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Mathematics, Volume 13, Issue 18 (September-2 2025) – 60 articles

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26 pages, 2373 KB  
Article
Enhancing Road Freight Price Forecasting Using Gradient Boosting Ensemble Supervised Machine Learning Algorithm
by Artur Budzyński and Maria Cieśla
Mathematics 2025, 13(18), 2964; https://doi.org/10.3390/math13182964 (registering DOI) - 12 Sep 2025
Abstract
For effective logistics planning and pricing strategies, it is essential to predict road freight transportation costs accurately. Using a real-world dataset with 45,569 freight offers and 52 different variables, including financial, logistical, geographical, and temporal characteristics, this study presents a data-driven method for [...] Read more.
For effective logistics planning and pricing strategies, it is essential to predict road freight transportation costs accurately. Using a real-world dataset with 45,569 freight offers and 52 different variables, including financial, logistical, geographical, and temporal characteristics, this study presents a data-driven method for forecasting transport prices. To create a strong predictive model, the approach combines hyperparameter optimization, evolutionary feature selection, and extensive feature engineering. Because gradient boosting works well for modelling intricate, nonlinear relationships, it was used as the main algorithm. Temporal dependencies were maintained through a nested cross-validation framework with a time-series split, which improved the generalizability of the model. With a mean absolute percentage error (MAPE) of 6.27%, the model showed excellent predictive accuracy. Key predictive factors included total transport distance, load and delivery quantities, temperature constraints, and aggregated categorical features such as route and vehicle type. The results confirm that evolutionary algorithms are capable of efficiently optimizing model parameters, as well as feature subsets, greatly enhancing interpretability and performance. In the freight logistics industry, this method offers useful insights for operational and dynamic pricing decision-making. This model may be expanded in future research to include external data sources and investigate its suitability for use in various geographic locations and modes of transportation. Full article
(This article belongs to the Special Issue Evolutionary Machine Learning for Real-World Applications)
19 pages, 1988 KB  
Article
Enhanced Fault Diagnosis of Drive-Fed Induction Motors Using a Multi-Scale Wide-Kernel CNN
by Prince, Byungun Yoon and Prashant Kumar
Mathematics 2025, 13(18), 2963; https://doi.org/10.3390/math13182963 (registering DOI) - 12 Sep 2025
Abstract
Induction motor (IM) drives are widely used in industrial applications, particularly within the renewable energy sector, owing to their fast dynamic response and robust performance. Reliable condition monitoring is essential to ensure uninterrupted operation, minimize unexpected downtime, and avoid associated financial losses. Although [...] Read more.
Induction motor (IM) drives are widely used in industrial applications, particularly within the renewable energy sector, owing to their fast dynamic response and robust performance. Reliable condition monitoring is essential to ensure uninterrupted operation, minimize unexpected downtime, and avoid associated financial losses. Although numerous studies have introduced advanced fault detection techniques for IMs, early fault identification remains a significant challenge, especially in systems powered by electronic drives. To address the limitations of manual feature extraction, deep learning methods, particularly conventional convolutional neural networks (CNNs), have emerged as promising tools for automated fault diagnosis. However, enhancing their capability to capture a broader spectrum of spatial features can further improve detection accuracy. This study presents a novel fault detection framework based on a multi-wide-kernel convolutional neural network (MWK-CNN) tailored for drive-fed induction motors. By integrating convolutional kernels of varying widths, the proposed architecture effectively captures both fine-grained details and large-scale patterns in the input signals, thereby enhancing its ability to distinguish between normal and faulty operating states. Electrical signals acquired from drive-fed IMs under diverse operating conditions were used to train and evaluate the MWK-CNN. Experimental results demonstrate that the proposed model exhibits heightened sensitivity to subtle fault signatures, leading to superior diagnostic accuracy and outperforming existing state-of-the-art approaches for fault detection in drive-fed IM systems. Full article
19 pages, 403 KB  
Article
On the Critical Parameters of Branching Random Walks
by Daniela Bertacchi and Fabio Zucca
Mathematics 2025, 13(18), 2962; https://doi.org/10.3390/math13182962 (registering DOI) - 12 Sep 2025
Abstract
Given a discrete spatial structure X, we define continuous-time branching processes {ηt}t≥0 that model a population breeding and dying on X. These processes are usually called branching random walks, and ηt(x) [...] Read more.
Given a discrete spatial structure X, we define continuous-time branching processes {ηt}t≥0 that model a population breeding and dying on X. These processes are usually called branching random walks, and ηt(x) denotes the number of individuals alive at site x at time t. They are characterised by breeding rates kxy (governing the rate at which individuals at x send offspring to y) and by a multiplicative speed parameter λ. These processes also serve as models for epidemic spreading, where λkxy represents the infection rate from x to y. In this context, ηt(x) represents the number of infected individuals at x at time t, and the removal of an individual is due to either death or recovery. Two critical parameters of interest are the global critical parameter λw, related to global survival, and the local critical parameter λs, related to survival within finite sets (with λw≤λs). In disease or pest control, the primary goal is to lower λ so that the process dies out, at least locally. Nevertheless, a process that survives globally can still pose a threat, especially if sudden changes cause global survival to transition into local survival. In fact, local modifications to the rates can affect the values of both critical parameters, making it important to understand when and how they can be increased. Using results on the comparison of the extinction probabilities for a single branching random walk across different sets, we extend the analysis to the extinction probabilities and critical parameters of pairs of branching random walks whose rates coincide outside a fixed set A⊆X. We say that two branching random walks are equivalent if their rates coincide everywhere except on a finite subset of X. Given an equivalence class of branching random walks, we prove that if one process has λw*≠λs*, then λw* is the maximal possible value of this parameter within the class. We describe the possible configurations for the critical parameters within these equivalence classes. Full article
(This article belongs to the Special Issue Applied Probability, Statistics and Operational Research)
17 pages, 6529 KB  
Article
Assessing the Credibility of AIS-Calculated Risks in Busy Waterways: A Case Study of Hong Kong Waters
by Yao Jiang, Wenyu Xu and Dong Yang
Mathematics 2025, 13(18), 2961; https://doi.org/10.3390/math13182961 - 12 Sep 2025
Abstract
The increasing complexity of maritime traffic, driven by the expansion of international trade and growing shipping demand, has resulted in frequent ship collisions with significant consequences. This paper evaluates the credibility of the risk, calculated using the automatic identification system (AIS), in busy [...] Read more.
The increasing complexity of maritime traffic, driven by the expansion of international trade and growing shipping demand, has resulted in frequent ship collisions with significant consequences. This paper evaluates the credibility of the risk, calculated using the automatic identification system (AIS), in busy waterways and integrates AIS data with video surveillance data to comprehensively analyze the risk of ship collision. Specifically, this study utilizes the IALA Waterways Risk Assessment Program (IWRAP) tool to simulate maritime traffic flow and assess collision risk probabilities across various study areas and time periods. In addition, we analyze data from 2019 to 2022 to explore the impact of the COVID-19 pandemic on maritime traffic and find that the number of ship arrivals during the epidemic has decreased, resulting in a decrease in accident risk. We identify four traffic conflict areas in the real-world study area and point out that there are multi-directional ship interactions in these areas, but compliance with traffic rules can effectively reduce the risk of accidents. Additionally, simulations suggest that even a 13.5% increase in ocean-going vessel (OGV) traffic would raise collision risk by only 0.0247 incidents/year. To more accurately analyze the risk of waterways, we investigate the capture of dynamic information for ships in waterways by using the learning-driven detection model for real-time ship detection. These findings highlight the effectiveness of combining AIS and visual data for waterway risk assessment, offering critical insights for improving safety measures and informing policy development. Full article
36 pages, 3354 KB  
Article
Optimization of EHA Hydraulic Cylinder Buffer Design Using Enhanced SBO–BP Neural Network and NSGA-II
by Shuai Cao, Weibo Li, Kangzheng Huang, Xiaoqing Deng and Rentai Li
Mathematics 2025, 13(18), 2960; https://doi.org/10.3390/math13182960 - 12 Sep 2025
Abstract
In order to solve a certain type of Electro-Hydrostatic Actuators (EHA) hydraulic cylinder small cavity buffer end impact problem, based on AMESim to establish a hydraulic cylinder small cavity buffer machine–hydraulic joint simulation model. First, four important structural parameters, namely, the fitting clearance [...] Read more.
In order to solve a certain type of Electro-Hydrostatic Actuators (EHA) hydraulic cylinder small cavity buffer end impact problem, based on AMESim to establish a hydraulic cylinder small cavity buffer machine–hydraulic joint simulation model. First, four important structural parameters, namely, the fitting clearance G of the buffer sleeve and buffer hole, the fixed orifice D, the wedge face angle , and the wedge face length L1 were selected to analyze their influence on the pressure of the buffer chamber and the end speed of the piston. Second, enhanced Social Behavior Optimization (SBO) was used to optimize the back-propagation neural network (BP) model to construct a prediction model for the buffer time T of the small chamber of the hydraulic cylinder, the end-piston speed Ve, the rate of change of the end-piston speed Vr, and the return speed of the hydraulic oil Vh. The SBO–BP model performed well in several key performance evaluation metrics, showing better prediction accuracy and generalization performance. Finally, the multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA-II) was used to optimize the hydraulic cylinder small-cavity buffer structure using the multi-objective NSGA-II with the objectives of the shortest buffer time, the minimum end-piston speed, the minimum change rate of the end-piston speed, and the minimum hydraulic oil reflux speed. The optimized design reduced the piston end speed from 0.060 m/s to 0.032 m/s, corresponding to a 46.7% improvement. The findings demonstrate that the proposed hybrid optimization approach effectively alleviates the end-impact problem of EHA small-cavity buffers and provides a novel methodology for achieving high-performance and reliable actuator designs. Full article
25 pages, 2747 KB  
Article
A Dynamic Information-Theoretic Network Model for Systemic Risk Assessment with an Application to China’s Maritime Sector
by Lin Xiao, Arash Sioofy Khoojine, Hao Chen and Congyin Wang
Mathematics 2025, 13(18), 2959; https://doi.org/10.3390/math13182959 - 12 Sep 2025
Abstract
This paper develops a dynamic information-theoretic network framework to quantify systemic risk in China’s maritime–commodity nexus with a focus on the Yangtze River Basin using eight monthly indicators, CCFI, CBCFI, BDI, YRCFI, GAUP, MPCT, CPUS, and ASMC. We resample, impute, standardize, and difference [...] Read more.
This paper develops a dynamic information-theoretic network framework to quantify systemic risk in China’s maritime–commodity nexus with a focus on the Yangtze River Basin using eight monthly indicators, CCFI, CBCFI, BDI, YRCFI, GAUP, MPCT, CPUS, and ASMC. We resample, impute, standardize, and difference series to achieve stationary time series. Nonlinear interdependencies are estimated via KSG mutual information (MI) within sliding windows; networks are filtered using the Planar Maximally Filtered Graph (PMFG) with bootstrap edge validation (95th percentile) and benchmarked against the MST. Average MI indicates moderate yet heterogeneous dependence (about 0.13–0.17), revealing a container/port core (CCFI–YRCFI–MPCT), a bulk/energy spine (BDI–CPUS), and commodity bridges via GAUP. Dynamic PMFG metrics show a generally resilient but episodically vulnerable structure: density and compactness decline in turbulence. Stress tests demonstrate high redundancy to diffuse link failures (connectivity largely intact until ∼70–80% edge removal) but pronounced sensitivity of diffusion capacity to targeted multi-node outages. Early-warning indicators based on entropy rate and percolation threshold Z-scores flag recurring windows of elevated fragility; change point detection evaluation of both metrics isolates clustered regime shifts (2015–2016, 2018–2019, 2021–2022, and late 2023–2024). A Systemic Importance Index (SII) combining average centrality and removal impact ranks MPCT and CCFI as most critical, followed by BDI, with GAUP/CPUS mid-peripheral and ASMC peripheral. The findings imply that safeguarding port throughput and stabilizing container freight conditions deliver the greatest resilience gains, while monitoring bulk/energy linkages is essential when macro shocks synchronize across markets. Full article
(This article belongs to the Section E: Applied Mathematics)
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37 pages, 1134 KB  
Article
SOMTreeNet: A Hybrid Topological Neural Model Combining Self-Organizing Maps and BIRCH for Structured Learning
by Yunus Doğan
Mathematics 2025, 13(18), 2958; https://doi.org/10.3390/math13182958 - 12 Sep 2025
Abstract
This study introduces SOMTreeNet, a novel hybrid neural model that integrates Self-Organizing Maps (SOMs) with BIRCH-inspired clustering features to address structured learning in a scalable and interpretable manner. Unlike conventional deep learning models, SOMTreeNet is designed with a recursive and modular topology that [...] Read more.
This study introduces SOMTreeNet, a novel hybrid neural model that integrates Self-Organizing Maps (SOMs) with BIRCH-inspired clustering features to address structured learning in a scalable and interpretable manner. Unlike conventional deep learning models, SOMTreeNet is designed with a recursive and modular topology that supports both supervised and unsupervised learning, enabling tasks such as classification, regression, clustering, anomaly detection, and time-series analysis. Extensive experiments were conducted using various publicly available datasets across five analytical domains: classification, regression, clustering, time-series forecasting, and image classification. These datasets cover heterogeneous structures including tabular, temporal, and visual data, allowing for a robust evaluation of the model’s generalizability. Experimental results demonstrate that SOMTreeNet consistently achieves competitive or superior performance compared to traditional machine learning and deep learning methods while maintaining a high degree of interpretability and adaptability. Its biologically inspired hierarchical structure facilitates transparent decision-making and dynamic model growth, making it particularly suitable for real-world applications that demand both accuracy and explainability. Overall, SOMTreeNet offers a versatile framework for learning from complex data while preserving the transparency and modularity often lacking in black-box models. Full article
(This article belongs to the Special Issue New Advances in Data Analytics and Mining)
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32 pages, 1551 KB  
Article
Free Vibration Analysis of Porous FGM Plates on Elastic Foundations with Temperature-Dependent Material Properties
by Aleksandar Radaković, Dragan Čukanović, Aleksandar Nešović, Petar Knežević, Milan T. Djordjević and Gordana Bogdanović
Mathematics 2025, 13(18), 2957; https://doi.org/10.3390/math13182957 - 12 Sep 2025
Abstract
This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel [...] Read more.
This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel shape functions are introduced to accurately model transverse shear deformation across the plate thickness without employing shear correction factors. These functions are constructed to satisfy shear stress boundary conditions and capture nonlinear effects induced by material gradation and porosity. A variational formulation is developed to describe the dynamic response of FGM plates in a thermo-mechanical environment, incorporating temperature-dependent material properties and three porosity distributions: uniform, linear, and trigonometric. Numerical solutions are obtained using in-house MATLAB codes, allowing complete control over the formulation and interpretation of the results. The model is validated through detailed comparisons with existing literature, demonstrating high accuracy. The findings reveal that the porosity distribution pattern and gradient intensity significantly influence natural frequencies and mode shapes. The trigonometric porosity distribution exhibits favorable dynamic performance due to preserved stiffness in the surface regions. Additionally, the Kerr-type elastic foundation enables fine tuning of the dynamic response, depending on its specific parameters. The proposed approach provides a reliable and efficient tool for analyzing FGM structures under complex loading conditions and lays the groundwork for future extensions involving nonlinear, time-dependent, and multiphysics analyses. Full article
(This article belongs to the Special Issue Mathematical Modelling, Analysis, and Optimization for Engineering and Mechanics)
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27 pages, 2378 KB  
Article
Advancing Graph Neural Networks for Complex Relational Learning: A Multi-Scale Heterogeneity-Aware Framework with Adversarial Robustness and Interpretable Analysis
by Hao Yang, Yunhong Zhou, Xianzhe Ji, Zifan Liu, Zhen Tian, Qiang Tang and Yanchao Shi
Mathematics 2025, 13(18), 2956; https://doi.org/10.3390/math13182956 - 12 Sep 2025
Abstract
Graph Neural Networks (GNNs) face fundamental algorithmic challenges in real-world applications due to a combination of data heterogeneity, adversarial heterophily, and severe class imbalance. A critical research gap exists for a unified framework that can simultaneously address these issues, limiting the deployment of [...] Read more.
Graph Neural Networks (GNNs) face fundamental algorithmic challenges in real-world applications due to a combination of data heterogeneity, adversarial heterophily, and severe class imbalance. A critical research gap exists for a unified framework that can simultaneously address these issues, limiting the deployment of GNNs in high-stakes domains like financial fraud detection and social network analysis. This paper introduces HAG-CFNet, a novel framework designed to bridge this gap by integrating three key innovations: (1) a heterogeneity-aware message-passing mechanism that uses relation-specific attention to capture rich semantic information; (2) a dual-channel heterophily detection module that explicitly identifies and neutralizes adversarial camouflage through separate aggregation pathways; and (3) a domain-aware counterfactual generator that produces plausible, actionable explanations by co-optimizing feature and structural perturbations. These are supported by a synergistic imbalance correction strategy combining graph-adapted oversampling with cost-sensitive learning. Extensive testing on large-scale financial datasets validates the framework’s impact: HAG-CFNet achieves a 4.2% AUC-PR improvement over state-of-the-art methods, demonstrates superior robustness by reducing performance degradation under structural noise by over 50%, and generates counterfactual explanations with 91.8% validity while requiring minimal perturbations. These advances provide a direct pathway to building more trustworthy and effective AI systems for critical applications ranging from financial risk management to supply chain analysis and social media content moderation. Full article
(This article belongs to the Special Issue New Advances in Graph Neural Networks (GNNs) and Applications)
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22 pages, 1633 KB  
Article
On the Autonomic Control of Heart Rate Variability: How the Mean Heart Rate Affects Spectral and Complexity Analysis and a Way to Mitigate Its Influence
by Paolo Castiglioni, Antonio Zaza, Giampiero Merati and Andrea Faini
Mathematics 2025, 13(18), 2955; https://doi.org/10.3390/math13182955 - 12 Sep 2025
Abstract
Heart Rate Variability (HRV) analysis allows for assessing autonomic control from the beat-by-beat dynamics of the time series of cardiac intervals. However, some HRV indices may strongly correlate with the mean heart rate, possibly flawed by the interpretation of HRV changes in terms [...] Read more.
Heart Rate Variability (HRV) analysis allows for assessing autonomic control from the beat-by-beat dynamics of the time series of cardiac intervals. However, some HRV indices may strongly correlate with the mean heart rate, possibly flawed by the interpretation of HRV changes in terms of autonomic control. Therefore, this study aims to (1) investigate how HRV indices of fluctuation amplitude and multiscale complex dynamics of cardiac time series faithfully describe the autonomic control at different heart rates through a mathematical model of the generation of cardiac action potentials driven by realistically synthesized autonomic modulations; and (2) propose an alternative procedure of HRV analysis less sensitive to the mean heart rate. Results on the synthesized series confirm a strong dependency of amplitude indices of HRV on the mean heart rate due to a nonlinearity in the model, which can be removed by our procedure. Application of our procedure to real cardiac intervals recorded in different postures suggests that the dependency of these indices on the heart rate may importantly affect the physiological interpretation of HRV. By contrast, multiscale complexity indices do not substantially depend on the heart rate provided that multiscale analyses are defined on a time- rather than a beat-basis. Full article
(This article belongs to the Special Issue Recent Advances in Time Series Analysis)
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49 pages, 3209 KB  
Article
SAFE-MED for Privacy-Preserving Federated Learning in IoMT via Adversarial Neural Cryptography
by Mohammad Zubair Khan, Waseem Abbass, Nasim Abbas, Muhammad Awais Javed, Abdulrahman Alahmadi and Uzma Majeed
Mathematics 2025, 13(18), 2954; https://doi.org/10.3390/math13182954 - 12 Sep 2025
Abstract
Federated learning (FL) offers a promising paradigm for distributed model training in Internet of Medical Things (IoMT) systems, where patient data privacy and device heterogeneity are critical concerns. However, conventional FL remains vulnerable to gradient leakage, model poisoning, and adversarial inference, particularly in [...] Read more.
Federated learning (FL) offers a promising paradigm for distributed model training in Internet of Medical Things (IoMT) systems, where patient data privacy and device heterogeneity are critical concerns. However, conventional FL remains vulnerable to gradient leakage, model poisoning, and adversarial inference, particularly in privacy-sensitive and resource-constrained medical environments. To address these challenges, we propose SAFE-MED, a secure and adversarially robust framework for privacy-preserving FL tailored for IoMT deployments. SAFE-MED integrates neural encryption, adversarial co-training, anomaly-aware gradient filtering, and trust-weighted aggregation into a unified learning pipeline. The encryption and decryption components are jointly optimized with a simulated adversary under a minimax objective, ensuring high reconstruction fidelity while suppressing inference risk. To enhance robustness, the system dynamically adjusts client influence based on behavioral trust metrics and detects malicious updates using entropy-based anomaly scores. Comprehensive experiments are conducted on three representative medical datasets: Cleveland Heart Disease (tabular), MIT-BIH Arrhythmia (ECG time series), and PhysioNet Respiratory Signals. SAFE-MED achieves near-baseline accuracy with less than 2% degradation, while reducing gradient leakage by up to 85% compared to vanilla FedAvg and over 66% compared to recent neural cryptographic FL baselines. The framework maintains over 90% model accuracy under 20% poisoning attacks and reduces communication cost by 42% relative to homomorphic encryption-based methods. SAFE-MED demonstrates strong scalability, reliable convergence, and practical runtime efficiency across heterogeneous network conditions. These findings validate its potential as a secure, efficient, and deployable FL solution for next-generation medical AI applications. Full article
(This article belongs to the Special Issue Securing the Future: Computational Innovations in IoT Network Resilience and Security)
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18 pages, 4319 KB  
Article
A Finite Volume and Levenberg–Marquardt Optimization Framework for Benchmarking MHD Flows over Backward-Facing Steps
by Spyridon Katsoudas, Grigorios Chrimatopoulos, Michalis Xenos and Efstratios Tzirtzilakis
Mathematics 2025, 13(18), 2953; https://doi.org/10.3390/math13182953 - 12 Sep 2025
Abstract
Understanding and modeling the effect of magnetic fields on flows that present separation properties, such as those over a backward-facing step (BFS), is critical due to its role in metallurgical processes, nuclear reactor cooling, plasma confinement, and biomedical applications. This study examines the [...] Read more.
Understanding and modeling the effect of magnetic fields on flows that present separation properties, such as those over a backward-facing step (BFS), is critical due to its role in metallurgical processes, nuclear reactor cooling, plasma confinement, and biomedical applications. This study examines the hydrodynamic and magnetohydrodynamic numerical solution of an electrically conducting fluid flow in a backward-facing step (BFS) geometry under the influence of an external, uniform magnetic field applied at an angle. The novelty of this work lies in employing an in-house finite-volume solver with a collocated grid configuration that directly applies a Newton–like method, in contrast to conventional iterative approaches. The computed hydrodynamic results are validated with experimental and numerical studies for an expansion ratio of two, while the MHD case is validated for Reynolds number Re=380 and Stuart number N=0.1. One of the most important findings is the reduction in the reattachment point and simultaneous increase in pressure as the magnetic field strength is amplified. The magnetic field angle with the greatest influence is observed at φ=π/2, where the main recirculation vortex is substantially suppressed. These results not only clarify the role of magnetic field orientation in BFS flows but also lay the foundation for future investigations of three-dimensional configurations and coupled MHD–thermal applications. Full article
(This article belongs to the Section E: Applied Mathematics)
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13 pages, 462 KB  
Article
Effective Resource Allocation to Combat Invasions of the Spotted Lanternfly (Lycorma delicatula) and Similar Pests
by Daniel Strömbom, Julianna Hoitt, Jinrong Hu, Swati Pandey and Elizabeth Batchelar
Mathematics 2025, 13(18), 2952; https://doi.org/10.3390/math13182952 - 12 Sep 2025
Abstract
The spotted lanternfly is rapidly establishing itself as a major insect pest with global implications. Despite substantial management efforts, its spread continues in invaded regions, highlighting the need for refined strategies. A recent model generalized results of empirical control studies by incorporating population [...] Read more.
The spotted lanternfly is rapidly establishing itself as a major insect pest with global implications. Despite substantial management efforts, its spread continues in invaded regions, highlighting the need for refined strategies. A recent model generalized results of empirical control studies by incorporating population dynamics and incomplete delivery, introducing a formula for the minimum proportion of a population that must be treated to induce decline. However, that model cannot address the more practical question of how to allocate control efforts. Here, we extend the model to identify effective deployment strategies. When control effects scale linearly with effort, we show that sequential application of stage-specific controls, ordered by efficacy, is optimal. When effects exhibit diminishing returns, we derive a switching criterion between controls that accommodates variable or uncertain resources. For fixed resources, we employ global optimization to obtain deployment strategies. Both approaches consistently outperform random deployment, which we show can lead to catastrophic outcomes. Our findings demonstrate the importance of adopting effective control strategies for the lanternfly. Despite this need, we found no prior studies addressing deployment strategies in the lanternfly literature. The methods developed here provide a foundation for ensuring that limited management resources are used effectively. Full article
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13 pages, 856 KB  
Article
An Implementation of the Python Code for Computing the Independent Number of Genus Graphs
by Sana Anjum and Amal S. Alali
Mathematics 2025, 13(18), 2951; https://doi.org/10.3390/math13182951 - 12 Sep 2025
Abstract
The computation of the independent number is a fundamental problem in graph theory. It has many applications, including route planning, computer graphics, network analysis, computational biology, and network architecture. Particularly in computational biology, it provides a powerful mathematical tool for modeling tumor robustness [...] Read more.
The computation of the independent number is a fundamental problem in graph theory. It has many applications, including route planning, computer graphics, network analysis, computational biology, and network architecture. Particularly in computational biology, it provides a powerful mathematical tool for modeling tumor robustness and optimizing cancer treatment. In this article, an algorithmic method for computing the independent number of genus graphs is presented. Moreover, a Python (version 3.10.5) implementation has been provided for constructing genus graphs and computing their independent number. Full article
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29 pages, 2697 KB  
Article
Robust D-Optimal Mixture Designs Under Manufacturing Tolerances via Multi-Objective NSGA-II
by Wanida Limmun, Boonorm Chomtee and John J. Borkowski
Mathematics 2025, 13(18), 2950; https://doi.org/10.3390/math13182950 - 12 Sep 2025
Abstract
This study proposes a multi-objective optimization framework for generating statistically efficient and operationally robust designs in constrained mixture experiments with irregular experimental regions. In industrial settings, manufacturing variability from batching inaccuracies, raw material inconsistencies, or process drift can degrade nominally optimal designs. Traditional [...] Read more.
This study proposes a multi-objective optimization framework for generating statistically efficient and operationally robust designs in constrained mixture experiments with irregular experimental regions. In industrial settings, manufacturing variability from batching inaccuracies, raw material inconsistencies, or process drift can degrade nominally optimal designs. Traditional methods focus on nominal efficiency but neglect robustness, and few explicitly incorporate percentile-based criteria. To address this limitation, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was employed to simultaneously maximize nominal D-efficiency and the 10th-percentile D-efficiency (R-D10), a conservative robustness metric representing the efficiency level exceeded by 90% of perturbed implementations. Six design generation methods were evaluated across seven statistical criteria using two case studies: a constrained concrete formulation and a glass chemical durability study. NSGA-II designs consistently achieved top rankings for D-efficiency, R-D10, A-efficiency, and G-efficiency, while maintaining competitive IV-efficiency and scaled prediction variance (SPV) values. Robustness improvements were notable, with R-D10 by 1.5–5.1% higher than the best alternative. Fraction of design space plots further confirmed its resilience, demonstrating low variance and stable performance across the design space. Full article
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24 pages, 441 KB  
Article
Promotion of Lattice Paths by Riordan Arrays
by Aoife Hennessy, Kieran Murphy, Narciso Gonzaga and Paul Barry
Mathematics 2025, 13(18), 2949; https://doi.org/10.3390/math13182949 - 11 Sep 2025
Abstract
This paper investigates the use of Riordan arrays in the enumeration and transformation of lattice paths through a combinatorial framework of promotion. We demonstrate how Dyck paths can be promoted to generalised Motzkin and Schröder paths via two key transformations: the Binomial and [...] Read more.
This paper investigates the use of Riordan arrays in the enumeration and transformation of lattice paths through a combinatorial framework of promotion. We demonstrate how Dyck paths can be promoted to generalised Motzkin and Schröder paths via two key transformations: the Binomial and Chebyshev transforms, each associated with specific Riordan arrays. These promotions yield classical integer sequences and continued fraction representations that enumerate weighted lattice paths. The framework is further extended to analyse grand paths, which are permitted to cross below the x-axis. We develop constructive bijections establishing explicit correspondences between promoted path families. The promotion framework offers new insights into known integer sequences and enables a unified approach to the generalisation and classification of lattice paths. Full article
(This article belongs to the Special Issue Combinatorics, Riordan Matrices and Umbral Calculus—in Memory of Prof. Emanuele Munarini)
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20 pages, 568 KB  
Article
On Some Classes of Enriched Cyclic Contractive Self-Mappings and Their Boundedness and Convergence Properties
by Manuel De la Sen
Mathematics 2025, 13(18), 2948; https://doi.org/10.3390/math13182948 - 11 Sep 2025
Abstract
This paper focuses on dealing with several types of enriched cyclic contractions defined in the union of a set of non-empty closed subsets of normed or metric spaces. In general, any finite number p ≥ 2 of subsets is permitted in the cyclic [...] Read more.
This paper focuses on dealing with several types of enriched cyclic contractions defined in the union of a set of non-empty closed subsets of normed or metric spaces. In general, any finite number p ≥ 2 of subsets is permitted in the cyclic arrangement. The types of examined single-valued enriched cyclic contractions are, in general, less stringent from the point of view of constraints on the self-mappings compared to p-cyclic contractions while the essential properties of these last ones are kept. The convergence of distances is investigated as well as that of sequences generated by the considered enriched cyclic mappings. It is proved that, both in normed spaces and in simple metric spaces, the distances of sequences of points in adjacent subsets converge to the distance between such subsets under weak extra conditions compared to the cyclic contractive case, which is simply that the contractive constant be less than one. It is also proved that if the metric space is a uniformly convex Banach space and one of the involved subsets is convex then all the sequences between adjacent subsets converge to a unique set of best proximity points, one of them per subset which conform a limit cycle, although the sets of best proximity points are not all necessarily singletons in all the subsets. Full article
(This article belongs to the Topic Fixed Point Theory and Measure Theory)
24 pages, 1411 KB  
Article
A Multi-View Fusion Data-Augmented Method for Predicting BODIPY Dye Spectra
by Xinwen Yang, Xuan Li and Qin Zhao
Mathematics 2025, 13(18), 2947; https://doi.org/10.3390/math13182947 - 11 Sep 2025
Abstract
Fluorescent molecules, particularly BODIPY dyes, have found wide applications in fields such as bioimaging and optoelectronics due to their excellent photostability and tunable spectral properties. In recent years, artificial intelligence methods have enabled more efficient screening of molecules, allowing the required molecules to [...] Read more.
Fluorescent molecules, particularly BODIPY dyes, have found wide applications in fields such as bioimaging and optoelectronics due to their excellent photostability and tunable spectral properties. In recent years, artificial intelligence methods have enabled more efficient screening of molecules, allowing the required molecules to be quickly obtained. However, existing methods remain inadequate to meet research needs, primarily due to incomplete molecular feature extraction and the scarcity of data under small-sample conditions. In response to the aforementioned challenges, this paper introduces a spectral prediction method that integrates multi-view feature fusion and data augmentation strategies. The proposed method consists of three modules. The molecular feature engineering module constructs a multi-view molecular fusion feature that includes molecular fingerprints, molecular descriptors, and molecular energy gaps, which can more comprehensively obtain molecular feature information. The data augmentation module introduces strategies such as SMILES randomization, molecular fingerprint bit-level perturbation, and Gaussian noise injection to enhance the performance of the model in small sample environments. The spectral prediction module captures the complex mapping relationship between molecular structure and spectrum. It is demonstrated that the proposed method provides considerable advantages in the virtual screening of organic fluorescent molecules and offers valuable support for the development of novel BODIPY derivatives based on data-driven strategies. Full article
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37 pages, 2470 KB  
Article
A Data-Driven Semi-Relaxed MIP Model for Decision-Making in Maritime Transportation
by Yanmeng Tao, Ying Yang and Shuaian Wang
Mathematics 2025, 13(18), 2946; https://doi.org/10.3390/math13182946 - 11 Sep 2025
Abstract
Maritime transportation companies operate in highly volatile environments, where data-driven decision-making is critical to navigating fluctuating freight revenue, fuel and transit costs, and dynamic trade-related policies. This study addresses the liner service network design and container flow management problem, with the objective of [...] Read more.
Maritime transportation companies operate in highly volatile environments, where data-driven decision-making is critical to navigating fluctuating freight revenue, fuel and transit costs, and dynamic trade-related policies. This study addresses the liner service network design and container flow management problem, with the objective of maximizing weekly profit, calculated as total freight revenue minus comprehensive operational costs associated with fuel, berthing, transit, and policy-driven extra fees. We formulate a mixed-integer programming (MIP) model for the problem and demonstrate that the constraint matrix associated with vessel leasing is totally unimodular. This property permits the reformulation of the original MIP model into a semi-relaxed MIP model, which maintains optimality while improving computational efficiency. Using shipping data in a realistic liner service network, the proposed model demonstrates its practical applicability in balancing complex trade-offs to optimize profitability. Sensitivity analyses provide actionable insights for data-driven decision-making, including when to expand service networks, discontinue unprofitable routes, and strategically deploy vessel leasing to mitigate rising operational costs and regulatory penalties. This study provides a practical, computationally efficient, and data-driven framework to support liner shipping companies in making robust tactical decisions amid economic and regulatory dynamics. Full article
(This article belongs to the Special Issue Data-Driven Decision Making: Models, Methods and Applications, 2nd Edition)
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30 pages, 11790 KB  
Article
Research on Dynamic Spatial Pose and Load of Hydraulic Support Under Inclined–Declined and Large-Dip-Angle Working Conditions for Product Design
by Longlong He, Lianwei Sun, Yue Wu, Zidi Zhao, Zhaoqiang Yuan, Haoqian Cai, Jiale Li, Xiangang Cao and Xuhui Zhang
Mathematics 2025, 13(18), 2945; https://doi.org/10.3390/math13182945 - 11 Sep 2025
Abstract
To address stability and safety issues in hydraulic support design under inclined–declined and large-dip-angle working conditions, this paper proposes a design-driven dynamic pose–load co-evolution solution method based on the physical entity of the ZFY12000/21/36D hydraulic support. The feasibility of the proposed method is [...] Read more.
To address stability and safety issues in hydraulic support design under inclined–declined and large-dip-angle working conditions, this paper proposes a design-driven dynamic pose–load co-evolution solution method based on the physical entity of the ZFY12000/21/36D hydraulic support. The feasibility of the proposed method is demonstrated through theoretical analysis, spatial modeling, and experimental verification. First, a spatial coordinate system describing hydraulic support pose is established based on Denavit–Hartenberg (DH) theory, constructing a “physical space-geometric coordinate system-DH parameter space” pose mapping model via DH principles, matrix iteration, and kinematic simulation. Second, a load-bearing characteristic analytical method is developed through systematic coupling analysis of dip angle, pose, and load distribution. Finally, coal mine field data collection and hydraulic support test platform experiments analyze load-bearing characteristics under varying poses and loads. Results show Root Mean Square Error (RMSE) values of 0.836° for the front link inclination, 0.756° for the rear link, 0.114° for the balance ram, and 0.372° for the column; load-bearing state evolution under pose–load synergy aligns with theoretical models, confirming method feasibility. This approach fills a domain gap in hydraulic support dip–pose–load co-solving and provides critical references for designing hydraulic support products under extreme dip-angle operations. Full article
(This article belongs to the Special Issue Mathematical Techniques and New ITs for Smart Manufacturing Systems)
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19 pages, 314 KB  
Article
Supercyclic Weighted Composition Operators on the Space of Smooth Functions
by Juan Bès and Christopher Foster
Mathematics 2025, 13(18), 2944; https://doi.org/10.3390/math13182944 - 11 Sep 2025
Abstract
A weighted composition operator on the space of scalar-valued smooth functions on an open subset of a d-dimensional Euclidean space is supercyclic if and only if it is weakly mixing, and it is strongly supercyclic if and only if it is mixing. Every [...] Read more.
A weighted composition operator on the space of scalar-valued smooth functions on an open subset of a d-dimensional Euclidean space is supercyclic if and only if it is weakly mixing, and it is strongly supercyclic if and only if it is mixing. Every such mixing operator is chaotic. In the one-dimensional case, it is supercyclic if and only if it is mixing and if and only if it is chaotic. Full article
(This article belongs to the Section C3: Real Analysis)
28 pages, 1816 KB  
Article
A Social Network Group Decision-Making Method for Flood Disaster Chains Considering Evolutionary Trends and Decision-Makers’ Risk Preferences
by Ruohan Ma, Zhiying Wang, Lemei Zhu, Anbang Zhang and Yiwen Wang
Mathematics 2025, 13(18), 2943; https://doi.org/10.3390/math13182943 - 11 Sep 2025
Abstract
To address the impact of the dynamic evolution of flood disaster chains and decision-makers’ (DMs’) risk preference heterogeneity on group decision-making, this study proposes a social network group decision-making method that integrates the evolutionary trend of the flood disaster chain with DMs’ risk [...] Read more.
To address the impact of the dynamic evolution of flood disaster chains and decision-makers’ (DMs’) risk preference heterogeneity on group decision-making, this study proposes a social network group decision-making method that integrates the evolutionary trend of the flood disaster chain with DMs’ risk preferences. First, a Bayesian network is constructed to quantify the disaster chain’s evolution, dynamically adjusting DMs’ evaluation values. Second, DMs’ risk preference types are identified based on the evaluation values, and a bounded confidence (BC) model, incorporating risk preferences, self-confidence and trust networks, is developed to promote consensus formation. Then, the optimal alternative is selected through weighted aggregation and used to update the Bayesian network dynamically during implementation. Finally, the effectiveness and superiority of the proposed method are verified using the flood disaster chain from the “7∙20” extreme rainfall disaster in Zhengzhou, Henan Province, China. The results show that risk-seeking DMs reduce BC values and resist consensus, whereas risk-averse DMs enlarge BC values and accelerate convergence. Moreover, worsening flood disaster chain trends drive DMs to update the optimal alternative. These findings show that the method captures both dynamic disaster evolution and behavioral heterogeneity, providing realistic and adaptive decision support in flood emergency scenarios. Full article
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11 pages, 2881 KB  
Article
Analytic Solution of Coupled Rolling Behaviors for Robotic Blimps
by Sungjin Cho
Mathematics 2025, 13(18), 2942; https://doi.org/10.3390/math13182942 - 11 Sep 2025
Abstract
Robotic blimps have been recently employed for the purpose of education and research. Both modeling and simulation for robotic blimp motions are significantly important due to uncontrollable movements. This paper presents the coupled rolling behaviors of robotic blimps. When horizontal and vertical motions [...] Read more.
Robotic blimps have been recently employed for the purpose of education and research. Both modeling and simulation for robotic blimp motions are significantly important due to uncontrollable movements. This paper presents the coupled rolling behaviors of robotic blimps. When horizontal and vertical motions are combined for vehicle maneuvering, rolling motion can be substantially increased. We propose an analytic solution of a simplified model that represents coupled rolling motion in order to analyze such instability. Furthermore, we prove that rolling motions under unknown disturbances are ultimately bounded from Lyapunov analysis. The proposed scheme is verified by simulation study. Full article
(This article belongs to the Special Issue Mathematical Modeling for Dynamics, Simulation and Control of Robotic and Industrial Systems)
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27 pages, 4238 KB  
Article
A Scalable Reinforcement Learning Framework for Ultra-Reliable Low-Latency Spectrum Management in Healthcare Internet of Things
by Adeel Iqbal, Ali Nauman, Tahir Khurshaid and Sang-Bong Rhee
Mathematics 2025, 13(18), 2941; https://doi.org/10.3390/math13182941 - 11 Sep 2025
Abstract
Healthcare Internet of Things (H-IoT) systems demand ultra-reliable and low-latency communication (URLLC) to support critical functions such as remote monitoring, emergency response, and real-time diagnostics. However, spectrum scarcity and heterogeneous traffic patterns pose major challenges for centralized scheduling in dense H-IoT deployments. This [...] Read more.
Healthcare Internet of Things (H-IoT) systems demand ultra-reliable and low-latency communication (URLLC) to support critical functions such as remote monitoring, emergency response, and real-time diagnostics. However, spectrum scarcity and heterogeneous traffic patterns pose major challenges for centralized scheduling in dense H-IoT deployments. This paper proposed a multi-agent reinforcement learning (MARL) framework for dynamic, priority-aware spectrum management (PASM), where cooperative MARL agents jointly optimize throughput, latency, energy efficiency, fairness, and blocking probability under varying traffic and channel conditions. Six learning strategies are developed and compared, including Q-Learning, Double Q-Learning, Deep Q-Network (DQN), Actor–Critic, Dueling DQN, and Proximal Policy Optimization (PPO), within a simulated H-IoT environment that captures heterogeneous traffic, device priorities, and realistic URLLC constraints. A comprehensive simulation study across scalable scenarios ranging from 3 to 50 devices demonstrated that PPO consistently outperforms all baselines, improving mean throughput by 6.2%, reducing 95th-percentile delay by 11.5%, increasing energy efficiency by 11.9%, lowering blocking probability by 33.3%, and accelerating convergence by 75.8% compared to the strongest non-PPO baseline. These findings establish PPO as a robust and scalable solution for QoS-compliant spectrum management in dense H-IoT environments, while Dueling DQN emerges as a competitive deep RL alternative. Full article
(This article belongs to the Special Issue Applied Mathematics in Artificial Intelligence: Methods, Algorithms, and Applications)
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16 pages, 3402 KB  
Article
Optimizing Commercial Teams and Territory Design Using a Mathematical Model Based on Clients’ Values: A Case Study in Canada
by Ana Miguel Carvalho, Cristina Lopes, Manuel Cruz, Jorge Santos, Sandra Ramos, Filipa Vieira and Pedro Louro
Mathematics 2025, 13(18), 2940; https://doi.org/10.3390/math13182940 - 11 Sep 2025
Abstract
This study, set in Nors Construction Equipment ST in Canada, addresses logistical challenges by enhancing commercial team evaluation and market sectorization. Traditional performance assessments relied only on sales, lacking other efficiency measures. This research proposes a mathematical function to combine diverse Key Performance [...] Read more.
This study, set in Nors Construction Equipment ST in Canada, addresses logistical challenges by enhancing commercial team evaluation and market sectorization. Traditional performance assessments relied only on sales, lacking other efficiency measures. This research proposes a mathematical function to combine diverse Key Performance Indicators (KPIs) to better evaluate team effectiveness. Additionally, it aims to optimize the sales territory assignment, improving resource allocation across Canada’s expansive, sparsely populated regions. Customer segmentation was conducted using the RFM model, classifying clients into Low-, Mid-, and High-Value groups based on purchasing behavior. For incorporating multiple KPIs in the evaluation of commercial teams’ performance, the Analytic Hierarchy Process (AHP) was used. Sectorization was modeled as a linear programming problem to minimize travel distances while ensuring compact sales territories. Constraints included balancing sales opportunities and customer types across assigned territories. As a result, the proposed optimization model significantly improves operational efficiency through better-balanced sales territories and reduced travel. Improved sectorization enhances market penetration and customer coverage, which is expected to lead to increased sales and support the company’s growth objectives. The mathematical models developed in this study allowed for a deeper understanding of the performance and provided management with tools to refine sales strategies and allocate resources more effectively. The article ends with a discussion on the possibility of ChatGPT being used to replace a mathematician in performing this analysis for the company. It was observed that ChatGPT (version GPT-4o) provided an extremely incomplete solution, evaluating the commercial teams solely based on profit and sales and not addressing the sectorization problem at hand. Full article
(This article belongs to the Special Issue Advances in Control Theory and Optimizations)
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16 pages, 343 KB  
Article
Multi-Delayed Discrete Matrix Functions and Their Applications in Solving Higher-Order Difference Equations
by Ahmed M. Elshenhab, Ghada AlNemer and Xing Tao Wang
Mathematics 2025, 13(18), 2939; https://doi.org/10.3390/math13182939 - 11 Sep 2025
Abstract
A new class of linear non-homogeneous discrete matrix equations with multiple delays and second-order differences is considered, where the coefficient matrices satisfy pairwise permutability conditions. First, new multi-delayed discrete matrix sine- and cosine-type functions are introduced, which generalize existing delayed discrete matrix functions. [...] Read more.
A new class of linear non-homogeneous discrete matrix equations with multiple delays and second-order differences is considered, where the coefficient matrices satisfy pairwise permutability conditions. First, new multi-delayed discrete matrix sine- and cosine-type functions are introduced, which generalize existing delayed discrete matrix functions. Based on the introduced matrix functions and appropriate commutativity conditions, an explicit matrix representation of the solution is derived. The importance of our results is shown by comparing them with related previous works, along with suggestions about some new open problems. Finally, an example is provided to illustrate the importance of the results. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
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18 pages, 333 KB  
Article
Existence and Uniqueness Theorem on Uncertain Nonlinear Switching Systems with Time Delay
by Yadong Shu and Ting Jin
Mathematics 2025, 13(18), 2938; https://doi.org/10.3390/math13182938 - 11 Sep 2025
Abstract
This paper considers an uncertain nonlinear switching system with time delay, which is denoted as a series of uncertain delay differential equations. Previously, there were few published results on such kinds of uncertain switching systems. To fill this void, the internal property of [...] Read more.
This paper considers an uncertain nonlinear switching system with time delay, which is denoted as a series of uncertain delay differential equations. Previously, there were few published results on such kinds of uncertain switching systems. To fill this void, the internal property of the solutions is thoroughly explored for uncertain switching systems with time delay in state. Under the linear growth condition and the Lipschitz condition, existence and uniqueness with respect to the solutions are derived almost surely in the form of a judgement theorem. The theorem is strictly verified by applying uncertainty theory and the contraction mapping principle. In the end, the validity of above theoretical results is illustrated through a microbial symbiosis model. Full article
(This article belongs to the Special Issue Advances in Optimal Decision Making Under Risk and Uncertainty)
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28 pages, 477 KB  
Article
An Enhanced Subgradient Extragradient Method for Fixed Points of Quasi-Nonexpansive Mappings Without Demi-Closedness
by Anchalee Sripattanet and Atid Kangtunyakarn
Mathematics 2025, 13(18), 2937; https://doi.org/10.3390/math13182937 - 11 Sep 2025
Abstract
This research focuses on developing a novel approach to finding fixed points of quasi-nonexpansive mappings without relying on the demi-closedness condition, a common requirement in previous studies. The approach is based on the Subgradient Extragradient technique, which builds upon the foundational extragradient method [...] Read more.
This research focuses on developing a novel approach to finding fixed points of quasi-nonexpansive mappings without relying on the demi-closedness condition, a common requirement in previous studies. The approach is based on the Subgradient Extragradient technique, which builds upon the foundational extragradient method introduced by G.M. Korpelevich. Korpelevich’s method is a widely recognized tool in the fields of optimization and variational inequalities. This study extends Korpelevich’s technique by adapting it to a broader class of operators while maintaining critical convergence properties. This research demonstrates the effectiveness and practical applicability of this new method through detailed computational examples, highlighting its potential to address complex mathematical problems across various domains. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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10 pages, 1488 KB  
Article
Electromigration of Aquaporins Controls Water-Driven Electrotaxis
by Pablo Sáez and Sohan Kale
Mathematics 2025, 13(18), 2936; https://doi.org/10.3390/math13182936 - 10 Sep 2025
Abstract
Cell motility is a process central to life and is undoubtedly influenced by mechanical and chemical signals. Even so, other stimuli are also involved in controlling cell migration in vivo and in vitro. Among these, electric fields have been shown to provide a [...] Read more.
Cell motility is a process central to life and is undoubtedly influenced by mechanical and chemical signals. Even so, other stimuli are also involved in controlling cell migration in vivo and in vitro. Among these, electric fields have been shown to provide a powerful and programmable cue to manipulate cell migration. There is now a clear consensus that the electromigration of membrane components represents the first response to an external electric field, which subsequently activates downstream signals responsible for controlling cell migration. Here, we focus on a specific mode of electrotaxis: frictionless, amoeboid-like migration. We used the Finite Element Method to solve an active gel model coupled with a mathematical model of the electromigration of aquaporins and investigate the effect of electric fields on ameboid migration. We demonstrate that an electric field can polarize aquaporins in a cell and, consequently, that the electromigration of aquaporins can be exploited to regulate water flux across the cell membrane. Our findings indicate that controlling these fluxes allows modulation of cell migration velocity, thereby reducing the cell’s migratory capacity. Our work provides a mechanistic framework to further study the impact of electrotaxis and to add new insights into specific modes by which electric fields modify cell motility. Full article
(This article belongs to the Special Issue Advances in Biological Systems with Mathematics)
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34 pages, 10460 KB  
Article
A Reinforcement Learning-Assisted Fractional-Order Differential Evolution for Solving Wind Farm Layout Optimization Problems
by Yiliang Wang, Yifei Yang, Sichen Tao, Lianzhi Qi and Hao Shen
Mathematics 2025, 13(18), 2935; https://doi.org/10.3390/math13182935 - 10 Sep 2025
Abstract
The Wind Farm Layout Optimization Problem (WFLOP) aims to improve wind energy utilization and reduce wake-induced power losses through optimal placement of wind turbines. Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been widely adopted due to their suitability for discrete optimization [...] Read more.
The Wind Farm Layout Optimization Problem (WFLOP) aims to improve wind energy utilization and reduce wake-induced power losses through optimal placement of wind turbines. Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been widely adopted due to their suitability for discrete optimization tasks, yet they suffer from limited global exploration and insufficient convergence depth. Differential evolution (DE), while effective in continuous optimization, lacks adaptability in discrete and nonlinear scenarios such as WFLOP. To address this, the fractional-order differential evolution (FODE) algorithm introduces a memory-based difference mechanism that significantly enhances search diversity and robustness. Building upon FODE, this paper proposes FQFODE, which incorporates reinforcement learning to enable adaptive adjustment of the evolutionary process. Specifically, a Q-learning mechanism is employed to dynamically guide key search behaviors, allowing the algorithm to flexibly balance exploration and exploitation based on problem complexity. Experiments conducted across WFLOP benchmarks involving three turbine quantities and five wind condition settings show that FQFODE outperforms current mainstream GA-, PSO-, and DE-based optimizers in both solution quality and stability. These results demonstrate that embedding reinforcement learning strategies into differential frameworks is an effective approach for solving complex combinatorial optimization problems in renewable energy systems. Full article
(This article belongs to the Special Issue Artificial Intelligence Techniques Applications on Power Systems)
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