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Keywords = heuristic functions

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23 pages, 1141 KB  
Article
Randomized Algorithms and Neural Networks for Communication-Free Multiagent Singleton Set Cover
by Guanchu He, Colton Hill, Joshua H. Seaton and Philip N. Brown
Games 2026, 17(1), 3; https://doi.org/10.3390/g17010003 - 12 Jan 2026
Abstract
This paper considers how a system designer can program a team of autonomous agents to coordinate with one another such that each agent selects (or covers) an individual resource with the goal that all agents collectively cover the maximum number of resources. Specifically, [...] Read more.
This paper considers how a system designer can program a team of autonomous agents to coordinate with one another such that each agent selects (or covers) an individual resource with the goal that all agents collectively cover the maximum number of resources. Specifically, we study how agents can formulate strategies without information about other agents’ actions so that system-level performance remains robust in the presence of communication failures. First, we use an algorithmic approach to study the scenario in which all agents lose the ability to communicate with one another, have a symmetric set of resources to choose from, and select actions independently according to a probability distribution over the resources. We show that the distribution that maximizes the expected system-level objective under this approach can be computed by solving a convex optimization problem, and we introduce a novel polynomial-time heuristic based on subset selection. Further, both of the methods are guaranteed to be within 11/e of the system’s optimal in expectation. Second, we use a learning-based approach to study how a system designer can employ neural networks to approximate optimal agent strategies in the presence of communication failures. The neural network, trained on system-level optimal outcomes obtained through brute-force enumeration, generates utility functions that enable agents to make decisions in a distributed manner. Empirical results indicate the neural network often outperforms greedy and randomized baseline algorithms. Collectively, these findings provide a broad study of optimal agent behavior and its impact on system-level performance when the information available to agents is extremely limited. Full article
(This article belongs to the Section Algorithmic and Computational Game Theory)
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31 pages, 4500 KB  
Article
Enhanced Social Group Optimization Algorithm for the Economic Dispatch Problem Including Wind Power
by Dinu Călin Secui, Cristina Hora, Florin Ciprian Dan, Monica Liana Secui and Horea Nicolae Hora
Processes 2026, 14(2), 254; https://doi.org/10.3390/pr14020254 - 11 Jan 2026
Viewed by 43
Abstract
The economic dispatch (ED) problem is a major challenge in power system optimization. In this article, an Enhanced Social Group Optimization (ESGO) algorithm is presented for solving the economic dispatch problem with or without wind units, considering various characteristics related to valve-point effects, [...] Read more.
The economic dispatch (ED) problem is a major challenge in power system optimization. In this article, an Enhanced Social Group Optimization (ESGO) algorithm is presented for solving the economic dispatch problem with or without wind units, considering various characteristics related to valve-point effects, ramp-rate constraints, prohibited operating zones, and transmission power losses. The Social Group Optimization (SGO) algorithm models the social dynamics of individuals within a group—through mechanisms of collective learning, behavioral adaptation, and information exchange—and leverages these interactions to guide the population efficiently towards optimal solutions. ESGO extends SGO along three complementary directions: redefining the update relations of the original SGO, introducing stochastic operators into the heuristic mechanisms, and dynamically updating the generated solutions. These modifications aim to achieve a more robust balance between exploration and exploitation, enable flexible adaptation of search steps, and rapidly integrate improved-fitness solutions into the evolutionary process. ESGO is evaluated in six distinct cases, covering systems with 6, 40, 110, and 220 units, to demonstrate its ability to produce competitive solutions as well as its performance in terms of stability, convergence, and computational efficiency. The numerical results show that, in the vast majority of the analyzed cases, ESGO outperforms SGO and other known or improved metaheuristic algorithms in terms of cost and stability. It incorporates wind generation results at an operating cost reduction of approximately 10% compared to the thermal-only system, under the adopted linear wind power model. Moreover, relative to the size of the analyzed systems, ESGO exhibits a reduced average execution time and requires a small number of function evaluations to obtain competitive solutions. Full article
(This article belongs to the Section Energy Systems)
26 pages, 4490 KB  
Article
A Bi-Level Intelligent Control Framework Integrating Deep Reinforcement Learning and Bayesian Optimization for Multi-Objective Adaptive Scheduling in Opto-Mechanical Automated Manufacturing
by Lingyu Yin, Zhenhua Fang, Kaicen Li, Jing Chen, Naiji Fan and Mengyang Li
Appl. Sci. 2026, 16(2), 732; https://doi.org/10.3390/app16020732 - 10 Jan 2026
Viewed by 106
Abstract
The opto-mechanical automated manufacturing process, characterized by stringent process constraints, dynamic disturbances, and conflicting optimization objectives, presents significant control challenges for traditional scheduling and control approaches. We formulate the scheduling problem within a closed-loop control paradigm and propose a novel bi-level intelligent control [...] Read more.
The opto-mechanical automated manufacturing process, characterized by stringent process constraints, dynamic disturbances, and conflicting optimization objectives, presents significant control challenges for traditional scheduling and control approaches. We formulate the scheduling problem within a closed-loop control paradigm and propose a novel bi-level intelligent control framework integrating Deep Reinforcement Learning (DRL) and Bayesian Optimization (BO). The core of our approach is a bi-level intelligent control framework. An inner DRL agent acts as an adaptive controller, generating control actions (scheduling decisions) by perceiving the system state and learning a near-optimal policy through a carefully designed reward function, while an outer BO loop automatically tunes the DRL’s hyperparameters and reward weights for superior performance. This synergistic BO-DRL mechanism facilitates intelligent and adaptive decision-making. The proposed method is extensively evaluated against standard meta-heuristics, including Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), on a complex 20-jobs × 20-machines flexible job shop scheduling benchmark specific to opto-mechanical automated manufacturing. The experimental results demonstrate that our BO-DRL algorithm significantly outperforms these benchmarks, achieving reductions in makespan of 13.37% and 25.51% compared to GA and PSO, respectively, alongside higher machine utilization and better on-time delivery. Furthermore, the algorithm exhibits enhanced convergence speed, superior robustness under dynamic disruptions (e.g., machine failures, urgent orders), and excellent scalability to larger problem instances. This study confirms that integrating DRL’s perceptual decision-making capability with BO’s efficient parameter optimization yields a powerful and effective solution for intelligent scheduling in high-precision manufacturing environments. Full article
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33 pages, 9237 KB  
Article
Optimized Model Predictive Controller Using Multi-Objective Whale Optimization Algorithm for Urban Rail Train Tracking Control
by Longda Wang, Lijie Wang and Yan Chen
Biomimetics 2026, 11(1), 60; https://doi.org/10.3390/biomimetics11010060 - 10 Jan 2026
Viewed by 84
Abstract
With the rapid development of urban rail transit, train operation control is required to meet increasingly stringent demands in terms of energy consumption, comfort, punctuality, and precise stopping. The optimization and tracking control of speed profiles are two critical issues in ensuring the [...] Read more.
With the rapid development of urban rail transit, train operation control is required to meet increasingly stringent demands in terms of energy consumption, comfort, punctuality, and precise stopping. The optimization and tracking control of speed profiles are two critical issues in ensuring the performance of automatic train operation systems. However, conventional model predictive control (MPC) methods are highly dependent on parameter settings and show limited adaptability, while heuristic optimization approaches such as the whale optimization algorithm (WOA) often suffer from premature convergence and insufficient robustness. To overcome these limitations, this study proposes an optimized model predictive controller using the multi-objective whale optimization algorithm (MPC-MOWOA) for urban rail train tracking control. In the improved optimization algorithm, a nonlinear convergence mechanism and the Tchebycheff decomposition method are introduced to enhance convergence accuracy and population diversity, which enables effective optimization of the initial parameters of the MPC. During real-time operation, the MPC is further enhanced by integrating a fuzzy satisfaction function that adaptively adjusts the softening factor. In addition, the control coefficients are corrected online according to the speed error and its rate of change, thereby improving adaptability of the control system. Taking the section from Lvshun New Port to Tieshan Town on Dalian Metro Line 12 as the study case, the proposed control algorithm was deployed on a TMS320F28335 embedded processor platform, and hardware-in-the-loop simulation experiments (HILSEs) were conducted under the same simulation environment, a unified train dynamic model, consistent operating conditions, and an identical evaluation index system. The results indicate that, compared with the Fuzzy-PID control method, the proposed control strategy reduces the integral of time-weighted absolute error nearly by 39.6% and decreases energy consumption nearly by 5.9%, while punctuality, stopping accuracy, and comfort are improved nearly by 33.2%, 12.4%, and 7.1%, respectively. These results not only verify the superior performance of the proposed MPC-MOWOA, but also demonstrate its capability for real-time implementation on embedded processors, thereby overcoming the limitations of purely MATLAB-based offline simulations and exhibiting strong potential for practical engineering applications in urban rail transit. Full article
(This article belongs to the Section Biological Optimisation and Management)
22 pages, 4277 KB  
Article
TGN-MCDS: A Temporal Graph Network-Based Algorithm for Cluster-Head Optimization in Large-Scale FANETs
by Xiangrui Fan, Yuxuan Yang, Shuo Zhang and Wenlong Cai
Sensors 2026, 26(1), 347; https://doi.org/10.3390/s26010347 - 5 Jan 2026
Viewed by 213
Abstract
With the growing deployment of Flying Ad hoc Networks (FANETs) in military and civilian applications, constructing a stable and efficient communication backbone has become a critical challenge. This paper tackles the Cluster Head (CH) optimization problem in large-scale and highly dynamic FANETs by [...] Read more.
With the growing deployment of Flying Ad hoc Networks (FANETs) in military and civilian applications, constructing a stable and efficient communication backbone has become a critical challenge. This paper tackles the Cluster Head (CH) optimization problem in large-scale and highly dynamic FANETs by formulating it as a Minimum Connected Dominating Set (MCDS) problem. However, since MCDS is NP-complete on general graphs, existing heuristic and exact algorithms suffer from limited coverage, poor connectivity, and high computational cost. To address these issues, we propose TGN-MCDS, a novel algorithm built upon the Temporal Graph Network (TGN) architecture, which leverages graph neural networks for cluster head selection and efficiently learns time-varying network topologies. The algorithm adopts a multi-objective loss function incorporating coverage, connectivity, size control, centrality, edge penalty, temporal smoothness, and information entropy to guide model training. Simulation results demonstrate that TGN-MCDS rapidly achieves near-optimal CH sets with full node coverage and strong connectivity. Compared with Greedy, Integer Linear Programming (ILP), and Branch-and-Bound (BnB) methods, TGN-MCDS produces fewer and more stable CHs, significantly improving cluster stability while maintaining high computational efficiency for real-time operations in large-scale FANETs. Full article
(This article belongs to the Section Sensor Networks)
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22 pages, 3874 KB  
Article
Cloud-Edge Collaboration-Based Data Processing Method for Distribution Terminal Unit Edge Clusters
by Ruijiang Zeng, Zhiyong Li, Sifeng Li, Jiahao Zhang and Xiaomei Chen
Energies 2026, 19(1), 269; https://doi.org/10.3390/en19010269 - 4 Jan 2026
Viewed by 142
Abstract
Distribution terminal units (DTUs) play critical roles in smart grid for supporting data acquisition, remote monitoring, and fault management. A single DTU generates continuous data streams, imposing new challenges on data processing. To tackle these issues, a cloud-edge collaboration-based data processing method is [...] Read more.
Distribution terminal units (DTUs) play critical roles in smart grid for supporting data acquisition, remote monitoring, and fault management. A single DTU generates continuous data streams, imposing new challenges on data processing. To tackle these issues, a cloud-edge collaboration-based data processing method is introduced for DTU edge clusters. First, considering the load imbalance degree of DTU data queues, a cloud-edge integrated data processing architecture is designed. It optimizes edge server selection, the offloading splitting ratio, and edge-cloud computing resource allocation in a collaboration mechanism. Second, an optimization problem is formulated to maximize the weighted difference between the total data processing volume and the load imbalance degree. Next, a cloud-edge collaboration-based data processing method is proposed. In the first stage, cloud-edge collaborative data offloading based on the load imbalance degree, and a data volume-aware deep Q-network (DQN) is developed. A penalty function based on load fluctuations and the data volume deficit is incorporated. It drives the DQN to evolve toward suppressing the fluctuation of load imbalance degree while ensuring differentiated long-term data volume constraints. In the second stage, cloud-edge computing resource allocation based on adaptive differential evolution is designed. An adaptive mutation scaling factor is introduced to overcome the gene overlapping issues of traditional heuristic approaches, enabling deeper exploration of the solution space and accelerating global optimum identification. Finally, the simulation results demonstrate that the proposed method effectively improves the data processing efficiency of DTUs while reducing the load imbalance degree. Full article
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36 pages, 14020 KB  
Article
Improved Two-Stage Theta* Algorithm for Path Planning with Uncertain Obstacles in Unstructured Rescuing Environments
by Jingrui Zhang, Mengxin Zhou, Houde Liu, Xiaojun Zhu, Bin Lan and Zhenhong Xu
Processes 2026, 14(1), 167; https://doi.org/10.3390/pr14010167 - 4 Jan 2026
Viewed by 263
Abstract
Path planning aims to find a safe and efficient path from a starting point to an end point, and it has been well developed in fields such as robot navigation, autonomous driving, and intelligent decision systems. However, traditional path planning faces challenges in [...] Read more.
Path planning aims to find a safe and efficient path from a starting point to an end point, and it has been well developed in fields such as robot navigation, autonomous driving, and intelligent decision systems. However, traditional path planning faces challenges in an uncertain rescuing environment due to limited sensing range and a lack of accurate obstacle information. In order to address this issue, this paper proposes an improved two-stage Theta* algorithm for handling multi-probability obstacle scenarios in unstructured rescue environments. First, a global probability raster map is constructed by integrating historical maps and expert prediction maps with probability weights quantifying the uncertainty in the spatial and temporal distribution of obstacles. Second, a probability-sensitive heuristic function (PSHF) is designed, and a Sigmoid function is used to map the probability field of obstacles, thereby enabling limited penetration in low-risk areas and enforced avoidance in high-risk areas. Furthermore, a multi-stage line-of-sight detection optimization mechanism is proposed, which combines probability soft threshold penetration and backtracking verification to improve the noise robustness. Finally, a hierarchical planning architecture is constructed to separate global probabilistic guidance from local strict obstacle avoidance, ensuring both the global optimality and local adaptability of the path. Extensive simulation results in mine rescue scenarios demonstrate that the proposed method achieves lower path cost and fewer path nodes compared to traditional A*, Dijkstra, and Theta* algorithms, while significantly reducing local replanning overhead and maintaining stable performance across multiple uncertain environments. Full article
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27 pages, 382 KB  
Article
Single Machine Scheduling Problems: Standard Settings and Properties, Polynomially Solvable Cases, Complexity and Approximability
by Nodari Vakhania, Frank Werner and Kevin Johedan Ramírez-Fuentes
Algorithms 2026, 19(1), 38; https://doi.org/10.3390/a19010038 - 4 Jan 2026
Viewed by 143
Abstract
Since the publication of the first scheduling paper in 1954, a huge number of works dealing with different types of single machine problems have appeared. They addressed many heuristics and enumerative procedures, complexity results or structural properties of certain problems. Regarding surveys, often [...] Read more.
Since the publication of the first scheduling paper in 1954, a huge number of works dealing with different types of single machine problems have appeared. They addressed many heuristics and enumerative procedures, complexity results or structural properties of certain problems. Regarding surveys, often particular subjects like special objective functions were discussed or more general scheduling problems were surveyed, in which a substantial part was devoted to single machine problems. In this paper, we focus on standard settings, basic structural properties of these settings, polynomial algorithms and complexity and approximation issues, which have not been reviewed so far, and suggest some future work in this area. Full article
(This article belongs to the Special Issue 2024 and 2025 Selected Papers from Algorithms Editorial Board Members)
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20 pages, 5039 KB  
Article
RL-PMO: A Reinforcement Learning-Based Optimization Algorithm for Parallel SFC Migration
by Hefei Hu, Zining Liu and Fan Wu
Sensors 2026, 26(1), 242; https://doi.org/10.3390/s26010242 - 30 Dec 2025
Viewed by 198
Abstract
In edge networks, hardware failures and resource pressure may disrupt Service Function Chains (SFCs) deployed on the failed node, making it necessary to efficiently migrate multiple Virtual Network Functions (VNFs) under limited resources. To address these challenges, this paper proposes an offline reinforcement [...] Read more.
In edge networks, hardware failures and resource pressure may disrupt Service Function Chains (SFCs) deployed on the failed node, making it necessary to efficiently migrate multiple Virtual Network Functions (VNFs) under limited resources. To address these challenges, this paper proposes an offline reinforcement learning-based parallel migration optimization algorithm (RL-PMO) to enable parallel migration of multiple VNFs. The method follows a two-stage framework: in the first stage, improved heuristic algorithms are used to generate high-quality migration trajectories and construct a multi-scenario dataset; in the second stage, the Decision Mamba model is employed to train the policy network. With its selective modeling capability for structured sequences, Decision Mamba can capture the dependencies between VNFs and underlying resources. Combined with a twin-critic architecture and CQL regularization, the model effectively mitigates distribution shift and Q-value overestimation. The simulation results show that RL-PMO maintains approximately a 95% migration success rate across different load conditions and improves performance by about 13% under low and medium loads and up to 17% under high loads compared with typical offline RL algorithms such as IQL. Overall, RL-PMO provides an efficient, reliable, and resource-aware solution for SFC migration in node failure scenarios. Full article
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27 pages, 6957 KB  
Article
Research on AGV Path Optimization Based on an Improved A* and DWA Fusion Algorithm
by Kun Wang, Shuai Li, Mingyang Zhang and Jun Zhang
Forests 2026, 17(1), 31; https://doi.org/10.3390/f17010031 - 26 Dec 2025
Viewed by 297
Abstract
Forestry environments—such as logging sites, transport trails, and resource monitoring areas—are characterized by rugged terrain and irregularly distributed obstacles, which pose substantial challenges for AGV route planning. This poses challenges for route planning in automated guided vehicles (AGVs) and forestry machinery. To address [...] Read more.
Forestry environments—such as logging sites, transport trails, and resource monitoring areas—are characterized by rugged terrain and irregularly distributed obstacles, which pose substantial challenges for AGV route planning. This poses challenges for route planning in automated guided vehicles (AGVs) and forestry machinery. To address these challenges, this study proposes a hybrid path optimization method that integrates an improved A* algorithm with the Dynamic Window Approach (DWA). At the global planning level, the improved A* incorporates a dynamically weighted heuristic function, a steering-penalty term, and Floyd-based path smoothing to enhance path feasibility and continuity. In terms of local planning, the improved DWA algorithm employs adaptive weight adjustment, risk-perception factors, a sub-goal guidance mechanism, and a non-uniform and adaptive sampling strategy, thereby strengthening obstacle avoidance in dynamic environments. Simulation experiments on two-dimensional grid maps demonstrate that this method reduces path lengths by an average of 6.82%, 8.13%, and 21.78% for 20 × 20, 30 × 30, and 100 × 100 maps, respectively; planning time was reduced by an average of 21.02%, 16.65%, and 9.33%; total steering angle was reduced by an average of 100°, 487.5°, and 587.5°. These results indicate that the proposed hybrid algorithm offers practical technical guidance for intelligent forestry operations in complex natural environments, including timber harvesting, biomass transportation, and precision stand management. Full article
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17 pages, 854 KB  
Article
From Presence to Proximity in Online Higher Education: Students’ Lived and Desired Relationships
by Luísa Aires
Educ. Sci. 2026, 16(1), 28; https://doi.org/10.3390/educsci16010028 - 24 Dec 2025
Viewed by 256
Abstract
This article examines how students experience and build relational ties in online higher education. Using a hermeneutic phenomenological approach, it analyses students’ lived and desired relationships across four domains: the online campus, the degree programme, teachers, and peers. One hundred and forty-four students [...] Read more.
This article examines how students experience and build relational ties in online higher education. Using a hermeneutic phenomenological approach, it analyses students’ lived and desired relationships across four domains: the online campus, the degree programme, teachers, and peers. One hundred and forty-four students completed an open-ended questionnaire. Their narratives informed the Relational Proximity Matrix (RPM), a framework used to map connections and distinguish transformative, functional, and residual modes of proximity. Findings indicate strong affective and supportive ties among peers, whereas interactions with teachers and the online campus are often formal or instrumental. The study concludes that relational proximity, rather than access alone, depends critically on recognition, reciprocity, and pedagogical care. The RPM offers a heuristic orientation that may inform educational design and support educators and institutions in cultivating practices that enhance relational quality. Full article
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23 pages, 2376 KB  
Article
Nested Grover’s Algorithm for Tree Search
by Andreas Wichert
Entropy 2026, 28(1), 24; https://doi.org/10.3390/e28010024 - 24 Dec 2025
Viewed by 160
Abstract
We investigate optimizing quantum tree search algorithms by employing a nested Grover Algorithm. This approach seeks to enhance results compared to previous Grover-based methods by expanding the tree of partial assignments to a specific depth and conducting a quantum search within the subset [...] Read more.
We investigate optimizing quantum tree search algorithms by employing a nested Grover Algorithm. This approach seeks to enhance results compared to previous Grover-based methods by expanding the tree of partial assignments to a specific depth and conducting a quantum search within the subset of remaining assignments. The study explores the implications and constraints of this approach, providing a foundation for quantum artificial intelligence applications. Instead of utilizing conventional heuristic functions that are incompatible with quantum tree search, we introduce the partial candidate solution, which indicates a node at a specific depth of the tree. By employing such a function, we define the concatenated oracle, which enables us to decompose the quantum tree search using Grover’s algorithm. With a branching factor of 2 and a depth of m, the costs of Grover’s algorithm are O(2m/2). The concatenated oracle allows us to reduce the cost to O(m·2m/4) for m partial candidate solutions. Full article
(This article belongs to the Special Issue The Future of Quantum Machine Learning and Quantum AI, 2nd Edition)
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24 pages, 1794 KB  
Article
Symmetry-Based Convergence Theory for Particle Swarm Optimization: From Heuristic to Provably Convergent Optimization
by Kai Cui
Symmetry 2026, 18(1), 28; https://doi.org/10.3390/sym18010028 - 23 Dec 2025
Viewed by 189
Abstract
This study establishes a rigorous theoretical framework for Particle Swarm Optimization (PSO) convergence by introducing a novel symmetry assumption governing the algorithm’s stochastic components and a monotonicity condition between function values and Euclidean distance to the global optimum. Under this assumption, we prove [...] Read more.
This study establishes a rigorous theoretical framework for Particle Swarm Optimization (PSO) convergence by introducing a novel symmetry assumption governing the algorithm’s stochastic components and a monotonicity condition between function values and Euclidean distance to the global optimum. Under this assumption, we prove linear convergence in expectation and almost sure linear convergence for a modified PSO algorithm with symmetric zero-mean random coefficients when parameters satisfy the explicit condition w+8(c12+c22)σr21w<1. This provides the first closed-form relationship between inertia weight w, learning factors c1,c2, and random variance σr2 that guarantees convergence. Building on this theoretical foundation, we develop three hierarchical applications: (1) static parameter design that replaces empirical tuning with theoretical calculation from desired convergence rates; (2) symmetric random factor optimization that eliminates directional bias and stabilizes velocity dynamics while preserving exploration variance; and (3) dynamic adaptive strategies that adjust parameters in real-time based on particle dispersion feedback. By bridging the gap between empirical performance and theoretical guarantees, this work transforms PSO from an empirically driven heuristic into a provably convergent optimization tool with rigorous performance guarantees for objective functions satisfying strict monotonicity between fitness and distance to the optimum (e.g., strictly convex functions). Full article
(This article belongs to the Section Mathematics)
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19 pages, 3993 KB  
Article
Coordinated Planning Method for Distribution Network Lines Considering Geographical Constraints and Load Distribution
by Linhuan Luo, Qilin Zhou, Wei Pan, Zhian He, Minghao Liu, Longfa Yang and Xiangang Peng
Processes 2026, 14(1), 47; https://doi.org/10.3390/pr14010047 - 22 Dec 2025
Viewed by 293
Abstract
This paper proposes a coordinated planning method for distribution network lines considering geographical constraints and load distribution, aiming to improve the economy and engineering feasibility of distribution network planning. First, a hierarchical system of geographical constraints based on the Interval Analytic Hierarchy Process [...] Read more.
This paper proposes a coordinated planning method for distribution network lines considering geographical constraints and load distribution, aiming to improve the economy and engineering feasibility of distribution network planning. First, a hierarchical system of geographical constraints based on the Interval Analytic Hierarchy Process (IAHP) is established to systematically quantify the influence weights of spatial factors such as terrain undulation, ecological protection zones, and construction obstacles. Second, the density peak clustering algorithm and load complementarity coefficient are introduced to generate equivalent load nodes, and a spatially continuous load density grid model is constructed to accurately characterize the distribution and complementary characteristics of the load. Third, an improved A-star algorithm is adopted, which integrates a heuristic function guided by geographical weights and load density to dynamically avoid high-cost areas and approach high-load areas. Additionally, Bézier curves are used to optimize the path, reducing crossings and obstacle interference, thus enhancing the implementability of line layout. Verification via a real distribution network case study in a certain area of Guangdong Province shows that the proposed method outperforms traditional planning strategies. It significantly improves the economy, safety, and engineering feasibility of the path, providing effective decision support for distribution network line planning in complex environments. Full article
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27 pages, 14794 KB  
Article
Terrain-Informed UAV Path Planning for Mountain Search: A Slope-Based Probabilistic Approach
by Xi Wang, Xing Wang, Pengliang Zhao, Weihua Tan, Hongqiang Zhang, Lihuang Chen and Longhua Zhou
Sensors 2026, 26(1), 62; https://doi.org/10.3390/s26010062 - 21 Dec 2025
Viewed by 355
Abstract
To enhance the efficiency of locating dynamic missing persons in complex mountain terrain, this study introduces an innovative Slope Probability Search (SPS) algorithm based on a modified A* framework. The algorithm’s core is a dynamic global probability map, constructed by linking terrain slope [...] Read more.
To enhance the efficiency of locating dynamic missing persons in complex mountain terrain, this study introduces an innovative Slope Probability Search (SPS) algorithm based on a modified A* framework. The algorithm’s core is a dynamic global probability map, constructed by linking terrain slope to the behavioral tendencies of missing persons. This fundamentally shifts the unmanned aerial vehicle (UAV) search paradigm from conventional coverage patterns to intelligent, guided exploration. To ensure a realistic evaluation, we designed three representative dynamic models for the missing persons: Terrain Constrained, Path Following, and Random Walk. The SPS algorithm, through its unique heuristic function, achieves an optimal balance between exploiting high probability areas and exploring new regions to maximize search efficiency. Simulation experiments using real-world geographic data demonstrated that even under severe constraints of limited search duration and sensor range, the algorithm achieved a success rate of 88.9% achieving an average search time substantially lower than that of conventional methods. This research provides a solid theoretical basis and a practical algorithmic framework for developing next generation intelligent search and rescue systems. Full article
(This article belongs to the Section Vehicular Sensing)
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