance of α-wolf, [...] Read more.
The grey wolf optimization (GWO) algorithm is a simple and effective meta-heuristic algorithm that mimics the leadership of grey wolves and the social behavior of wolves in nature. However, the updating of GWO population positions only relies on the guidance of α-wolf, β-wolf, and δ-wolf, and individuals are updated with equal weights. This results in the GWO search process being unable to utilize the knowledge of superior wolves better. Therefore, in this study, we propose for the first time an attention mechanism-based GWO (AtGWO). Firstly, when each position is updated, the attention strategy can adaptively assign the weight of the corresponding leader wolf to improve the global exploration ability. Second, with the introduction of omega-wolves, each position update is not only guided by the three leader wolves but also learns from their current optimal values. Finally, a hyperbolic tangent nonlinear function is used to control the convergence factor to better balance exploration and exploitation. To validate its effectiveness, AtGWO is compared with the latest GWO variant with other popular algorithms on the CEC-2014 (dim 30, 50) and CEC-2017 (dim 30, 50, 100) benchmark function sets. The experimental results indicate that AtGWO outperforms the GWO-related variants almost all the time in terms of mean, variance, and best value, which indicates its superior ability and robustness to find optimal solutions. And it is also competitive when compared to other algorithms in multimodal functions. AtGWO outperforms the comparison algorithms in terms of the mean and best value in six real-world engineering optimization problems. Full article
(This article belongs to the Section Engineering and Materials)
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<p>The most popular meta-heuristic classifications and the year they were proposed; all meta-heuristic variants are excluded from this figure for the sake of brevity.</p>
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<p>(<bold>a</bold>,<bold>b</bold>) Denote the social structure of the grey wolf and <inline-formula><mml:math id="mm281"><mml:semantics><mml:mover accent="true"><mml:mi>A</mml:mi><mml:mo>→</mml:mo></mml:mover></mml:semantics></mml:math></inline-formula> control population searching for prey, respectively.</p>
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<p>Flowchart of the GWO.</p>
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<p>The embedding function curves (<bold>a</bold>) and control factor function curves (<bold>b</bold>), respectively.</p>
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<p>The computational process of the attention mechanism.</p>
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<p>The social hierarchy and characteristics of wolves.</p>
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<p>(<bold>a</bold>,<bold>b</bold>) comparisons of images with different convergence factors and different values of <inline-formula><mml:math id="mm282"><mml:semantics><mml:mi>γ</mml:mi></mml:semantics></mml:math></inline-formula>, respectively.</p>
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<p>Flowchart of the AtGWO.</p>
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<p>Subfigures (<bold>a</bold>–<bold>c</bold>) represent the average convergence plots for unimodal, hybrid, and composition functions in CEC-2014 (50-D), respectively.</p>
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<p>Average convergence curves of multimodal functions for CEC-2014 (50-D).</p>
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<p>Radar chart of the results of CEC-2014 (50-D).</p>
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<p>Box plots of multimodal functions for CEC-2014 (50-D).</p>
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<p>Subfigures (<bold>a</bold>–<bold>c</bold>) show boxplots of unimodal, hybrid, and composite functions in CEC-2014 (50-D), respectively.</p>
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<p>Subfigures (<bold>a</bold>–<bold>c</bold>) show boxplots of unimodal, hybrid, and composite functions in CEC-2014 (50-D), respectively.</p>
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<p>Radar chart of the results of CEC-2017 (30-D).</p>
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<p>Average convergence curves of unimodal/multimodal functions for CEC-2017 (100-D).</p>
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<p>Average convergence curves of hybrid functions for CEC-2017 (100-D).</p>
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<p>Average convergence curves of composition functions for CEC-2017 (100-D).</p>
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<p>Box plots of hybrid/composition functions for CEC-2017 (100-D).</p>
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<p>Box plots of unimodal/multimodal functions for CEC-2017 (100-D).</p>
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<p>Box plots of CEC-2014(30-D) functions.</p>
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<p>Average convergence curves of CEC-2014 (30-D) functions.</p>
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<p>Average convergence curves of unimodal/multimodal functions for CEC-2017 (50-D).</p>
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<p>Average convergence curves of hybrid functions for CEC-2017 (50-D).</p>
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<p>Average convergence curves of composite functions for CEC-2017 (50-D).</p>
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<p>Box plots of CEC-2017 (50-D) functions.</p>
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<p>Box plots of CEC-2017 (50-D) functions.</p>
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<p>Box plots of CEC-2017 (50-D) functions.</p>
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<p>Radar charts of the results of CEC-2017 (50-D).</p>
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<p>Schematic representation of problem T/CSD.</p>
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<p>Schematic diagram of the problem PVD.</p>
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<p>Schematic representation of problem 3-BTD.</p>
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<p>Schematic illustration of the WBD problem.</p>
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<p>Schematic representation of problem SRD.</p>
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<p>Schematic of the problem GTD.</p>
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24 pages, 1649 KiB  
Article
Heterogeneous Multi-Agent Risk-Aware Graph Encoder with Continuous Parameterized Decoder for Autonomous Driving Trajectory Prediction
by Shaoyu Sun, Chunyang Wang, Bo Xiao, Xuelian Liu, Chunhao Shi, Rongliang Sun and Ruijie Han
Electronics 2025, 14(1), 105; https://doi.org/10.3390/electronics14010105 - 30 Dec 2024
Viewed by 288
Abstract
Trajectory prediction is a critical component of autonomous driving, intelligent transportation systems, and human–robot interactions, particularly in complex environments like intersections, where diverse road constraints and multi-agent interactions significantly increase the risk of collisions. To address these challenges, a Heterogeneous Risk-Aware Graph Encoder [...] Read more.
Trajectory prediction is a critical component of autonomous driving, intelligent transportation systems, and human–robot interactions, particularly in complex environments like intersections, where diverse road constraints and multi-agent interactions significantly increase the risk of collisions. To address these challenges, a Heterogeneous Risk-Aware Graph Encoder with Continuous Parameterized Decoder for Trajectory Prediction (HRGC) is proposed. The architecture integrates a heterogeneous risk-aware local graph attention encoder, a low-rank temporal transformer, a fusion lane and global interaction encoder layer, and a continuous parameterized decoder. First, a heterogeneous risk-aware edge-enhanced local attention encoder is proposed, which enhances edge features using risk metrics, constructs graph structures through graph optimization and spectral clustering, maps these enhanced edge features to corresponding graph structure indices, and enriches node features with local agent-to-agent attention. Risk-aware edge attention is aggregated to update node features, capturing spatial and collision-aware representations, embedding crucial risk information into agents’ features. Next, the low-rank temporal transformer is employed to reduce computational complexity while preserving accuracy. By modeling agent-to-lane relationships, it captures critical map context, enhancing the understanding of agent behavior. Global interaction further refines node-to-node interactions via attention mechanisms, integrating risk and spatial information for improved trajectory encoding. Finally, a trajectory decoder utilizes the aforementioned encoder to generate control points for continuous parameterized curves. These control points are multiplied by dynamically adjusted basis functions, which are determined by an adaptive knot vector that adjusts based on velocity and curvature. This mechanism ensures precise local control and the superior handling of sharp turns and speed variations, resulting in more accurate real-time predictions in complex scenarios. The HRGC network achieves superior performance on the Argoverse 1 benchmark, outperforming state-of-the-art methods in complex urban intersections. Full article
(This article belongs to the Section Artificial Intelligence)
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<p>Autonomous driving trajectory prediction.</p>
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<p>The overall architecture of HRGC trajectory predictor. It comprises four main blocks, processing heterogeneous multi-agent local feature embedding through a risk-aware edge enhanced node graph attention. Initially, we process node representation with rotation matrix, then construct heterogeneous graph by designing and aggregating risk aware edge and update node with attention. Subsequently, we apply low-rank temporal transformer layer to extract temporal features. These features are then fed into agent to lane layer, which fuses agent and lane feature for better local scene feature embedding, and last global interaction layer to extract agent and lane local features. Finally, we utilize a continuous parameterized trajectory decoder to decode rich and accurate features, generating continuous parameterized trajectories.</p>
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<p>Risk-aware edge layer.</p>
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<p>Moving direction with velocity risk.</p>
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<p>Time to collision.</p>
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<p>Edge index via graph optimization and clustering. First, we use Gaussian kernel to compute every two-node similarity and obtain the adjacency matrix. We compute Laplacian matrix by Equation (<a href="#FD6-electronics-14-00105" class="html-disp-formula">6</a>); susbsequently, we use the minimum cut graph optimization operate on Laplacian matrix to obtain the cluster index of node <math display="inline"><semantics> <msubsup> <mi>C</mi> <mi>i</mi> <mi>t</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>C</mi> <mi>j</mi> <mi>t</mi> </msubsup> </semantics></math>.</p>
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<p>B-spline with control points.</p>
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<p>Ablation study of decoder variants with continuous trajectory decoder.</p>
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<p>Inference speed and paramters with minADE comparison with state-of-the-art methods.</p>
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<p>The red column represents the intersection successful case, while the green column represents the continuous parameterized trajectory prediction performance analysis.</p>
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<p>Failure case.</p>
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15 pages, 2237 KiB  
Article
Wireless Sensor Network Coverage Optimization Using a Modified Marine Predator Algorithm
by Guohao Wang and Xun Li
Sensors 2025, 25(1), 69; https://doi.org/10.3390/s25010069 - 26 Dec 2024
Viewed by 303
Abstract
To solve the coverage problem caused by the random deployment of wireless sensor network nodes in the forest fire-monitoring system, a modified marine predator algorithm (MMPA) is proposed. Four modifications have been made based on the standard marine predator algorithm (MPA). Firstly, tent [...] Read more.
To solve the coverage problem caused by the random deployment of wireless sensor network nodes in the forest fire-monitoring system, a modified marine predator algorithm (MMPA) is proposed. Four modifications have been made based on the standard marine predator algorithm (MPA). Firstly, tent mapping is integrated into the initialization step to improve the searching ability of the early stage. Secondly, a hybrid search strategy is used to enhance the ability to search and jump out of local optimum. Thirdly, the golden sine guiding mechanism is applied to accelerate the convergence of the algorithm. Finally, a stage-adjustment strategy is proposed to make the transition of stages more smoothly. Six specific test functions chosen from the CEC2017 function and the benchmark function are used to evaluate the performance of MMPA. It shows that this modified algorithm has good optimization capability and stability compared to MPA, grey wolf optimizer, sine cosine algorithm, and sea horse optimizer. The results of coverage tests show that MMPA has a better uniformity of node distribution compared to MPA. The average coverage rates of MMPA are the highest compared to the commonly used metaheuristic-based algorithms, which are 91.8% in scenario 1, 95.98% in scenario 2, and 93.88% in scenario 3, respectively. This demonstrates the superiority of this proposed algorithm in coverage optimization of the wireless sensor network. Full article
(This article belongs to the Section Sensor Networks)
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<p>Flow chart of MMPA.</p>
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<p>Convergence plot comparison between the proposed MMPA and the other four algorithms on the test functions of (<b>a</b>) F1, (<b>b</b>) F2, (<b>c</b>) F3, (<b>d</b>) F4, (<b>e</b>) F5, and (<b>f</b>) F6.</p>
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<p>Distribution maps of sensor nodes at (<b>a</b>) scenario 1 using MPA, (<b>b</b>) scenario 1 using MMPA, (<b>c</b>) scenario 2 using MPA, (<b>d</b>) scenario 2 using MMPA, (<b>e</b>) scenario 3 using MPA, and (<b>f</b>) scenario 3 using MMPA, respectively.</p>
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<p>Distribution maps of sensor nodes at (<b>a</b>) scenario 1 using MPA, (<b>b</b>) scenario 1 using MMPA, (<b>c</b>) scenario 2 using MPA, (<b>d</b>) scenario 2 using MMPA, (<b>e</b>) scenario 3 using MPA, and (<b>f</b>) scenario 3 using MMPA, respectively.</p>
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25 pages, 4420 KiB  
Article
Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming
by Hamoud Bin Obaid, Theodore B. Trafalis, Mastoor M. Abushaega, Abdulhadi Altherwi and Ahmed Hamzi
Mathematics 2025, 13(1), 12; https://doi.org/10.3390/math13010012 - 24 Dec 2024
Viewed by 313
Abstract
This study presents a new approach to optimize the dynamic evacuation process through a dynamic traffic assignment model formulated using mixed-integer linear programming (MILP). The model approximates the travel time for evacuee groups with a piecewise linear function that accounts for variations in [...] Read more.
This study presents a new approach to optimize the dynamic evacuation process through a dynamic traffic assignment model formulated using mixed-integer linear programming (MILP). The model approximates the travel time for evacuee groups with a piecewise linear function that accounts for variations in travel time due to load-dependent factors. Significant delays are transferred to subsequent groups to simulate delay propagation. The primary objective is to minimize the network clearance time—the total time required for the last group of evacuees to reach safety from the start of the evacuation. Given the model’s computational intensity, a simplified version is introduced for comparison. Both the original and simplified models are tested on small networks and benchmarked against the Cell Transmission Model, a well-regarded method in dynamic traffic assignment literature. Additional objectives, including average travel time and average evacuation time, are explored. A sensitivity analysis is conducted to assess how varying the number of evacuee groups impacts model outcomes. Full article
(This article belongs to the Special Issue Advances in Mathematical Analytics and Operations Research)
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<p>Linearizing the travel time function using piecewise linear approximation.</p>
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<p>A small network example with 5 nodes and 4 arcs.</p>
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<p>Results of the network example of the 3 scenarios.</p>
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<p>The time paths of the full model and the reduced model.</p>
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<p>Road segment with 60 min travel time between each pair of consecutive nodes at free-flow speed.</p>
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<p>A small network for illustration.</p>
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<p>The NCT in minutes for the LBM is compared with the CTM output.</p>
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<p>Random network with 27 nodes and 43 bidirected arcs.</p>
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<p>The ATT and AET behavior of 25,000 evacuees when changing the number of groups of evacuees.</p>
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<p>The ATT and AET behavior of 45,000 evacuees when the number of groups is changed.</p>
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<p>The number of evacuees in each group from community <span class="html-italic">k</span>, on route <span class="html-italic">r</span>, and evacuated at time <span class="html-italic">t</span>.</p>
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<p>The travel time (<b>a</b>) and evacuation time (<b>b</b>) in minutes for each group of evacuees evacuated on route <span class="html-italic">r</span> at time <span class="html-italic">t</span>.</p>
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<p>The NCT for the LBM I and LBM II models for demand ranging from 10,000 to 40,000 evacuees.</p>
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<p>The computational times for the LBM I and LBM II models in seconds when the demand ranges from 10,000 to 40,000 evacuees.</p>
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26 pages, 6088 KiB  
Article
A Genetic Algorithm Based ESC Model to Handle the Unknown Initial Conditions of State of Charge for Lithium Ion Battery Cell
by Kristijan Korez, Dušan Fister and Riko Šafarič
Batteries 2025, 11(1), 1; https://doi.org/10.3390/batteries11010001 - 24 Dec 2024
Viewed by 327
Abstract
Classic enhanced self-correcting battery equivalent models require proper model parameters and initial conditions such as the initial state of charge for its unbiased functioning. Obtaining parameters is often conducted by optimization using evolutionary algorithms. Obtaining the initial state of charge is often conducted [...] Read more.
Classic enhanced self-correcting battery equivalent models require proper model parameters and initial conditions such as the initial state of charge for its unbiased functioning. Obtaining parameters is often conducted by optimization using evolutionary algorithms. Obtaining the initial state of charge is often conducted by measurements, which can be burdensome in practice. Incorrect initial conditions can introduce bias, leading to long-term drift and inaccurate state of charge readings. To address this, we propose two simple and efficient equivalent model frameworks that are optimized by a genetic algorithm and are able to determine the initial conditions autonomously. The first framework applies the feedback loop mechanism that gradually with time corrects the externally given initial condition that is originally a biased arbitrary value within a certain domain. The second framework applies the genetic algorithm to search for an unbiased estimate of the initial condition. Long-term experiments have demonstrated that these frameworks do not deviate from controlled benchmarks with known initial conditions. Additionally, our experiments have shown that all implemented models significantly outperformed the well-known ampere-hour coulomb counter integration method, which is prone to drift over time and the extended Kalman filter, that acted with bias. Full article
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<p>The flowchart of estimating the SOC with the ESC: (1) identify the static and dynamic battery characteristics, (2) build the ESC model, three frameworks are proposed and (3) utilize the identified ESC model parameters for exploitation and testing.</p>
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<p>Battery, load and underlying sensors.</p>
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<p>Equivalent electric circuit of the ESC model.</p>
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<p>The GA-ESC method. The initial condition of SOC0 needs to be known prior to the exploitation of this method. The <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>[</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math> is predicted from the SOC block which in the next time step <span class="html-italic">k</span> becomes the <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </semantics></math>, hence the symbolic feedback time-delayed representation given by <math display="inline"><semantics> <msup> <mi>z</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p>
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<p>The GA-ESC+FB method. The initial condition of <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <msup> <mi>C</mi> <mo>∗</mo> </msup> <mrow> <mo>[</mo> <mn>0</mn> <mo>]</mo> </mrow> </mrow> </semantics></math> is input arbitrarily. Then, the <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <msup> <mi>C</mi> <mo>∗</mo> </msup> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </mrow> </semantics></math> is updated each time step regularly, again following the time delay representation of <math display="inline"><semantics> <msup> <mi>z</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. The error corrected <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </semantics></math> is then calculated by subtracting the error from <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <msup> <mi>C</mi> <mo>∗</mo> </msup> <mrow> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>The GA-(ESC+SOC0). Initial condition of SOC0 calculated by the GA as additional input dimension. Then, the <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>[</mo> <mi>k</mi> <mo>]</mo> </mrow> </semantics></math> is updated each time step regularly, again following the time delay representation of <math display="inline"><semantics> <msup> <mi>z</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p>
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<p>The DC power supply, electronic load, and built battery cell measurement card. On the right image a detailed view of the battery cell measurement card and a temperature chamber.</p>
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<p>The upper subplot depicts the <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>C</mi> <mi>V</mi> </mrow> </semantics></math> as a function of the percentage of the <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <mi>C</mi> </mrow> </semantics></math>. Multiple lines are plotted, each of them corresponding to a given ambient temperature, varying from <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>a</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>5</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>a</mi> </msub> <mo>=</mo> <mn>45</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>. The lower subplot depicts the temperature correction factor <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>C</mi> <mi>V</mi> <mi>r</mi> <mi>e</mi> <mi>l</mi> <mo>(</mo> <mo>)</mo> </mrow> </semantics></math> in units of <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mo>°</mo> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>.</p>
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<p>The experimental cycle to tune the ESC model parameters with GA. The full red vertical lines denote the start and end of the two cycles for the GA-ESC tuning of model parameters, the red dotted line represents the end of the first cycle and the start of the second cycle.</p>
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<p>The ESC involving the FB as used during the experimental testing or exploitation. Three separate sets of GA-tuned ESC parameters were tested: GA-ESC, GA-(ESC+SOC0), and GA-ESC+FB. The FB allowed the ESC’s state-space vector component of SOC to converge to the unbiased estimate. Thus, the externally given initial condition was set to <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>O</mi> <msup> <mi>C</mi> <mo>∗</mo> </msup> <mrow> <mo>[</mo> <mn>0</mn> <mo>]</mo> </mrow> <mo>=</mo> <mn>50</mn> <mo>%</mo> </mrow> </semantics></math> to allow just convergence to any extreme value, e.g., 0 or 100 %.</p>
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<p>The experimental testing cycle. Positive current <span class="html-italic">i</span> represents discharging the battery, negative current charging it. Red dotted lines represent SOC equal to 100% which is an end of the single cycle. Black dotted lines in second subplot represent minimum and maximum voltages. The reference rate <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mi>C</mi> <mo>/</mo> <mn>30</mn> </mrow> </semantics></math> equals to <math display="inline"><semantics> <mrow> <mn>43.33</mn> </mrow> </semantics></math> mA.</p>
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<p>Complete experimental test. Exhibited are estimated voltages and SOCs. The black dotted line markers exhibit extreme values of terminal voltage and SOC.</p>
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<p>The first experimental cycle. Exhibited are estimated voltages and SOCs. The start of the first cycle is at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. Red dotted lines represent SOC equal to 100% (end of the first cycle). The black dotted line markers exhibit allowed end voltages.</p>
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<p>The last experimental cycle. Exhibited are estimated voltages and SOCs. Red dotted lines represent SOC equal to 100% (start and end of the first cycle). The black dotted line markers exhibit allowed end voltages.</p>
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