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Keywords = three-dimensional hybrid wireless sensor networks

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40 pages, 32270 KB  
Article
Teaching–Learning–Studying-Based Optimization with Dance Learning Strategies for Global Optimization Problems and Real-World Applications
by Keyu Shi, Wenchen Sun and Jianfeng Wang
Symmetry 2026, 18(5), 837; https://doi.org/10.3390/sym18050837 - 13 May 2026
Viewed by 204
Abstract
This paper addresses two key challenges: low solution accuracy and premature convergence in high-dimensional optimization problems, as well as the difficulty of jointly optimizing coverage, redundancy, and movement cost in wireless sensor network (WSN) deployment. To solve these issues, an improved Teaching–Learning–Studying-Based Optimization [...] Read more.
This paper addresses two key challenges: low solution accuracy and premature convergence in high-dimensional optimization problems, as well as the difficulty of jointly optimizing coverage, redundancy, and movement cost in wireless sensor network (WSN) deployment. To solve these issues, an improved Teaching–Learning–Studying-Based Optimization algorithm, named TLSBO-DLS, is proposed. Within the original TLSBO framework, three enhancement strategies are incorporated: (1) a dimension-adaptive update probability mechanism to improve fine-grained search capability; (2) a dance learning strategy that enhances dynamic exploration through oscillatory cooperative learning; and (3) an elite adaptive perturbation mechanism based on a Cauchy–Gaussian hybrid distribution to improve convergence accuracy and help escape local optima. Empirical evaluations conducted on the CEC2017, CEC2020, and CEC2022 benchmark datasets indicate that TLSBO-DLS achieves superior performance compared to nine alternative algorithms, exhibiting higher solution precision and faster convergence behavior. Furthermore, its advantage is rigorously confirmed through statistical analyses using the Wilcoxon rank-sum test and the Friedman ranking test. Furthermore, a two-dimensional multi-objective WSN node deployment model is constructed, and TLSBO-DLS is applied to a practical scenario with 30 sensor nodes. The results show that the proposed algorithm achieves a coverage rate of 85.50%, a redundant coverage rate of only 5.15%, and an average node movement distance as low as 15.8471. In terms of global performance, the proposed method surpasses PSO, GWO, WOA, as well as several enhanced TLSBO variants, thereby demonstrating its strong capability and practical value when addressing high-dimensional challenging optimization tasks and real-world engineering problems. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
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58 pages, 87068 KB  
Article
Enhanced Enterprise Development Optimization Algorithm with Business Management Strategies for Global Optimization and Real-World Engineering Applications
by Xiao Lin and Yu Fang
Symmetry 2026, 18(5), 786; https://doi.org/10.3390/sym18050786 - 3 May 2026
Viewed by 309
Abstract
Wireless sensor network (WSN) coverage optimization is a challenging high-dimensional and nonlinear problem that directly affects network performance, including sensing quality, energy efficiency, and system reliability. Although metaheuristic algorithms have been widely applied to this problem, many existing methods still suffer from premature [...] Read more.
Wireless sensor network (WSN) coverage optimization is a challenging high-dimensional and nonlinear problem that directly affects network performance, including sensing quality, energy efficiency, and system reliability. Although metaheuristic algorithms have been widely applied to this problem, many existing methods still suffer from premature convergence, insufficient population diversity, and an imbalance between exploration and exploitation. To address these issues, this paper proposes a multi-strategy enhanced enterprise development optimization algorithm (MEEDOA) inspired by business management mechanisms. The proposed method integrates a hybrid population initialization strategy, an adaptive activity switching mechanism based on performance feedback, a multi-elite collaborative learning strategy, and a Lévy flight-based stagnation escape mechanism. These strategies are tightly coupled within a unified adaptive framework to improve global search capability, convergence speed, and robustness. Furthermore, a mathematical model for WSN deployment is constructed based on a binary sensing model and discrete coverage evaluation. From the perspective of symmetry, the sensing regions of sensor nodes exhibit significant geometric symmetry in both two-dimensional and three-dimensional deployment spaces. In the two-dimensional case, the sensing and communication regions are modeled as concentric circular structures, while in the three-dimensional case, the sensing regions are represented by isotropic spheres with symmetric spatial distributions. Such symmetry properties provide an effective basis for describing coverage behavior, reducing redundant overlap, and improving the uniformity of node deployment. Meanwhile, the proposed MEEDOA preserves population diversity and enhances search balance, enabling the algorithm to better capture symmetric coverage patterns and more effectively explore complex spatial deployment configurations. Extensive experiments on CEC2014, CEC2017, CEC2020, and CEC2022 benchmark functions demonstrate that MEEDOA achieves superior convergence accuracy, faster convergence speed, and stronger robustness compared with several state-of-the-art algorithms. Additional simulation results in WSN deployment applications verify its effectiveness in improving coverage performance under both symmetric and irregular spatial deployment scenarios. The results indicate that the proposed MEEDOA provides a reliable and efficient solution for complex global optimization problems and practical engineering applications. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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34 pages, 22620 KB  
Article
Improved Secretary Bird Optimization Algorithm Based on Financial Investment Strategy for Global Optimization and Real Application Problems
by Yiming Liu, Bingchun Yuan and Shuqi Yuan
Symmetry 2026, 18(4), 688; https://doi.org/10.3390/sym18040688 - 21 Apr 2026
Cited by 1 | Viewed by 430
Abstract
This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation [...] Read more.
This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation through the synergistic integration of multiple enhancement strategies, including a hybrid initialization scheme combining Latin hypercube sampling and quasi-opposition-based learning, a success-history-based adaptive parameter learning mechanism, a finance-inspired market-state trading operator, and an elite-guided population regulation strategy. Experimental results on the IEEE CEC2020 and CEC2022 benchmark test suites demonstrate that MS-SBOA significantly outperforms nine comparative algorithms, including VPPSO, IAGWO, and QHSBOA, under both 10-dimensional and 20-dimensional settings. The proposed algorithm exhibits superior optimization accuracy, faster convergence speed, and stronger robustness. Statistical analyses using the Wilcoxon rank-sum test and the Friedman mean rank test further confirm that the observed performance improvements are statistically significant. Moreover, MS-SBOA is applied to three-dimensional wireless sensor network (3D WSN) deployment optimization problems, where the average coverage rates reach 76.22% and 82.32% for 30-node and 50-node deployment scenarios, respectively. The resulting node distributions are more uniform, and the computational efficiency is improved compared with competing algorithms. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
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39 pages, 11265 KB  
Article
A Multi-Strategy Hybrid-Enhanced Educational Competition Optimizer for Global Optimization and Real-World Engineering Applications
by Min Sun, Shicen Zhang and Wenjun Jiang
Symmetry 2026, 18(4), 602; https://doi.org/10.3390/sym18040602 - 1 Apr 2026
Cited by 2 | Viewed by 598
Abstract
This paper proposes a multi-strategy hybrid-enhanced Educational Competition Optimizer (MEECO) to improve the performance of swarm-based optimization algorithms in complex search environments. From the perspective of symmetry, population-based optimization algorithms inherently rely on the symmetric distribution and evolution of individuals in the search [...] Read more.
This paper proposes a multi-strategy hybrid-enhanced Educational Competition Optimizer (MEECO) to improve the performance of swarm-based optimization algorithms in complex search environments. From the perspective of symmetry, population-based optimization algorithms inherently rely on the symmetric distribution and evolution of individuals in the search space, while the imbalance between exploration and exploitation often leads to symmetry breaking, resulting in premature convergence and loss of diversity. Unlike the standard ECO, which suffers from limited information exchange, premature convergence, and boundary stagnation, the proposed method integrates three complementary mechanisms: adaptive differential evolution, vertical crossover, and global-best-guided boundary handling. Specifically, the adaptive differential evolution strategy enhances global exploration and maintains population distribution symmetry through dynamic mutation, the vertical crossover mechanism improves inter-dimensional symmetry and information interaction, and the boundary-handling strategy restores symmetry by guiding infeasible solutions back to promising regions. These strategies jointly improve population diversity, exploration–exploitation balance, and convergence efficiency while preserving structural symmetry in the search process. Extensive experiments on CEC2017 and CEC2022 benchmark suites demonstrate that MEECO consistently achieves superior optimization accuracy, faster convergence speed, and stronger robustness compared with several state-of-the-art algorithms. Statistical analyses further confirm the significance and reliability of the improvements. In addition, the proposed method is applied to a wireless sensor network node deployment problem, where it significantly improves coverage rate and deployment uniformity. The results indicate that MEECO provides an effective, robust, and symmetry-preserving optimization framework for both benchmark problems and real-world engineering applications. Full article
(This article belongs to the Special Issue Symmetry in Optimization: From Algorithmic Design to Applications)
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32 pages, 9386 KB  
Article
Hybrid Manta Ray Foraging Algorithm with Cuckoo Search for Global Optimization and Three-Dimensional Wireless Sensor Network Deployment Problem
by Meiyan Wang, Qifang Luo, Yuanfei Wei and Yongquan Zhou
Biomimetics 2023, 8(5), 411; https://doi.org/10.3390/biomimetics8050411 - 5 Sep 2023
Cited by 6 | Viewed by 2423
Abstract
In this paper, a new hybrid Manta Ray Foraging Optimization (MRFO) with Cuckoo Search (CS) algorithm (AMRFOCS) is proposed. Firstly, quantum bit Bloch spherical coordinate coding is used for the initialization of the population, which improves the diversity of the expansion of the [...] Read more.
In this paper, a new hybrid Manta Ray Foraging Optimization (MRFO) with Cuckoo Search (CS) algorithm (AMRFOCS) is proposed. Firstly, quantum bit Bloch spherical coordinate coding is used for the initialization of the population, which improves the diversity of the expansion of the traversal ability of the search space. Secondly, the dynamic disturbance factor is introduced to balance the exploratory and exploitative search ability of the algorithm. Finally, the unique nesting strategy of the cuckoo and Levy flight is introduced to enhance the search ability. AMRFOCS is tested on CEC2017 and CEC2020 benchmark functions, which is also compared and tested by using different dimensions and other state-of-the-art metaheuristic algorithms. Experimental results reveal that the AMRFOCS algorithm has a superior convergence rate and optimization precision. At the same time, the nonparametric Wilcoxon signed-rank test and Friedman test show that the AMRFOCS has good stability and superiority. In addition, the proposed AMRFOCS is applied to the three-dimensional WSN coverage problem. Compared with the other four 3D deployment methods optimized by metaheuristic algorithms, the AMRFOCS effectively reduces the redundancy of sensor nodes, possesses a faster convergence speed and higher coverage and then provides a more effective and practical deployment scheme. Full article
(This article belongs to the Special Issue Biomimicry for Optimization, Control, and Automation)
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27 pages, 14047 KB  
Article
DHD-MEPO: A Novel Distributed Coverage Hole Detection and Repair Method for Three-Dimensional Hybrid Wireless Sensor Networks
by Pingzhang Gou, Miao Guo, Baoyong Guo and Shun Mao
Electronics 2023, 12(11), 2445; https://doi.org/10.3390/electronics12112445 - 28 May 2023
Cited by 7 | Viewed by 2910
Abstract
A coverage hole is a problem that cannot be completely avoided in three-dimensional hybrid wireless sensor networks. It can lead to hindrances in monitoring tasks and adversely affect network performance. To address the problem of coverage holes caused by the uneven initial deployment [...] Read more.
A coverage hole is a problem that cannot be completely avoided in three-dimensional hybrid wireless sensor networks. It can lead to hindrances in monitoring tasks and adversely affect network performance. To address the problem of coverage holes caused by the uneven initial deployment of the network and node damage during operation, we propose a distributed hole detection and multi-objective optimization emperor penguin repair algorithm (DHD-MEPO). In the detection phase, the monitoring region is zoned as units according to the quantity of nodes and the sensing range, and static nodes use the sum-of-weights method to campaign for group nodes on their terms, determining the location of holes by calculating the coverage of each cell. In the repair phase, the set of repair nodes is determined by calculating the mobile node coverage redundancy. Based on the characteristics of complex environments, the regions of high hole levels are prioritized. Moreover, the residual energy homogeneity of nodes is considered for the design of multi-objective functions. A lens-imaging mapping learning strategy is introduced to perturb the location of repair nodes for the optimization of the emperor penguin algorithm. Experimental results illustrate that the DHD-MEPO, compared with the C-CICHH, 3D-VPCA, RA, EMSCOLER, and IERP algorithms, can balance the uniformity of the residual energy of each node while satisfying the network coverage requirements and network connectivity, which effectively improves the network coverage performance. Full article
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21 pages, 3485 KB  
Article
Position-Monitoring-Based Hybrid Routing Protocol for 3D UAV-Based Networks
by Saif Ullah, Khalid Hussain Mohammadani, Muhammad Asghar Khan, Zhi Ren, Reem Alkanhel, Ammar Muthanna and Usman Tariq
Drones 2022, 6(11), 327; https://doi.org/10.3390/drones6110327 - 28 Oct 2022
Cited by 19 | Viewed by 4198
Abstract
Unmanned aerial vehicles (UAV) have emerged as prime technologies due to their compatible size and flexible architecture. UAV technology offers services in vast application such as inter-UAV communication, wireless sensors, and the future Internet of Things (IoT) due to its compatible architecture. A [...] Read more.
Unmanned aerial vehicles (UAV) have emerged as prime technologies due to their compatible size and flexible architecture. UAV technology offers services in vast application such as inter-UAV communication, wireless sensors, and the future Internet of Things (IoT) due to its compatible architecture. A UAV’s speed varies while roaming, which may increase the risk of a connection failure. Various routing schemes have provided solutions to address this essential issue for three-dimensional (3D) UAV-based networks. The main category of UAV routing schemes is position-based routing schemes, which choose the best route based on the UAV’s location. However, position-based routing has the drawback that it depends on exact positioning and tracking. An efficient routing scheme can resolve the significant issue associated with UAV mobility in a 3D environment. This paper aims to address the issues of static preloaded location values by presenting a hybrid routing scheme named the Position-Monitor-based Hybrid Routing Protocol (PMHRP), which takes advantage of both geographic and topology-based routing protocols. The PMHRP establishes the shortest possible route based on a UAV’s Global Positioning System (GPS). Moreover, the proposed protocol utilizes the links for data forwarding. Furthermore, a disaster-based UAV scenario is adopted to provide connections to IoT devices. A detailed comparison analysis shows the proposed scheme’s extreme performance and results in up to 65% to 73% better packet delivery ratio (PDR) than batch mark schemes under standard 3D UAV scenarios. Compared to earlier work, the proposed scheme reduces the average delay by up to 68% to 75%. Further proposed routing schemes offer 70% to 72% more throughput than the existing routing schemes, and NRL (%) is 42% to 49% lower than the existing routing schemes. This happens because of the global routing information available at each UAV which is provided by the position head coordinator (PHC) UAV in the proposed work. Full article
(This article belongs to the Section Drone Communications)
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23 pages, 3705 KB  
Article
Hybrid Path Planning for Efficient Data Collection in UAV-Aided WSNs for Emergency Applications
by Sabitri Poudel and Sangman Moh
Sensors 2021, 21(8), 2839; https://doi.org/10.3390/s21082839 - 17 Apr 2021
Cited by 50 | Viewed by 5037
Abstract
In unmanned aerial vehicle (UAV)-aided wireless sensor networks (UWSNs), a UAV is employed as a mobile sink to gather data from sensor nodes. Incorporating UAV helps prolong the network lifetime and avoid the energy-hole problem faced by sensor networks. In emergency applications, timely [...] Read more.
In unmanned aerial vehicle (UAV)-aided wireless sensor networks (UWSNs), a UAV is employed as a mobile sink to gather data from sensor nodes. Incorporating UAV helps prolong the network lifetime and avoid the energy-hole problem faced by sensor networks. In emergency applications, timely data collection from sensor nodes and transferal of the data to the base station (BS) is a prime requisite. The timely and safe path of UAV is one of the fundamental premises for effective UWSN operations. It is essential and challenging to identify a suitable path in an environment comprising various obstacles and to ensure that the path can efficiently reach the target point. This paper proposes a hybrid path planning (HPP) algorithm for efficient data collection by assuring the shortest collision-free path for UAV in emergency environments. In the proposed HPP scheme, the probabilistic roadmap (PRM) algorithm is used to design the shortest trajectory map and the optimized artificial bee colony (ABC) algorithm to improve different path constraints in a three-dimensional environment. Our simulation results show that the proposed HPP outperforms the PRM and conventional ABC schemes significantly in terms of flight time, energy consumption, convergence time, and flight path. Full article
(This article belongs to the Section Sensor Networks)
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12 pages, 1576 KB  
Communication
An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks
by Marcelo Salgueiro Costa, Slavisa Tomic and Marko Beko
Sensors 2021, 21(5), 1731; https://doi.org/10.3390/s21051731 - 3 Mar 2021
Cited by 11 | Viewed by 2991
Abstract
This work addresses the problem of target localization in three-dimensional wireless sensor networks (WSNs). The proposed algorithm is based on a hybrid system that employs angle of arrival (AOA) and received signal strength (RSS) measurements, where the target’s transmit power is considered as [...] Read more.
This work addresses the problem of target localization in three-dimensional wireless sensor networks (WSNs). The proposed algorithm is based on a hybrid system that employs angle of arrival (AOA) and received signal strength (RSS) measurements, where the target’s transmit power is considered as an unknown parameter. Although both cases of a known and unknown target’s transmit power have been addressed in the literature, most of the existing approaches for unknown transmit power are either carried out recursively, or require a high computational cost. This results in an increased execution time of these algorithms, which we avoid in this work by proposing a single-iteration solution with moderate computational complexity. By exploiting the measurement models, a non-convex least squares (LS) estimator is derived first. Then, to tackle its nonconvexity, we resort to second-order cone programming (SOCP) relaxation techniques to transform the non-convex estimator into a convex one. Additionally, to make the estimator tighter, we exploit the angle between two vectors by using the definition of their inner product, which arises naturally from the derivation steps that are taken. The proposed method not only matches the performance of a computationally more complex state-of-the-art method, but it outperforms it for small N. This result is of a significant value in practice, since one desires to localize the target using the least number of anchor nodes as possible due to network costs. Full article
(This article belongs to the Special Issue Sensor Network Signal Processing)
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16 pages, 1069 KB  
Article
An Efficient Hybrid RSS-AoA Localization for 3D Wireless Sensor Networks
by Thu L. N. Nguyen, Tuan D. Vy and Yoan Shin
Sensors 2019, 19(9), 2121; https://doi.org/10.3390/s19092121 - 7 May 2019
Cited by 34 | Viewed by 4040
Abstract
Wireless sensor networks (WSNs) enable many applications such as intelligent control, prediction, tracking, and other communication network services, which are integrated into many technologies of the Internet-of-Things. The conventional localization frameworks may not function well in practical environments since they were designed either [...] Read more.
Wireless sensor networks (WSNs) enable many applications such as intelligent control, prediction, tracking, and other communication network services, which are integrated into many technologies of the Internet-of-Things. The conventional localization frameworks may not function well in practical environments since they were designed either for two-dimensional space only, or have high computational costs, or are sensitive to measurement errors. In order to build an accurate and efficient localization scheme, we consider in this paper a hybrid received signal strength and angle-of-arrival localization in three-dimensional WSNs, where sensors are randomly deployed with the transmit power and the path loss exponent unknown. Moreover, in order to avoid the difficulty of solving the conventional maximum-likelihood estimator due to its non-convex and highly complex natures, we derive a weighted least squares estimate to estimate jointly the location of the unknown node and the two aforementioned channel components through some suitable approximations. Simulation results confirm the effectiveness of the proposed method. Full article
(This article belongs to the Section Sensor Networks)
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