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Search Results (521)

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Keywords = global optimal path planning

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41 pages, 22538 KB  
Article
IALA: An Improved Artificial Lemming Algorithm for Unmanned Aerial Vehicle Path Planning
by Xiaojun Zheng, Rundong Liu, Shiming Huang and Zhicong Duan
Technologies 2026, 14(2), 91; https://doi.org/10.3390/technologies14020091 (registering DOI) - 1 Feb 2026
Abstract
With the increasing application of unmanned aerial vehicle (UAV) in multiple fields, the path planning problem has become a key challenge in the optimization domain. This paper proposes an Improved Artificial Lemming Algorithm (IALA), which incorporates three strategies: the optimal information retention strategy [...] Read more.
With the increasing application of unmanned aerial vehicle (UAV) in multiple fields, the path planning problem has become a key challenge in the optimization domain. This paper proposes an Improved Artificial Lemming Algorithm (IALA), which incorporates three strategies: the optimal information retention strategy based on individual historical memory, the hybrid search strategy based on differential evolution operators, and the local refined search strategy based on directed neighborhood perturbation. These strategies are designed to enhance the algorithm’s global exploration and local exploitation capabilities in tackling complex optimization problems. Subsequently, comparative experiments are conducted on the CEC2017 benchmark suite across three dimensions (30D, 50D, and 100D) against eight state-of-the-art algorithms proposed in recent years, including SBOA and DBO. The results demonstrate that IALA achieves superior performance across multiple metrics, ranking first in both the Wilcoxon rank-sum test and the Friedman ranking test. Analyses of convergence curves and data distributions further verify its excellent optimization performance and robustness. Finally, IALA and the comparative algorithms are applied to eight 3D UAV path planning scenarios and two amphibious UAV path planning models. In the independent repeated experiments across the eight scenarios, IALA attains the optimal performance 13 times in terms of the two metrics, Mean and Std. It also ranks first in the Monte Carlo experiments for the two amphibious UAV path planning models. Full article
(This article belongs to the Section Information and Communication Technologies)
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32 pages, 27015 KB  
Article
ESDBO: A Multi-Strategy Enhanced Dung Beetle Optimization Algorithm for Urban Path Planning of UGV
by Chenhui Wei, Zhifang Wei, Yanlan Li, Jie Cui and Yanfei Su
Sensors 2026, 26(3), 930; https://doi.org/10.3390/s26030930 (registering DOI) - 1 Feb 2026
Abstract
In the complex urban path planning of unmanned ground vehicles (UGVs), the dung beetle optimization (DBO) algorithm is widely used due to its simple structure and fast convergence speed. However, it still has the disadvantages of poor convergence accuracy and is easy to [...] Read more.
In the complex urban path planning of unmanned ground vehicles (UGVs), the dung beetle optimization (DBO) algorithm is widely used due to its simple structure and fast convergence speed. However, it still has the disadvantages of poor convergence accuracy and is easy to fall into a local optimum. To solve these problems, this paper proposes a multi-strategy enhanced DBO algorithm (ESDBO). Firstly, sine mapping is introduced in the population initialization stage to enhance solution diversity. Secondly, an adaptive information volatilization mutation strategy is proposed, which dynamically balances the convergence and global search ability. Finally, a multi-mechanism co-evolution strategy is designed, which significantly improves the local search ability and stability. Through ablation experiments and CEC2017 benchmark tests, the optimization ability of the proposed strategy and the convergence accuracy and stability of ESDBO are verified. Further path planning experiments are carried out on the public Random MAPF benchmark map. The results show that ESDBO can generate global optimal paths with short path length, few turns, and high safety margin on different obstacle densities and map scales. The algorithm provides an efficient and reliable solution for autonomous navigation in complex urban environments. Full article
(This article belongs to the Section Navigation and Positioning)
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35 pages, 8263 KB  
Article
Multi-Strategy Variable Secretary Bird Optimization Algorithm (MSVSBOA) for Global Optimization and UAV 3D Path Planning
by Amir Seyyedabbasi
Symmetry 2026, 18(2), 273; https://doi.org/10.3390/sym18020273 (registering DOI) - 31 Jan 2026
Abstract
In this study, an enhanced variant of the Secretary Bird Optimization Algorithm (SBOA), named MSVSBOA, is proposed to address the limitations of the SBOA in global optimization and UAV 3D path-planning. The proposed MSVSBOA integrates three complementary strategies to achieve a balanced exploration [...] Read more.
In this study, an enhanced variant of the Secretary Bird Optimization Algorithm (SBOA), named MSVSBOA, is proposed to address the limitations of the SBOA in global optimization and UAV 3D path-planning. The proposed MSVSBOA integrates three complementary strategies to achieve a balanced exploration and exploitation trade-off. First, a Levy-based Directed Exploration mechanism is introduced to enrich the global search capability and prevent premature convergence. Second, a spiral movement mechanism is incorporated to strengthen the local exploitation behavior and improve convergence accuracy. Third, a Differential Evolution-inspired refinement strategy (DE-Refinement) is employed to accelerate fine-grained exploitation during the later stages of optimization. The performance of the MSVSBOA is extensively evaluated on the CEC 2014 and CEC 2022 benchmark suites. Experimental results demonstrate that the MSVSBOA achieves superior accuracy, faster convergence, and improved robustness compared to the SBOA and other multi-strategy variants. Furthermore, the MSVSBOA is applied to a challenging UAV 3D path planning problem, where it successfully generates safe, smooth, and collision-free trajectories while outperforming competing algorithms. These findings confirm the effectiveness of the proposed MSVSBOA for both global optimization problems and real-world UAV applications. Full article
23 pages, 3009 KB  
Article
Simultaneous Incremental Map-Prediction-Driven UAV Trajectory Planning for Unknown Environment Exploration
by Jianing Tang, Guoran Jiang, Jingkai Yang and Sida Zhou
Aerospace 2026, 13(2), 139; https://doi.org/10.3390/aerospace13020139 - 30 Jan 2026
Abstract
Efficient autonomous exploration in unknown environments is a core challenge for Unmanned Aerial Vehicle (UAV) applications in unstructured settings. The primary challenges are exploration speed, coverage efficiency, and the autonomous, efficient, and obstacle-/threat-avoiding global guidance of UAV under local observational information. This paper [...] Read more.
Efficient autonomous exploration in unknown environments is a core challenge for Unmanned Aerial Vehicle (UAV) applications in unstructured settings. The primary challenges are exploration speed, coverage efficiency, and the autonomous, efficient, and obstacle-/threat-avoiding global guidance of UAV under local observational information. This paper proposes an autonomous exploration method driven by simultaneous incremental map prediction and the fusion of global frontier information to enhance the exploration efficiency of UAVs in unknown unstructured environments. Based on generative deep learning, we introduce an incremental map prediction method for 3D unstructured mountainous terrain, enabling the simultaneous acquisition of map predictions and their uncertainty estimates. Map prediction and trajectory planning are conducted concurrently: by utilizing the simultaneously predicted 3D map and its confidence (i.e., the uncertainty estimates), an overlap analysis is conducted between the flyable areas in the predicted map and the high-confidence regions. Dynamic guidance subspaces are generated by extracting global frontier points, within which shortest-time optimization is adopted for trajectory planning to maximize information gain and coverage per step. Experimental results demonstrate that compared to classical methods, our proposed approach achieves significant performance improvements in key metrics, including map coverage rate, total exploration time, and average path length. Full article
(This article belongs to the Section Aeronautics)
28 pages, 1061 KB  
Article
Lexicographic A*: Hierarchical Distance and Turn Optimization for Mobile Robots
by Wei-Chang Yeh, Jiun-Yu Tu, Tsung-Yan Huang, Yi-Zhen Liao and Chia-Ling Huang
Electronics 2026, 15(3), 599; https://doi.org/10.3390/electronics15030599 - 29 Jan 2026
Viewed by 68
Abstract
Autonomous mobile robots require efficient path planning algorithms for navigation in grid-based environments. While the A* algorithm guarantees optimally short paths using admissible heuristics, it exhibits path degeneracy: multiple geometrically distinct paths often share identical length. Classical A* arbitrarily selects among these equal-cost [...] Read more.
Autonomous mobile robots require efficient path planning algorithms for navigation in grid-based environments. While the A* algorithm guarantees optimally short paths using admissible heuristics, it exhibits path degeneracy: multiple geometrically distinct paths often share identical length. Classical A* arbitrarily selects among these equal-cost candidates, frequently producing trajectories with excessive directional changes. Each turn induces deceleration–acceleration cycles that degrade energy efficiency and accelerate mechanical wear. To address this, we propose Turn-Minimizing A* (TM-A*), a lexicographic optimization approach that maintains distance optimality while minimizing cumulative heading changes. Unlike weighted-cost methods that require parameter calibration, TM-A* applies a dual-objective framework: distance takes strict priority, with turn count serving as a tie-breaker among equal-length paths. A key contribution of this work is the explicit guarantee that the generated path has the minimum number of turns among all shortest paths. By formulating path planning as a lexicographic optimization problem, TM-A* strictly prioritizes path length optimality and deterministically selects, among all equal-length candidates, the one with the fewest directional changes. Unlike classical A*, which arbitrarily resolves path degeneracy, TM-A* provably eliminates this ambiguity. As a result, the method ensures globally shortest paths with minimal turning, directly improving trajectory smoothness and operational efficiency. We prove that TM-A* preserves the O(|E|log|V|) time complexity of classical A*. Validation across 30 independent Monte Carlo trials at resolutions from 200 × 200 to 1000 × 1000 demonstrates that TM-A* reduces turn count by 39–43% relative to baseline A* (p < 0.001). Although the inclusion of orientation expands the search space four-fold, the computation time increases by only a factor of approximately 3 (»200%), indicating efficient scalability relative to problem complexity. With absolute latency remaining below 3300 ms for 1000 × 1000 grids, the approach is highly suitable for static global planning. Consequently, TM-A* provides a deterministic and scalable solution for generating smooth trajectories in industrial mobile robot applications. Full article
(This article belongs to the Special Issue Feature Papers in Networks: 2025–2026 Edition)
39 pages, 4819 KB  
Article
Adaptive Path Planning of UAV Based on A* Algorithm and Artificial Potential Field Method
by Jinchao Zhao, Ya Zhang, Luoyin Ning, Xuran Xiao, Chenrui Bai, Jianwu Zhang and Min Yang
Drones 2026, 10(2), 93; https://doi.org/10.3390/drones10020093 - 28 Jan 2026
Viewed by 97
Abstract
This paper presents an adaptive UAV path planning algorithm, A*-APF, which combines the A* algorithm with the artificial potential field method (APF) to overcome challenges such as lengthy paths, lack of smoothness, and local optima in traditional path planning algorithms within intricate environments. [...] Read more.
This paper presents an adaptive UAV path planning algorithm, A*-APF, which combines the A* algorithm with the artificial potential field method (APF) to overcome challenges such as lengthy paths, lack of smoothness, and local optima in traditional path planning algorithms within intricate environments. The A*-APF algorithm utilizes the global heuristic search abilities of A* and integrates a dynamic adaptive mechanism for gravitational and repulsive coefficients based on target distance, obstacle density, and path curvature. This mechanism enables real-time adjustments of potential field parameters, improving both global optimality and local path smoothness. Simulation results demonstrate that the A*-APF algorithm surpasses A*, RRT, PRM, and GWO algorithms in terms of path length, smoothness, computational efficiency, and stability. Specifically, it reduces the average path length by 15–25%, enhances smoothness by 30–45%, and decreases computation time by nearly 90%. Physical experiments confirm that the algorithm achieves the shortest path, optimal obstacle avoidance, and superior stability in real-world environments, highlighting its global optimization capability, real-time performance, and potential for engineering applications in complex dynamic environments. These results emphasize the algorithm’s ability to enhance UAV stability during task execution. Full article
(This article belongs to the Section Artificial Intelligence in Drones (AID))
23 pages, 7458 KB  
Article
A Safe Maritime Path Planning Fusion Algorithm for USVs Based on Reinforcement Learning A* and LSTM-Enhanced DWA
by Zhenxing Zhang, Qiujie Wang, Xiaohui Wang and Mingkun Feng
Sensors 2026, 26(3), 776; https://doi.org/10.3390/s26030776 - 23 Jan 2026
Viewed by 134
Abstract
In complex maritime environments, the safety of path planning for Unmanned Surface Vehicles (USVs) remains a significant challenge. Existing methods for handling dynamic obstacles often suffer from inadequate predictability and generate non-smooth trajectories. To address these issues, this paper proposes a reliable hybrid [...] Read more.
In complex maritime environments, the safety of path planning for Unmanned Surface Vehicles (USVs) remains a significant challenge. Existing methods for handling dynamic obstacles often suffer from inadequate predictability and generate non-smooth trajectories. To address these issues, this paper proposes a reliable hybrid path planning approach that integrates a reinforcement learning-enhanced A* algorithm with an improved Dynamic Window Approach (DWA). Specifically, the A* algorithm is augmented by incorporating a dynamic five-neighborhood search mechanism, a reinforcement learning-based adaptive weighting strategy, and a path post-optimization procedure. These enhancements collectively shorten the path length and significantly improve trajectory smoothness. While ensuring that the global path avoids dynamic obstacles smoothly, a Kalman Filter (KF) is integrated into the Long Short-Term Memory (LSTM) network to preprocess historical data. This mechanism suppresses transient outliers and stabilizes the trajectory prediction of dynamic obstacles. Moreover, the evaluation function of the DWA is refined by incorporating the International Regulations for Preventing Collisions at Sea (COLREGs) constraints, enabling compliant navigation behaviors. Simulation results in MATLAB demonstrate that the enhanced A* algorithm better conforms to the kinematic model of the USVs. The improved DWA significantly reduces collision risks, thereby ensuring safer navigation in dynamic marine environments. Full article
(This article belongs to the Section Navigation and Positioning)
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23 pages, 6893 KB  
Article
A New Hyperchaotic Map and Its Manifold of Conditional Symmetry
by Zhenxin Hu, Chunbiao Li, Xiaolong Qi, Ioannis P. Antoniades and Christos Volos
Symmetry 2026, 18(2), 212; https://doi.org/10.3390/sym18020212 - 23 Jan 2026
Viewed by 190
Abstract
In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the [...] Read more.
In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the construction of conditional symmetry by introducing an absolute value function. The corresponding evolution of the discrete sequences from the system is verified by the circuit implementation based on the microcontroller of CH32V307. The pseudorandom data from the map increases its adaptability for applications in information security. The hyperchaotic sequence-injected Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA) show their improved performance in the optimization algorithm. Robot path planning experiments confirm that all three algorithms exhibit superior convergence performance, global search capability, and path smoothness compared with the original algorithms. Full article
(This article belongs to the Section Engineering and Materials)
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25 pages, 4225 KB  
Article
Proactive Path Planning Using Centralized UAV-UGV Coordination in Semi-Structured Agricultural Environments
by Dimitris Katikaridis, Lefteris Benos, Dimitrios Kateris, Elpiniki Papageorgiou, George Karras, Ioannis Menexes, Remigio Berruto, Claus Grøn Sørensen and Dionysis Bochtis
Appl. Sci. 2026, 16(2), 1143; https://doi.org/10.3390/app16021143 - 22 Jan 2026
Viewed by 88
Abstract
Unmanned ground vehicles (UGVs) in agriculture face challenges in navigating complex environments due to the presence of dynamic obstacles. This causes several practical problems including mission delays, higher energy consumption, and potential safety risks. This study addresses the challenge by shifting path planning [...] Read more.
Unmanned ground vehicles (UGVs) in agriculture face challenges in navigating complex environments due to the presence of dynamic obstacles. This causes several practical problems including mission delays, higher energy consumption, and potential safety risks. This study addresses the challenge by shifting path planning from reactive local avoidance to proactive global optimization. To that end, it integrates aerial imagery from an unmanned aerial vehicle (UAV) to identify dynamic obstacles using a low-latency YOLOv8 detection pipeline. These are translated into georeferenced exclusion zones for the UGV. The UGV follows the optimized path while relying on a LiDAR-based reactive protocol to autonomously detect and respond to any missed obstacles. A farm management information system is used as the central coordinator. The system was tested in 30 real-field trials in a walnut orchard for two distinct scenarios with varying worker and vehicle loads. The system achieved high mission success, with the UGV completing all tasks safely, with four partial successes caused by worker detection failures under afternoon shadows. UAV energy consumption remained stable, while UGV energy and mission time increased during reactive maneuvers. Communication latency was low and consistent. This enabled timely execution of both proactive and reactive navigation protocols. In conclusion, the present UAV–UGV system ensured efficient and safe navigation, demonstrating practical applicability in real orchard conditions. Full article
(This article belongs to the Special Issue The Use of Evolutionary Algorithms in Robotics)
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36 pages, 13674 KB  
Article
A Reference-Point Guided Multi-Objective Crested Porcupine Optimizer for Global Optimization and UAV Path Planning
by Zelei Shi and Chengpeng Li
Mathematics 2026, 14(2), 380; https://doi.org/10.3390/math14020380 - 22 Jan 2026
Viewed by 53
Abstract
Balancing convergence accuracy and population diversity remains a fundamental challenge in multi-objective optimization, particularly for complex and constrained engineering problems. To address this issue, this paper proposes a novel Multi-Objective Crested Porcupine Optimizer (MOCPO), inspired by the hierarchical defensive behaviors of crested porcupines. [...] Read more.
Balancing convergence accuracy and population diversity remains a fundamental challenge in multi-objective optimization, particularly for complex and constrained engineering problems. To address this issue, this paper proposes a novel Multi-Objective Crested Porcupine Optimizer (MOCPO), inspired by the hierarchical defensive behaviors of crested porcupines. The proposed algorithm integrates four biologically motivated defense strategies—vision, hearing, scent diffusion, and physical attack—into a unified optimization framework, where global exploration and local exploitation are dynamically coordinated. To effectively extend the original optimizer to multi-objective scenarios, MOCPO incorporates a reference-point guided external archiving mechanism to preserve a well-distributed set of non-dominated solutions, along with an environmental selection strategy that adaptively partitions the objective space and enhances solution quality. Furthermore, a multi-level leadership mechanism based on Euclidean distance is introduced to provide region-specific guidance, enabling precise and uniform coverage of the Pareto front. The performance of MOCPO is comprehensively evaluated on 18 benchmark problems from the WFG and CF test suites. Experimental results demonstrate that MOCPO consistently outperforms several state-of-the-art multi-objective algorithms, including MOPSO and NSGA-III, in terms of IGD, GD, HV, and Spread metrics, achieving the best overall ranking in Friedman statistical tests. Notably, the proposed algorithm exhibits strong robustness on discontinuous, multimodal, and constrained Pareto fronts. In addition, MOCPO is applied to UAV path planning in four complex terrain scenarios constructed from real digital elevation data. The results show that MOCPO generates shorter, smoother, and more stable flight paths while effectively balancing route length, threat avoidance, flight altitude, and trajectory smoothness. These findings confirm the effectiveness, robustness, and practical applicability of MOCPO for solving complex real-world multi-objective optimization problems. Full article
(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)
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17 pages, 1467 KB  
Article
Generalized Voronoi Diagram-Guided and Contact-Optimized Motion Planning for Snake Robots
by Mhd Ali Shehadeh and Milos Seda
Mathematics 2026, 14(2), 332; https://doi.org/10.3390/math14020332 - 19 Jan 2026
Viewed by 188
Abstract
In robot motion planning in a space with obstacles, the goal is to find a collision-free path for robots from the start to the target position. Numerous fundamentally different approaches, and their many variants, address this problem depending on the types of obstacles, [...] Read more.
In robot motion planning in a space with obstacles, the goal is to find a collision-free path for robots from the start to the target position. Numerous fundamentally different approaches, and their many variants, address this problem depending on the types of obstacles, the dimensionality of the space and the restrictions on robot movements. We present a hierarchical motion planning framework for snake-like robots navigating cluttered environments. At the global level, a bounded Generalized Voronoi Diagram (GVD) generates a maximal-clearance path through complex terrain. To overcome the limitations of pure avoidance strategies, we incorporate a local trajectory optimization layer that enables Obstacle-Aided Locomotion (OAL). This is realized through a simulation-in-the-loop system in CoppeliaSim, where gait parameters are optimized using Particle Swarm Optimization (PSO) based on contact forces and energy efficiency. By coupling high-level deliberative planning with low-level contact-aware control, our approach enhances both adaptability and locomotion efficiency. Experimental results demonstrate improved motion performance compared to conventional planners that neglect environmental contact. Full article
(This article belongs to the Special Issue Computational Geometry: Theory, Algorithms and Applications)
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23 pages, 11346 KB  
Article
Improved Multi-Objective Crested Porcupine Optimizer for UAV Forest Fire Cruising Strategy
by Yiqing Xu, Dejie Huang, Long Zhang and Fuquan Zhang
Fire 2026, 9(1), 40; https://doi.org/10.3390/fire9010040 - 16 Jan 2026
Viewed by 264
Abstract
When forest fires occur, timely detection and initial attack are critical for fire prevention. This study focuses on optimizing the cruise path of Unmanned Aerial Vehicles (UAVs) from the perspective of initial attack. It aims to maximize coverage of regions where initial attack [...] Read more.
When forest fires occur, timely detection and initial attack are critical for fire prevention. This study focuses on optimizing the cruise path of Unmanned Aerial Vehicles (UAVs) from the perspective of initial attack. It aims to maximize coverage of regions where initial attack success rates are low, shorten the time taken to detect fires, and, in turn, boost detection effectiveness and the initial attack success. In this paper, a path planning strategy, Improved Multi-Objective Crested Porcupine Optimizer (IMOCPO), is proposed. This strategy employs a weighted sum approach to formulate a composite objective function that balances global search and local optimization capabilities, considering practical requirements such as UAV endurance and uneven distribution of risk areas, thus enhancing adaptability in complex forest environments. The weight selection is justified through systematic grid search and validated by sensitivity analysis. The proposed strategy was compared and evaluated with a related strategy using four metrics: high-risk coverage rate, grid coverage rate, Average Distance Risk (ADR), and Average Grid Risk (AGR). Results show that the proposed path planning strategy performs better in these metrics. This study provides an effective solution for optimizing UAV cruise strategies in forest fire monitoring and has practical significance for improving the intelligence of forest fire prevention. Full article
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43 pages, 32899 KB  
Article
MEPEOA: A Multi-Strategy Enhanced Preschool Education Optimization Algorithm for Real-World Problems
by Shuping Ni, Chaofang Zhong, Yi Zhu and Meng Wang
Symmetry 2026, 18(1), 154; https://doi.org/10.3390/sym18010154 - 14 Jan 2026
Viewed by 123
Abstract
To address the limitations of the original Preschool Education Optimization Algorithm (PEOA) in population diversity preservation and late-stage convergence accuracy, this paper proposes a Multi-strategy Enhanced Preschool Education Optimization Algorithm (MEPEOA). The proposed algorithm integrates an improved population initialization strategy, a multi-strategy collaborative [...] Read more.
To address the limitations of the original Preschool Education Optimization Algorithm (PEOA) in population diversity preservation and late-stage convergence accuracy, this paper proposes a Multi-strategy Enhanced Preschool Education Optimization Algorithm (MEPEOA). The proposed algorithm integrates an improved population initialization strategy, a multi-strategy collaborative search mechanism, adaptive regulation, and boundary control to achieve a more effective balance between global exploration and local exploitation. The performance of MEPEOA is comprehensively evaluated on IEEE CEC2017 and CEC2022 benchmark suites and compared with several state-of-the-art metaheuristic algorithms, including EWOA, MPSO, L_SHADE, BKA, ALA, BPBO, and the original PEOA. Experimental results demonstrate that MEPEOA achieves superior optimization accuracy and stability on the majority of benchmark functions. For example, on CEC2017 with 30 dimensions, MEPEOA reduces the average fitness value of multimodal function F9 by approximately 73.6% compared with PEOA and by more than 47% compared with EWOA. In terms of stability, the standard deviation of MEPEOA on function F6 is only 4.13 × 10−3, which is several orders of magnitude lower than those of EWOA, MPSO, and BKA, indicating highly consistent convergence behavior. Furthermore, MEPEOA exhibits clear advantages in convergence speed and robustness, achieving the best Friedman mean rank across all tested benchmark suites. In addition, MEPEOA is applied to a two-dimensional grid-based path planning problem, where it consistently generates shorter and more stable collision-free paths than competing algorithms. Overall, the proposed MEPEOA demonstrates strong robustness, fast convergence, and superior stability, making it an effective and extensible solution for complex numerical optimization and practical engineering problems. Full article
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38 pages, 12112 KB  
Article
Enhanced Educational Optimization Algorithm Based on Student Psychology for Global Optimization Problems and Real Problems
by Wenyu Miao, Katherine Lin Shu and Xiao Yang
Biomimetics 2026, 11(1), 70; https://doi.org/10.3390/biomimetics11010070 - 14 Jan 2026
Viewed by 358
Abstract
To address the insufficient exploration ability, susceptibility to local optima, and limited convergence accuracy of the standard Student Psychology-Based Optimization (SPBO) algorithm in three-dimensional UAV trajectory planning, we propose an enhanced variant, Enhanced SPBO (ESPBO). ESPBO augments SPBO with three complementary strategies: (i) [...] Read more.
To address the insufficient exploration ability, susceptibility to local optima, and limited convergence accuracy of the standard Student Psychology-Based Optimization (SPBO) algorithm in three-dimensional UAV trajectory planning, we propose an enhanced variant, Enhanced SPBO (ESPBO). ESPBO augments SPBO with three complementary strategies: (i) Time-Adaptive Scheduling, which uses normalized time (τ=t/T) to schedule global step-size shrinking, Gaussian fine-tuning, and Lévy flight intensity, enabling strong early exploration and fine late-stage exploitation; (ii) Mentor Pool Guidance, which selects a top-K mentor set and applies time-varying guidance weights to reduce misleading attraction and improve directional stability; and (iii) Directional Jump Exploration, which couples a differential vector with Lévy flights to strengthen basin-crossing while keeping the differential step bounded for robustness. Numerical experiments on CEC2017, CEC2020 and CEC2022 benchmark functions compare ESPBO with Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Improved multi-strategy adaptive Grey Wolf Optimization (IAGWO), Dung Beetle Optimization (DBO), Snake Optimization (SO), Rime Optimization (RIME), and the original SPBO. We evaluate best path length, mean trajectory length, standard deviation, and convergence curves and assess statistical stability via Wilcoxon rank-sum tests (p = 0.05) and the Friedman test. ESPBO significantly outperforms the comparison algorithms in path-planning accuracy and convergence stability, ranking first on both test suites. Applied to 3D UAV trajectory planning in mountainous terrain with no-fly zones, ESPBO achieves an optimal path length of 199.8874 m, an average path length of 205.8179 m, and a standard deviation of 5.3440, surpassing all baselines; notably, ESPBO’s average path length is even lower than the optimal path length of other algorithms. These results demonstrate that ESPBO provides an efficient and robust solution for UAV trajectory optimization in intricate environments and extends the application of swarm intelligence algorithms in autonomous navigation. Full article
(This article belongs to the Special Issue Exploration of Bio-Inspired Computing: 2nd Edition)
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28 pages, 6456 KB  
Article
IB-DARP: An Algorithm for Multi-Vessel Collaborative Task and Path Planning
by Yuhao Wang and Liang Luo
J. Mar. Sci. Eng. 2026, 14(2), 165; https://doi.org/10.3390/jmse14020165 - 12 Jan 2026
Cited by 1 | Viewed by 170
Abstract
This paper presents IB-DARP (Iteration Balancing—Divide Areas Routing Problem), an enhanced multi-vessel cooperative mission and path planning method designed to address the limitations of traditional approaches, including uneven task allocation, workload imbalance, and path conflicts. The proposed method integrates four key mechanisms to [...] Read more.
This paper presents IB-DARP (Iteration Balancing—Divide Areas Routing Problem), an enhanced multi-vessel cooperative mission and path planning method designed to address the limitations of traditional approaches, including uneven task allocation, workload imbalance, and path conflicts. The proposed method integrates four key mechanisms to improve planning robustness and computational efficiency. A historical data mining mechanism is first employed to extract stable navigation patterns from accumulated vessel trajectories and construct a high-confidence maritime route network. Based on this network, a precomputation mechanism significantly reduces planning-stage computational complexity by calculating essential inter-node distances in advance. A heading-aware partitioning mechanism further decomposes the multi-vessel planning problem into tractable single-vessel subproblems, while an iterative auction–equilibrium mechanism dynamically adjusts task assignments to enhance global load balance and suppress conflicts. To evaluate the effectiveness of IB-DARP, comprehensive ablation studies and large-scale scenario experiments were conducted, demonstrating its advantages in mission allocation, conflict mitigation, and cooperative path optimization. The results confirm that IB-DARP provides a scalable and efficient solution for multi-vessel cooperative mission planning in complex maritime environments. Full article
(This article belongs to the Section Ocean Engineering)
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