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20 pages, 3558 KB  
Article
Functional Trait Space and Multiscale Allometric Scaling of Different Architectural Types in Malus
by Yuerong Fan, Yiting Shen, Ruomiao Zhou and Wangxiang Zhang
Plants 2026, 15(9), 1347; https://doi.org/10.3390/plants15091347 - 28 Apr 2026
Viewed by 88
Abstract
Tree architecture is a critical determinant of plant performance, light capture, biomechanical stability, and resource allocation. However, the multidimensional functional trait space and multiscale allometric scaling mechanisms underlying different architectural types in Malus remain poorly understood. This study investigates the multidimensional functional trait [...] Read more.
Tree architecture is a critical determinant of plant performance, light capture, biomechanical stability, and resource allocation. However, the multidimensional functional trait space and multiscale allometric scaling mechanisms underlying different architectural types in Malus remain poorly understood. This study investigates the multidimensional functional trait space and multiscale allometric scaling relationships among three typical architectural types (weeping, upright, and spreading) in Malus. A total of 206 germplasm accessions were analyzed by integrating nine core functional traits spanning macro-architectural, branch biomechanical, and leaf economic dimensions. Principal component analysis revealed that architectural differentiation is primarily driven by macro-architectural and branch biomechanical traits, alongside coordinated contributions from leaf economic traits. Functional diversity analysis indicated that the upright and spreading types exhibited higher functional richness, while the weeping type displayed the highest functional divergence but minimal or no functional overlap with the upright and spreading type, reflecting strong niche specialization under artificial selection. Multiscale allometric analyses demonstrated significant divergence in resource allocation strategies across hierarchical levels. At the whole-tree level, architectural types differed markedly in height–diameter and height–crown scaling relationships. At the branch level, conserved positive allometric scaling was observed, with the weeping type showing higher intercepts indicative of increased mechanical investment. At the leaf level, consistent negative allometry between petiole length and leaf area suggested optimized resource allocation for light capture. These pronounced differences suggest distinct ecological adaptation strategies: the weeping type prioritizes biomechanical compensation for pendulous branches and optimized light capture in loose canopies; the upright type emphasizes vertical light competition and mechanical compactness; the spreading type balances lateral expansion and spatial filling efficiency, reflecting differentiated resource allocation patterns shaped by artificial selection. Overall, this study reveals that tree architecture in Malus is shaped by coordinated trait interactions across multiple scales, leading to distinct ecological strategies and resource allocation patterns. These findings provide new insights into the structure–function co-evolution of woody plants and offer a theoretical framework for functional trait-assisted breeding of ornamental tree architectures. Full article
(This article belongs to the Section Plant Development and Morphogenesis)
15 pages, 663 KB  
Article
Fitness Consequences of Urban Green Space Management in Eurasian Tree Sparrow (Passer montanus) in Madrid, Spain
by Beatriz Martínez-Miranzo, Alejandro López-García, Ana Payo-Payo, José I. Aguirre and Eva Banda
Urban Sci. 2026, 10(5), 229; https://doi.org/10.3390/urbansci10050229 - 25 Apr 2026
Viewed by 271
Abstract
In urban areas, green spaces have become the main refuge for biodiversity, providing essential habitat and resources for urban-adapted species. However, scientific evidence on the fitness consequences of urban green space management for urban populations remains scarce, limiting our ability to design successful [...] Read more.
In urban areas, green spaces have become the main refuge for biodiversity, providing essential habitat and resources for urban-adapted species. However, scientific evidence on the fitness consequences of urban green space management for urban populations remains scarce, limiting our ability to design successful conservation and management strategies. Here, we assess the fitness consequences of different levels of management practices in green spaces (i.e., high for areas with continuous intervention such as regular mowing and irrigation, and low for areas with minimal, sporadic maintenance) based on a 19-year long-term monitoring of the Eurasian Tree Sparrow (Passer montanus), a species with high behavioural plasticity in response to human-altered habitats. We formulated a unistate capture–mark–recapture model to estimate age-dependent survival while accounting for uncertainty in recapture probability. Furthermore, by means of GLMMs, we tested if the level of management influences reproductive parameters (i.e., breeding failure, number of eggs, nestlings, fledglings, brood number from the same year, breeding success). We found that high urban green space management caused a decline in adult survival, but we found no effect on juvenile survival. We also found lower breeding failure, a greater number of eggs, and larger brood numbers in the low management areas, but no differences were found in the number of nestlings and fledglings. Consequently, we found no differences in overall breeding success. Our results highlight the reduction in survival in a near-threatened passerine species due to routine green urban space management, in addition to differences in reproductive parameters depending on the degree of green urban space management. Overall, we confirm that the same species show several reproductive strategies with different breeding effort to reach similar breeding success, whatever the human context is. However, birds pay the cost in adult survival, and probably in shortening life span. Therefore, the management of urban green spaces has a negative impact on biodiversity in cities. It is necessary to review the management practices of these urban areas and promote practices that are friendly to biodiversity. Full article
(This article belongs to the Special Issue Biodiversity in Urban Landscapes)
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32 pages, 14398 KB  
Article
An Intelligent Airflow Regulation Method for Mine Ventilation Networks Based on MIST Topological Dimensionality Reduction and the IDBO Algorithm
by Zhenguo Yan, Longcheng Zhang, Yanping Wang, Lipeng Dang and Tianhe Fu
Mathematics 2026, 14(9), 1446; https://doi.org/10.3390/math14091446 - 25 Apr 2026
Viewed by 111
Abstract
Mine ventilation network (MVN) regulation faces severe challenges: strong variable coupling, high search dimensionality, and the inherent conflict between energy conservation and safety constraints. To address these issues, we propose a novel airflow optimization framework integrating a Minimum Influence Spanning Tree (MIST), sensitivity [...] Read more.
Mine ventilation network (MVN) regulation faces severe challenges: strong variable coupling, high search dimensionality, and the inherent conflict between energy conservation and safety constraints. To address these issues, we propose a novel airflow optimization framework integrating a Minimum Influence Spanning Tree (MIST), sensitivity attenuation boundaries, and an Improved Dung Beetle Optimizer (IDBO). Initially, high-influence co-tree chords are strategically extracted via MIST to compress the mathematical optimization dimensionality. Subsequently, effective ventilation resistance search intervals are bounded using sensitivity attenuation, preventing the algorithm from performing invalid searches in high-resistance regions. Furthermore, the standard DBO is enhanced via Fuchs chaotic initialization, Golden Sine and Lens Imaging collaborative learning, and differential mutation to minimize system power consumption. A 46-branch MVN case study validates the approach, identifying an 8-dimensional control combination as the absolute minimum requirement for full compliance. Compared to state-of-the-art baselines (DBO, SSA, WOA, DE), IDBO achieved the lowest power consumption. Post-optimization, the airflow constraint satisfaction rate improved from 89.13% to 100%, and total system power decreased by 11.87% (from 185.03 kW to 163.08 kW). Ultimately, this method robustly achieves Ventilation on Demand (VoD), providing a reliable computational tool for intelligent underground mining. Full article
27 pages, 2530 KB  
Article
On Wind Effects in a Hyperbolic Advection–Reaction–Diffusion Forest Fire Model: Analytical Solutions, Stability, and Bifurcation Analysis
by Elena V. Nikolova, Gergana N. Nikolova and Tsvetomir Ch. Pavlov
Mathematics 2026, 14(7), 1118; https://doi.org/10.3390/math14071118 - 26 Mar 2026
Viewed by 436
Abstract
We revisit a hyperbolic wildfire model based on reaction–diffusion dynamics with relaxation effects and extend it by incorporating an advection transport term that accounts for wind-driven fire spread. After a planar two-dimensional reformulation and non-dimensionalization of the model, the analysis is restricted to [...] Read more.
We revisit a hyperbolic wildfire model based on reaction–diffusion dynamics with relaxation effects and extend it by incorporating an advection transport term that accounts for wind-driven fire spread. After a planar two-dimensional reformulation and non-dimensionalization of the model, the analysis is restricted to the minimal ignition regime characterized by the presence of a logistic reaction term governing the evolution of the fire-affected tree fraction. The focus of the study is to assess the influence of the effective wind velocity on the propagation dynamics of the fire-affected tree fraction. For this purpose, analytical solutions of the extended wildfire model are derived by applying the Simple Equations Method (SEsM) in its (1,1) variant using a Riccati-type ordinary differential equation as a simple equation. The obtained families of exact solutions describe physically relevant transition fronts connecting fire-unaffected and fully fire-affected states, or vice versa. Numerical simulations of the derived analytical solutions are performed to demonstrate how the internal front thickness and the profile morphology depend on the specific variant of the Riccati-type solution and on the magnitude of the effective wind velocity. A phase-plane stability and bifurcation analysis of the reduced traveling wave system is carried out. Hopf bifurcation thresholds with respect to the effective wind velocity parameter are identified, revealing transitions between monotone front propagation and oscillatory regimes. A regime map is constructed in the parameter plane spanned by the effective wind velocity and the traveling wave speed. This regime diagram delineates regions of qualitatively different propagation behavior, including monotone advancing fronts, possible oscillatory regimes, and regimes in which traveling wave fronts cease to exist. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis: Theory, Methods and Applications)
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32 pages, 999 KB  
Article
A Robust Hybrid Metaheuristic Framework for Training Support Vector Machines
by Khalid Nejjar, Khalid Jebari and Siham Rekiek
Algorithms 2026, 19(1), 70; https://doi.org/10.3390/a19010070 - 13 Jan 2026
Viewed by 319
Abstract
Support Vector Machines (SVMs) are widely used in critical decision-making applications, such as precision agriculture, due to their strong theoretical foundations and their ability to construct an optimal separating hyperplane in high-dimensional spaces. However, the effectiveness of SVMs is highly dependent on the [...] Read more.
Support Vector Machines (SVMs) are widely used in critical decision-making applications, such as precision agriculture, due to their strong theoretical foundations and their ability to construct an optimal separating hyperplane in high-dimensional spaces. However, the effectiveness of SVMs is highly dependent on the efficiency of the optimization algorithm used to solve their underlying dual problem, which is often complex and constrained. Classical solvers, such as Sequential Minimal Optimization (SMO) and Stochastic Gradient Descent (SGD), present inherent limitations: SMO ensures numerical stability but lacks scalability and is sensitive to heuristics, while SGD scales well but suffers from unstable convergence and limited suitability for nonlinear kernels. To address these challenges, this study proposes a novel hybrid optimization framework based on Open Competency Optimization and Particle Swarm Optimization (OCO–PSO) to enhance the training of SVMs. The proposed approach combines the global exploration capability of PSO with the adaptive competency-based learning mechanism of OCO, enabling efficient exploration of the solution space, avoidance of local minima, and strict enforcement of dual constraints on the Lagrange multipliers. Across multiple datasets spanning medical (diabetes), agricultural yield, signal processing (sonar and ionosphere), and imbalanced synthetic data, the proposed OCO-PSO–SVM consistently outperforms classical SVM solvers (SMO and SGD) as well as widely used classifiers, including decision trees and random forests, in terms of accuracy, macro-F1-score, Matthews correlation coefficient (MCC), and ROC-AUC. On the Ionosphere dataset, OCO-PSO achieves an accuracy of 95.71%, an F1-score of 0.954, and an MCC of 0.908, matching the accuracy of random forest while offering superior interpretability through its kernel-based structure. In addition, the proposed method yields a sparser model with only 66 support vectors compared to 71 for standard SVC (a reduction of approximately 7%), while strictly satisfying the dual constraints with a near-zero violation of 1.3×103. Notably, the optimal hyperparameters identified by OCO-PSO (C=2, γ0.062) differ substantially from those obtained via Bayesian optimization for SVC (C=10, γ0.012), indicating that the proposed approach explores alternative yet equally effective regions of the hypothesis space. The statistical significance and robustness of these improvements are confirmed through extensive validation using 1000 bootstrap replications, paired Student’s t-tests, Wilcoxon signed-rank tests, and Holm–Bonferroni correction. These results demonstrate that the proposed metaheuristic hybrid optimization framework constitutes a reliable, interpretable, and scalable alternative for training SVMs in complex and high-dimensional classification tasks. Full article
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66 pages, 3439 KB  
Systematic Review
Artificial Intelligence Models for Forecasting Mosquito-Borne Viral Diseases in Human Populations: A Global Systematic Review and Comparative Performance Analysis
by Flavia Pennisi, Antonio Pinto, Fabio Borgonovo, Giovanni Scaglione, Riccardo Ligresti, Omar Enzo Santangelo, Sandro Provenzano, Andrea Gori, Vincenzo Baldo, Carlo Signorelli and Vincenza Gianfredi
Mach. Learn. Knowl. Extr. 2026, 8(1), 15; https://doi.org/10.3390/make8010015 - 7 Jan 2026
Cited by 2 | Viewed by 1877
Abstract
Background: Mosquito-borne viral diseases are a growing global health threat, and artificial intelligence (AI) and machine learning (ML) are increasingly proposed as forecasting tools to support early-warning and response. However, the available evidence is fragmented across pathogens, settings and modelling approaches. This review [...] Read more.
Background: Mosquito-borne viral diseases are a growing global health threat, and artificial intelligence (AI) and machine learning (ML) are increasingly proposed as forecasting tools to support early-warning and response. However, the available evidence is fragmented across pathogens, settings and modelling approaches. This review provides, to the best of our knowledge, the first comprehensive comparative assessment of AI/ML models forecasting mosquito-borne viral diseases in human populations, jointly synthesising predictive performance across model families and appraising both methodological quality and operational readiness. Methods: Following PRISMA 2020, we searched PubMed, Embase and Scopus up to August 2025. We included studies applying AI/ML or statistical models to predict arboviral incidence, outbreaks or temporal trends and reporting at least one quantitative performance metric. Given the substantial heterogeneity in outcomes, predictors and time–space scales, we conducted a descriptive synthesis. Risk of bias and applicability were evaluated using PROBAST. Results: Ninety-eight studies met the inclusion criteria, of which 91 focused on dengue. The forecasts spanned national to city-level settings and annual-to-weekly resolutions. Across classification tasks, tree-ensemble models showed the most consistent performance, with accuracies typically above 0.85, while classical ML and deep-learning models showed wider variability. For regression tasks, errors increased with temporal horizon and spatial aggregation: short-term, fine-scale forecasts (e.g., weekly city level) often achieved low absolute errors, whereas long-horizon national models frequently exhibited very large errors and unstable performance. PROBAST assessment indicated that most studies (63/98) were at high risk of bias, with only 24 judged at low risk and limited external validation. Conclusions: AI/ML models, especially tree-ensemble approaches, show strong potential for short-term, fine-scale forecasting, but their reliability drops substantially at broader spatial and temporal scales. Most remain research-stage, with limited external validation and minimal operational deployment. This review clarifies current capabilities and highlights three priorities for real-world use: standardised reporting, rigorous external validation, and context-specific calibration. Full article
(This article belongs to the Section Thematic Reviews)
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24 pages, 1738 KB  
Article
Design and Analysis of k-Connectivity Restoration Algorithms for Fault-Tolerant Drone Swarms in Harsh Civil Environments
by Orhan Ceylan, Zuleyha Akusta Dagdeviren, Moharram Challenger and Orhan Dagdeviren
Drones 2026, 10(1), 16; https://doi.org/10.3390/drones10010016 - 28 Dec 2025
Viewed by 908
Abstract
Drone swarms are increasingly used in critical civil applications like agriculture, machine maintenance and search-and-rescue, where maintaining network connectivity is essential for effective coordination. However, harsh environmental conditions can lead to drone failures, risking network fragmentation. To improve resilience, designing k-connected networks, [...] Read more.
Drone swarms are increasingly used in critical civil applications like agriculture, machine maintenance and search-and-rescue, where maintaining network connectivity is essential for effective coordination. However, harsh environmental conditions can lead to drone failures, risking network fragmentation. To improve resilience, designing k-connected networks, where up to k1 drone failures can be tolerated without losing connectivity, offers a practical solution by providing multiple independent communication paths between drones. The k-connectivity restoration problem is repositioning drones to achieve k-connectivity with minimal movement. In this study, we address this NP-Hard problem and propose novel solutions. Unlike existing k-connectivity restoration algorithms that constrain drones to predefined points, our model allows free repositioning within the mission area, increasing flexibility but also expanding the solution space and complexity. To address this problem, we propose three center-based algorithms that guide drones toward different central points computed from the network layout: in the first algorithm (ORIGIN), the center point is the geometric origin of the mission area; in the second algorithm (CENTROID), nodes move toward the centroid of all drone positions; and in the third algorithm, the center position is defined as the CENTer of the FARthest nodes (CENTFAR). We also introduce a Minimum Spanning Tree-based (MST) algorithm that moves drones along a minimum spanning tree to achieve and theoretically guarantee k-connectivity. Besides checking k-connectivity after each individual move, we also develop group-based variants where all drones move simultaneously and k-connectivity is checked afterward. We conduct comprehensive simulations under varying drone counts, network sizes, k values, and transmission ranges to evaluate the effectiveness and scalability of the proposed algorithms. CENTFAR provides the best movement efficiency among the center-based algorithms, slightly outperforming CENTROID and ORIGIN and achieving up to 21% lower total and 29% lower maximum movement than MST in smaller areas and higher k values. MST, however, performs best under low k and high transmission ranges, offering up to 57% lower total movement and 20% lower execution time than CENTFAR. Group-based variants accelerate convergence (up to a tenfold speedup) at the cost of a slight increase in movement. Our findings reveal that MST is ideal for low-k settings, while CENTFAR is better suited for high-connectivity deployments. Full article
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31 pages, 635 KB  
Article
Joint Feeder Routing and Conductor Sizing in Rural Unbalanced Three-Phase Distribution Networks: An Exact Optimization Approach
by Brandon Cortés-Caicedo, Oscar Danilo Montoya, Luis Fernando Grisales-Noreña, Santiago Bustamante-Mesa and Carlos Andrés Torres-Pinzón
Sci 2025, 7(4), 165; https://doi.org/10.3390/sci7040165 - 7 Nov 2025
Viewed by 828
Abstract
This paper addresses the simultaneous feeder routing and conductor sizing problem in unbalanced three-phase distribution systems, formulated as a nonconvex mixed-integer nonlinear program (MINLP) that minimizes the equivalent annualized expansion cost—combining investment and loss costs—under voltage, ampacity, and radiality constraints. The model captures [...] Read more.
This paper addresses the simultaneous feeder routing and conductor sizing problem in unbalanced three-phase distribution systems, formulated as a nonconvex mixed-integer nonlinear program (MINLP) that minimizes the equivalent annualized expansion cost—combining investment and loss costs—under voltage, ampacity, and radiality constraints. The model captures nonconvex voltage–current–power couplings, Δ/Y load asymmetries, and discrete conductor selections, creating a large combinatorial design space that challenges heuristic methods. An exact MINLP formulation in complex variables is implemented in Julia/JuMP and solved with the Basic Open-source Nonlinear Mixed Integer programming (BONMIN) solver, which integrates branch-and-bound for discrete variables and interior-point methods for nonlinear subproblems. The main contributions are: (i) a rigorous, reproducible formulation that jointly optimizes routing and conductor sizing; (ii) a transparent, replicable implementation; and (iii) a benchmark against minimum spanning tree (MST)-based and metaheuristic approaches, clarifying the trade-off between computational time and global optimality. Tests on 10- and 30-node rural feeders show that, although metaheuristics converge faster, they often yield suboptimal solutions. The proposed MINLP achieves globally optimal, technically feasible results, reducing annualized cost by 14.6% versus MST and 2.1% versus metaheuristics in the 10-node system, and by 17.2% and 2.5%, respectively, in the 30-node system. These results highlight the advantages of exact optimization for rural network planning, providing reproducible and verifiable decisions in investment-intensive scenarios. Full article
(This article belongs to the Section Computer Science, Mathematics and AI)
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38 pages, 5909 KB  
Article
A Hybrid TLBO-Cheetah Algorithm for Multi-Objective Optimization of SOP-Integrated Distribution Networks
by Abdulaziz Alanazi, Mohana Alanazi and Mohammed Alruwaili
Mathematics 2025, 13(21), 3419; https://doi.org/10.3390/math13213419 - 27 Oct 2025
Viewed by 780
Abstract
The integration of Soft Open Points (SOPs) into distribution networks has been an essential method for enhancing operational flexibility and efficiency. But simultaneous optimization of network reconfiguration and SOP scheduling constitutes a difficult mixed-integer nonlinear programming (MINLP) problem that is likely to suffer [...] Read more.
The integration of Soft Open Points (SOPs) into distribution networks has been an essential method for enhancing operational flexibility and efficiency. But simultaneous optimization of network reconfiguration and SOP scheduling constitutes a difficult mixed-integer nonlinear programming (MINLP) problem that is likely to suffer from premature convergence with standard metaheuristic solvers, particularly in large power networks. This paper proposes a novel hybrid algorithm, hTLBO–CO, which synergistically integrates the exploitative capability of Teaching–Learning-Based Optimization (TLBO) with the explorative capability of the Cheetah Optimizer (CO). One of the notable contributions of our framework is an in-depth problem formulation that enables SOP locations on both tie and sectionalizing switches with an efficient constraint-handling scheme, preserving topo-logical feasibility through a minimum spanning tree repair scheme. The evolved hTLBO–CO algorithm is systematically validated across IEEE 33-, 69-, and 119-bus test feeders with differential operational scenarios. Results indicate consistent dominance over established metaheuristics (TLBO, CO, PSO, JAYA), showing significant efficiency improvement in power loss minimization, voltage profile enhancement, and convergence rate. Remarkably, in a situation with a large-scale 119-bus power grid, hTLBO–CO registered a significant 50.30% loss reduction in the single-objective reconfiguration-only scheme, beating existing state-of-the-art approaches by over 15 percentage points. These findings, further substantiated by comprehensive statistical and multi-objective analyses, confirm the proposed framework’s superiority, robustness, and scalability, establishing hTLBO–CO as a robust computational tool for the advanced optimization of future distribution networks. Full article
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20 pages, 20380 KB  
Article
Connectivity-Oriented Optimization of Scalable Wireless Sensor Topologies for Urban Smart Water Metering
by Esteban Inga, Yanpeng Dai, Juan Inga and Kesheng Zhang
Smart Cities 2025, 8(5), 167; https://doi.org/10.3390/smartcities8050167 - 9 Oct 2025
Viewed by 3426
Abstract
The growing need for efficient and sustainable urban water management has accelerated the adoption of smart monitoring infrastructures based on wireless sensor networks (WSNs). This study proposes a connectivity-aware methodology for the optimal deployment of wireless sensor networks (WSNs) in smart water metering [...] Read more.
The growing need for efficient and sustainable urban water management has accelerated the adoption of smart monitoring infrastructures based on wireless sensor networks (WSNs). This study proposes a connectivity-aware methodology for the optimal deployment of wireless sensor networks (WSNs) in smart water metering systems. The approach models the wireless sensors as nodes embedded in household water meters and determines the minimal yet sufficient set of Data Aggregation Points required to ensure complete network coverage and transmission reliability. A scalable and hierarchical topology is generated by integrating an enhanced minimum spanning tree algorithm with set covering techniques and geographic constraints, leading to a robust intermediate layer of aggregation nodes. These nodes are wirelessly linked to a single cellular base station, minimizing infrastructure costs while preserving communication quality. Simulation results on realistic urban layouts demonstrate that the proposed strategy reduces network fragmentation, improves energy efficiency, and simplifies routing paths compared to traditional ad hoc designs. The results offer a practical framework for deploying resilient and cost-effective smart water metering solutions in densely populated urban environments. Full article
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35 pages, 4926 KB  
Article
Hybrid MOCPO–AGE-MOEA for Efficient Bi-Objective Constrained Minimum Spanning Trees
by Dana Faiq Abd, Haval Mohammed Sidqi and Omed Hasan Ahmed
Computers 2025, 14(10), 422; https://doi.org/10.3390/computers14100422 - 2 Oct 2025
Viewed by 1185
Abstract
The constrained bi-objective Minimum Spanning Tree (MST) problem is a fundamental challenge in network design, as it simultaneously requires minimizing both total edge weight and maximum hop distance under strict feasibility limits; however, most existing algorithms tend to emphasize one objective over the [...] Read more.
The constrained bi-objective Minimum Spanning Tree (MST) problem is a fundamental challenge in network design, as it simultaneously requires minimizing both total edge weight and maximum hop distance under strict feasibility limits; however, most existing algorithms tend to emphasize one objective over the other, resulting in imbalanced solutions, limited Pareto fronts, or poor scalability on larger instances. To overcome these shortcomings, this study introduces a Hybrid MOCPO–AGE-MOEA algorithm that strategically combines the exploratory strength of Multi-Objective Crested Porcupines Optimization (MOCPO) with the exploitative refinement of the Adaptive Geometry-based Evolutionary Algorithm (AGE-MOEA), while a Kruskal-based repair operator is integrated to strictly enforce feasibility and preserve solution diversity. Moreover, through extensive experiments conducted on Euclidean graphs with 11–100 nodes, the hybrid consistently demonstrates superior performance compared with five state-of-the-art baselines, as it generates Pareto fronts up to four times larger, achieves nearly 20% reductions in hop counts, and delivers order-of-magnitude runtime improvements with near-linear scalability. Importantly, results reveal that allocating 85% of offspring to MOCPO exploration and 15% to AGE-MOEA exploitation yields the best balance between diversity, efficiency, and feasibility. Therefore, the Hybrid MOCPO–AGE-MOEA not only addresses critical gaps in constrained MST optimization but also establishes itself as a practical and scalable solution with strong applicability to domains such as software-defined networking, wireless mesh systems, and adaptive routing, where both computational efficiency and solution diversity are paramount Full article
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20 pages, 575 KB  
Article
Uncertainty-Driven Stability Analysis of Minimum Spanning Tree Under Multiple Risk Variations
by Ahmad Hosseini
Mathematics 2025, 13(19), 3100; https://doi.org/10.3390/math13193100 - 27 Sep 2025
Viewed by 1035
Abstract
The Minimum Spanning Tree (MST) problem addresses the challenge of identifying optimal network pathways for critical infrastructure systems, including transportation grids, communication backbones, power distribution networks, and reliability optimization frameworks. However, inherent uncertainties stemming from disruptive events demand robust analytical models for effective [...] Read more.
The Minimum Spanning Tree (MST) problem addresses the challenge of identifying optimal network pathways for critical infrastructure systems, including transportation grids, communication backbones, power distribution networks, and reliability optimization frameworks. However, inherent uncertainties stemming from disruptive events demand robust analytical models for effective decision-making. This research introduces an uncertainty-theoretic framework to assess MST stability in uncertain network environments through novel constructs: lower set tolerance (LST) and dual lower set tolerance (DLST). Both LST and DLST provide quantifiable measures characterizing the resilience of element sets relative to edge-weighted MST configurations. LST captures the maximum simultaneous risk variation preserving current MST optimality, while DLST identifies the minimal variation required to invalidate it. We evaluate MST robustness by integrating uncertain reliability measures and risk factors, with emphasis on computational methods for set tolerance determination. To overcome computational hurdles in set tolerance derivation, we establish bounds and exact formulations within an uncertainty programming paradigm, offering enhanced efficiency compared with conventional re-optimization techniques. Full article
(This article belongs to the Section E: Applied Mathematics)
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19 pages, 647 KB  
Article
Max+Sum Spanning Tree Interdiction and Improvement Problems Under Weighted l Norm
by Qiao Zhang, Junhua Jia and Xiao Li
Axioms 2025, 14(9), 691; https://doi.org/10.3390/axioms14090691 - 11 Sep 2025
Viewed by 776
Abstract
The Max+Sum Spanning Tree (MSST) problem, with applications in secure communication systems, seeks a spanning tree T minimizing maxeTw(e)+eTc(e) on a given edge-weighted undirected network [...] Read more.
The Max+Sum Spanning Tree (MSST) problem, with applications in secure communication systems, seeks a spanning tree T minimizing maxeTw(e)+eTc(e) on a given edge-weighted undirected network G(V,E,c,w), where the sets V and E are the sets of vertices and edges, respectively. The functions c and w are defined on the edge set, representing transmission cost and verification delay in secure communication systems, respectively. This problem can be solved within O(|E|log|V|) time. We investigate its interdiction (MSSTID) and improvement (MSSTIP) problems under the weighted l norm. MSSTID seeks minimal edge weight adjustments (to either c or w) to degrade network performance by ensuring the optimal MSST’s weight is at least K, while MSSTIP similarly aims to enhance performance by making the optimal MSST’s weight at most K through minimal weight modifications. These problems naturally arise in adversarial and proactive performance enhancement scenarios, respectively, where network robustness or efficiency must be guaranteed through constrained resource allocation. We first establish their mathematical models. Subsequently, we analyze the properties of the optimal value to determine the relationship between the magnitude of a given number and the optimal value. Then, utilizing binary search methods and greedy techniques, we design four algorithms with time complexity O(|E|2log|V|) to solve the above problems by modifying w or c. Finally, numerical experiments are conducted to demonstrate the effectiveness of the algorithms. Full article
(This article belongs to the Special Issue Graph Theory and Combinatorics: Theory and Applications)
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39 pages, 1281 KB  
Article
Sustainable Metaheuristic-Based Planning of Rural Medium- Voltage Grids: A Comparative Study of Spanning and Steiner Tree Topologies for Cost-Efficient Electrification
by Lina María Riaño-Enciso, Brandon Cortés-Caicedo, Oscar Danilo Montoya, Luis Fernando Grisales-Noreña and Jesús C. Hernández
Sustainability 2025, 17(18), 8145; https://doi.org/10.3390/su17188145 - 10 Sep 2025
Cited by 2 | Viewed by 951
Abstract
This paper presents a heuristic methodology for the optimal expansion of unbalanced three-phase distribution systems in rural areas, simultaneously addressing feeder routing and conductor sizing to minimize the total annualized cost—defined as the sum of investments in conductors and operational energy losses. The [...] Read more.
This paper presents a heuristic methodology for the optimal expansion of unbalanced three-phase distribution systems in rural areas, simultaneously addressing feeder routing and conductor sizing to minimize the total annualized cost—defined as the sum of investments in conductors and operational energy losses. The planning strategy explores two radial topological models: the Minimum Spanning Tree (MST) and the Steiner Tree (ST). The latter incorporates auxiliary nodes to reduce the total line length. For each topology, an initial conductor sizing is performed based on three-phase power flow calculations using Broyden’s method, capturing the unbalanced nature of the rural networks. These initial solutions are refined via four metaheuristic algorithms—the Chu–Beasley Genetic Algorithm (CBGA), Particle Swarm Optimization (PSO), the Sine–Cosine Algorithm (SCA), and the Grey Wolf Optimizer (GWO)—under a master–slave optimization framework. Numerical experiments on 15-, 25- and 50-node rural test systems show that the ST combined with GWO consistently achieves the lowest total costs—reducing expenditures by up to 70.63% compared to MST configurations—and exhibits superior robustness across all performance metrics, including best-, average-, and worst-case solutions, as well as standard deviation. Beyond its technical contributions, the proposed methodology supports the United Nations Sustainable Development Goals by promoting universal energy access (SDG 7), fostering cost-effective rural infrastructure (SDG 9), and contributing to reductions in urban–rural inequalities in electricity access (SDG 10). All simulations were implemented in MATLAB 2024a, demonstrating the practical viability and scalability of the method for planning rural distribution networks under unbalanced load conditions. Full article
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24 pages, 2488 KB  
Article
UAM Vertiport Network Design Considering Connectivity
by Wentao Zhang and Taesung Hwang
Systems 2025, 13(7), 607; https://doi.org/10.3390/systems13070607 - 18 Jul 2025
Cited by 1 | Viewed by 2104
Abstract
Urban Air Mobility (UAM) is envisioned to revolutionize urban transportation by improving traffic efficiency and mitigating surface-level congestion. One of the fundamental challenges in implementing UAM systems lies in the optimal siting of vertiports, which requires a delicate balance among infrastructure construction costs, [...] Read more.
Urban Air Mobility (UAM) is envisioned to revolutionize urban transportation by improving traffic efficiency and mitigating surface-level congestion. One of the fundamental challenges in implementing UAM systems lies in the optimal siting of vertiports, which requires a delicate balance among infrastructure construction costs, passenger access costs to their assigned vertiports, and the operational connectivity of the resulting vertiport network. This study develops an integrated mathematical model for vertiport location decision, aiming to minimize total system cost while ensuring UAM network connectivity among the selected vertiport locations. To efficiently solve the problem and improve solution quality, a hybrid genetic algorithm is developed by incorporating a Minimum Spanning Tree (MST)-based connectivity enforcement mechanism, a fundamental concept in graph theory that connects all nodes in a given network with minimal total link cost, enhanced by a greedy initialization strategy. The effectiveness of the proposed algorithm is demonstrated through numerical experiments conducted on both synthetic datasets and the real-world transportation network of New York City. The results show that the proposed hybrid methodology not only yields high-quality solutions but also significantly reduces computational time, enabling faster convergence. Overall, this study provides practical insights for UAM infrastructure planning by emphasizing demand-oriented vertiport siting and inter-vertiport connectivity, thereby contributing to both theoretical development and large-scale implementation in complex urban environments. Full article
(This article belongs to the Special Issue Modelling and Simulation of Transportation Systems)
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