Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (372)

Search Parameters:
Keywords = Lévy flights

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
20 pages, 4107 KB  
Article
Research on Master–Slave Game Strategy of Integrated Energy System Considering Integrated Demand Response: Improved Snake Optimizer-Quadratic Programming
by Dequan Yang, Chang Peng, Zeming Yang, Miao Zhang, Haotian Wang, Pengchong Dou and Zhihua Wang
Energies 2026, 19(13), 2968; https://doi.org/10.3390/en19132968 (registering DOI) - 24 Jun 2026
Abstract
With the advancement of energy market reform, integrated energy systems (IESs) have achieved rapid development. Considering insufficient research on an electricity–heat coupled master–slave game and the local optimum defect of traditional algorithms, this paper proposes a Stackelberg game optimization strategy for IES considering [...] Read more.
With the advancement of energy market reform, integrated energy systems (IESs) have achieved rapid development. Considering insufficient research on an electricity–heat coupled master–slave game and the local optimum defect of traditional algorithms, this paper proposes a Stackelberg game optimization strategy for IES considering integrated demand response (IDR), with microgrid operator (MGO) as the leader and load aggregator (LA) as the follower. Firstly, an IDR model containing rigid, shiftable electric loads and reducible thermal loads is established, and a bi-level game model is built: the upper MGO optimizes electricity and heat pricing to maximize profit, while the lower LA adjusts flexible loads for maximum consumer surplus. Secondly, an improved snake optimizer (ISO) is constructed via Hammersley sequence initialization, Lévy flight and random perturbation and combined with quadratic programming (QP) to form the ISO-QP hybrid solving method. Benchmark function and CEC2017 tests verify the superior convergence and stability of ISO against multiple classical intelligent algorithms. Case simulation obtains the Stackelberg equilibrium result, and repeated experiments and parameter sensitivity analysis verify model robustness. Results show that the proposed method smooths load fluctuations via price guidance and synchronously improves MGO revenue and LA consumer surplus on the premise of guaranteed user satisfaction. Full article
Show Figures

Figure 1

21 pages, 38386 KB  
Article
A Hybrid Framework for Offshore Wind Power Forecasting: Integration of Adaptive Decomposition and Collaborative Temporal-Channel Modeling
by Tiandong Zhang, Xiaolong Zhou and Zixiang Shen
Energies 2026, 19(13), 2962; https://doi.org/10.3390/en19132962 (registering DOI) - 24 Jun 2026
Abstract
Accurate forecasting of offshore wind power is essential for the stability of power systems, yet it remains challenging due to the strong non-stationarity and complex multivariate coupling of meteorological data. To address the tendency of error accumulation in medium- and long-term predictions, this [...] Read more.
Accurate forecasting of offshore wind power is essential for the stability of power systems, yet it remains challenging due to the strong non-stationarity and complex multivariate coupling of meteorological data. To address the tendency of error accumulation in medium- and long-term predictions, this paper proposes a novel framework, termed ISSAVMD-TCN-SOFTS, which integrates adaptive signal decomposition with lightweight deep temporal modeling. Specifically, an improved sparrow search algorithm, enhanced by Lévy flight and sine–cosine modulation mechanisms, is introduced to adaptively optimize the parameters of variational mode decomposition (VMD). This optimization ensures the robust decomposition of highly non-stationary power series. Furthermore, the framework combines the capability of temporal convolutional networks (TCN) to extract multiscale local temporal features with the efficiency of the STAR module in SOFTS for modeling global channel dependencies. Experiments on multi-site, multi-horizon SCADA data from real offshore wind farms show that the proposed model reduces MAE and RMSE by 10–45% compared with mainstream linear models, recurrent neural networks, and Transformer-based models, and maintains high stability over extended forecasting horizons. The results confirm that the integration of adaptive decomposition and collaborative temporal-channel modeling provides an effective solution for the accurate and stable forecasting of offshore wind power. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
Show Figures

Figure 1

30 pages, 5412 KB  
Article
Rapid Recovery and Self-Healing Strategies for Power Distribution Systems Based on Dynamic Mesh Networks
by Ye Tian, Taiyu Gu, Rui Li, Jie Zhao, Fugen He, Yidong Zhu and Kejian Shi
Electronics 2026, 15(12), 2629; https://doi.org/10.3390/electronics15122629 - 14 Jun 2026
Viewed by 138
Abstract
With the increasing integration of distributed energy sources, fault restoration in power distribution systems faces challenges in terms of real-time performance and adaptability. To effectively manage the uncertainty and volatility of distributed generation, this paper proposes a rapid self-healing strategy based on a [...] Read more.
With the increasing integration of distributed energy sources, fault restoration in power distribution systems faces challenges in terms of real-time performance and adaptability. To effectively manage the uncertainty and volatility of distributed generation, this paper proposes a rapid self-healing strategy based on a dynamic operational grid. By enabling real-time topological reconfiguration and utilizing adaptive resource allocation, the proposed method accommodates the inherent fluctuations of distributed energy sources. First, a dynamic grid weighted graph theory model is constructed, and an emergency control strategy combining particle preprocessing and stepwise optimization is designed to achieve rapid fault response. Then, a “primary-secondary” two-tier restoration mechanism is established: the primary layer integrates the Floyd algorithm with optimized adaptive dynamic programming to achieve millisecond-level restoration of critical loads; the secondary layer employs an improved particle swarm algorithm incorporating Lévy flight perturbations and adaptive weighting to maximize the restoration of general loads. Simulations on a 56-node system demonstrate that this method achieves 100% restoration of critical loads under various fault scenarios. Even under extreme conditions, it can restore 90.88% of secondary loads and 44.63% of tertiary loads, forming a self-healing system characterized by “second-level detection and minute-level restoration,” thereby significantly enhancing system resilience. Full article
Show Figures

Figure 1

29 pages, 12165 KB  
Article
HDE-CGWO-Based Optimal Load Frequency Control for Nonlinear Power Systems
by Yaya Li, Qing Hu, Xingyue Liu, Yu Jiang, Xuanqi Liao and Kaibo Shi
Energies 2026, 19(12), 2783; https://doi.org/10.3390/en19122783 - 10 Jun 2026
Viewed by 129
Abstract
In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes [...] Read more.
In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes a model-constraint-aware optimal PID tuning method based on a Hybrid Differential Evolution–Chaotic Grey Wolf Optimizer (HDE-CGWO). First, a nonlinear LFC model incorporating data sampling, communication delay, governor deadband (GDB), and generation rate constraint (GRC) is established, and a PID-based LFC model is formulated. Next, an objective function based on the integral of time-weighted absolute area control error (ACE), namely ACE-based integral of time-weighted absolute error (ITAE), is constructed. Accordingly, quasi-opposition-based learning (QOBL), chaotic warm-up, Lévy flight, and differential evolution (DE) are incorporated into the standard Grey Wolf Optimizer (GWO) to develop an HDE-CGWO-based PID design scheme for LFC under sampled-data delay and nonlinear unit constraints. Finally, simulation studies are carried out on a multi-area LFC system. The resulting time-domain responses and statistical results show that, compared with standard GWO in the single-area test, HDE-CGWO reduces the ACE-based ITAE by about 43.3%. In the three-area system, the ACE-based ITAE is reduced by about 3.0% under step disturbances and about 1.4% under random disturbances compared with the warm-up Grey Wolf Optimizer (WGWO), indicating that the proposed method can reduce frequency deviations, attenuate post-disturbance oscillations, and accelerate the dynamic recovery process under the considered disturbance conditions. Full article
(This article belongs to the Section A1: Smart Grids and Microgrids)
Show Figures

Figure 1

20 pages, 4671 KB  
Article
An Improved IHBA-BP Neural Network for Temperature Compensation of Load Cells
by Zhen-Jie Zhang, Wan-Sheng Cheng and Dai-Xing Zhang
Sensors 2026, 26(12), 3691; https://doi.org/10.3390/s26123691 - 10 Jun 2026
Viewed by 220
Abstract
Temperature variations degrade load cell accuracy. To address this problem, an Improved Honey Badger Algorithm (IHBA) was developed to optimize the weights and biases of a BP neural network. IHBA incorporates uniform initialization, a nonlinear weight factor, and Lévy flight with stagnation-aware triggering [...] Read more.
Temperature variations degrade load cell accuracy. To address this problem, an Improved Honey Badger Algorithm (IHBA) was developed to optimize the weights and biases of a BP neural network. IHBA incorporates uniform initialization, a nonlinear weight factor, and Lévy flight with stagnation-aware triggering to overcome the uneven initialization, poor exploration–exploitation balance, and weak local optima escape capability of the standard HBA. To validate the proposed method, a dedicated calibration experimental system was constructed. A 7075 T6 aluminum load cell (50 kN) was tested under 0–50 kN loading–unloading cycles over a temperature range of 0–60 °C. To eliminate random errors, three identical elastomers were fabricated, each tested three times, and the measured values were averaged. The results show that after IHBA-BP compensation, the zero-temperature drift coefficient of the load cell was reduced from 374.8 ppm/°C to 35.09 ppm/°C, and the sensitivity-temperature coefficient was reduced from 936.94 ppm/°C to 45.75 ppm/°C. On the unseen test set, the relative error after compensation was 0.01207, the mean square error was 2.84 × 10−5, and the root mean square error was 0.00533. Compared with IMA-BP, PSO-BP, BP, and polynomial fitting methods, IHBA-BP achieved the lowest error. The proposed method shows strong potential for industrial load cell temperature compensation. Full article
(This article belongs to the Topic AI Sensors and Transducers)
Show Figures

Figure 1

39 pages, 6705 KB  
Article
High-Dimensional Feature Selection Using Improved Hybrid Breeding Optimization Algorithm with Feature Grouping
by Zhiwei Ye, Yawen Yan, Yujun Ma, Fan Ma and Ting Cai
Biomimetics 2026, 11(6), 406; https://doi.org/10.3390/biomimetics11060406 - 8 Jun 2026
Viewed by 340
Abstract
Feature selection is essential for improving classification performance in high-dimensional biomedical data, yet conventional metaheuristic algorithms often suffer from premature convergence and loss of population diversity. To address these issues, this paper proposes a Feature Grouping and Improved Hybrid Breeding Optimization framework (FGIHBO). [...] Read more.
Feature selection is essential for improving classification performance in high-dimensional biomedical data, yet conventional metaheuristic algorithms often suffer from premature convergence and loss of population diversity. To address these issues, this paper proposes a Feature Grouping and Improved Hybrid Breeding Optimization framework (FGIHBO). First, the original feature space is hierarchically partitioned using the Maximum Relevance Minimum Redundancy criterion and Symmetric Uncertainty analysis to alleviate the curse of dimensionality. Then, a Multi-Strategy Synergistic Improved Hybrid Breeding Optimization (MSIHBO) algorithm is developed by incorporating Grey Wolf Optimizer (GWO) guidance and a Shannon entropy-adaptive simulated annealing mechanism to balance exploration and exploitation. Experimental results on the CEC2022 benchmark suite demonstrate that MSIHBO provides robust optimization performance across diverse problem categories. Furthermore, evaluations on eleven high-dimensional biomedical datasets show that FGIHBO achieves average classification accuracies ranging from 92.77% to 97.66%. Compared with representative algorithms, including Multi-strategy Improved Grey Wolf Optimizer (MIGWO), Hybrid Whale Optimization Algorithm based on Gathering strategy (HWOAG), Dynamic Crow Search Algorithm (DCSA), GWO, Hybrid Breeding Optimization (HBO), Hybrid Breeding Optimization based on Lévy flight and Elite Opposition-Based Learning strategy (LEHBO), and MSIHBO, the proposed framework improves average classification accuracy by 1.47–27.46%, with the largest gain observed on dataset D10 relative to HWOAG. These results confirm the effectiveness, robustness, and scalability of the proposed framework for high-dimensional biomedical feature selection. Full article
(This article belongs to the Section Biological Optimisation and Management)
Show Figures

Figure 1

26 pages, 628 KB  
Article
A Two-Stage PPO–RLMPA Framework for Dynamic Economic Dispatch with Renewable Energy and Storage Integration
by Kemal Keskin
Biomimetics 2026, 11(6), 400; https://doi.org/10.3390/biomimetics11060400 - 6 Jun 2026
Viewed by 245
Abstract
The Dynamic Economic Dispatch (DED) problem underpins the cost-efficient and reliable operation of modern power systems, yet valve-point loading, ramp-rate coupling, and the growing share of intermittent wind, photovoltaic, and pumped-storage hydro (PSH) resources render it highly non-convex. Metaheuristic methods typically require large [...] Read more.
The Dynamic Economic Dispatch (DED) problem underpins the cost-efficient and reliable operation of modern power systems, yet valve-point loading, ramp-rate coupling, and the growing share of intermittent wind, photovoltaic, and pumped-storage hydro (PSH) resources render it highly non-convex. Metaheuristic methods typically require large computational budgets and hand-crafted constraint-handling rules, whereas deep reinforcement learning agents rarely guarantee the feasibility of the schedules they produce. To address both limitations, this paper proposes a Two-Stage PPO–RLMPA framework that couples data-driven policy learning with a biomimetic metaheuristic search inspired by marine predator–prey dynamics. In the first stage, a Proximal Policy Optimization (PPO) agent is trained on a Markov Decision Process reformulation of DED in which a deterministic Safety Layer projects every raw action onto the feasible set defined by capacity, ramp-rate, and power-balance constraints, so the policy only observes physically viable transitions. In the second stage, the PPO dispatch is refined by the RLMPA module, a Marine Predators Algorithm (MPA) whose exploration–exploitation balance, Lévy-flight foraging, and Fish Aggregating Devices (FADs) attraction mechanisms emulate strategies documented in marine ecosystems; its step-size factor and FADs probability are further adapted online by a Deep Q-Network. This biomimetics-informed refinement translates predator–prey foraging intelligence into economically efficient thermal dispatch under valve-point non-convexity. Across 30 independent runs on ten- and twenty-unit benchmark systems with wind, PV, and PSH integration, the framework attains best costs of USD 368,763 and USD 737,348 on Test Systems 1 and 2, corresponding to reductions of approximately 1.1% and 4.4% over the CFCEP baseline, with zero post-repair constraint violations in every run. Full article
(This article belongs to the Special Issue Nature-Inspired Sustainable Engineering)
Show Figures

Figure 1

21 pages, 1251 KB  
Article
Robust Fast 3D Beam Alignment for UAV-Assisted mmWave and Terahertz Communications
by Loubna Gafari, Wissal Attaoui, Essaid Sabir and Elmahdi Driouch
Sensors 2026, 26(11), 3612; https://doi.org/10.3390/s26113612 - 5 Jun 2026
Viewed by 370
Abstract
Unmanned aerial vehicle (UAV)-assisted millimeter-wave (mmWave) and terahertz (THz) communications are promising enablers of ultra-reliable and low-latency communication in next-generation wireless networks. However, the initial access and beam alignment process remains challenging because highly directional beams must be rapidly aligned in a three-dimensional [...] Read more.
Unmanned aerial vehicle (UAV)-assisted millimeter-wave (mmWave) and terahertz (THz) communications are promising enablers of ultra-reliable and low-latency communication in next-generation wireless networks. However, the initial access and beam alignment process remains challenging because highly directional beams must be rapidly aligned in a three-dimensional environment. In this paper, we investigate a risk-aware beam alignment framework for UAV-assisted mmWave/THz systems, where user equipment scans a 3D spherical region to detect UAV base stations. The objective is to jointly minimize the expected cell-search latency and its variance while satisfying detection-failure and link-quality constraints. To solve this non-convex optimization problem efficiently, we employ the Lévy Self-Renewable Flow Direction Algorithm (LSRFDA), which combines Lévy-flight exploration with self-renewal to improve convergence robustness. A unified propagation model is adopted to cover both mmWave and THz regimes by incorporating free-space spreading loss and frequency-dependent molecular absorption. Extensive Monte Carlo simulations compare the proposed approach with Particle Swarm Optimization, Random Search, Reinforcement Learning, and PPO-Lagrangian methods. The results show that LSRFDA achieves lower latency, lower latency variation, more reliable detection, and lower energy consumption across a wide range of UAV densities and coverage radii. These outcomes highlight the effectiveness of risk-aware geometric optimization for fast and dependable initial access in UAV-assisted 5G mmWave and 6G THz networks. Full article
Show Figures

Figure 1

25 pages, 6622 KB  
Article
Coordinated Optimization of Configuration and Control for Reversible Substations Equipped with Bidirectional Converter Devices Considering Life-Cycle Cost
by Jiayi Wu, Wei Liu, Jian Zhang, Xiaodong Zhang and Dingxin Xia
Electricity 2026, 7(2), 52; https://doi.org/10.3390/electricity7020052 - 4 Jun 2026
Viewed by 153
Abstract
The growing demand for energy-efficient urban rail transit has led to the increasing deployment of reversible substations (RS) in traction power supply systems. These substations, equipped with bidirectional converter devices (BCDs), involve high initial costs and complex parameter optimization challenges. This paper presents [...] Read more.
The growing demand for energy-efficient urban rail transit has led to the increasing deployment of reversible substations (RS) in traction power supply systems. These substations, equipped with bidirectional converter devices (BCDs), involve high initial costs and complex parameter optimization challenges. This paper presents a coordinated optimization method for BCD-equipped RS using a two-layer model. In the upper layer, the model determines the siting of RS and the capacity of BCD to minimize life-cycle cost (LCC). In the lower layer, it adjusts the control parameters of BCDs to reduce annual operating cost. An improved salp swarm algorithm (ISSA), incorporating Tent chaotic mapping and Levy flight, is developed to solve the model. A case study based on an 18.2 km subway line shows that the optimized configuration reduces overall cost by 5.12% and electricity cost by 10.53% compared with a conventional rectifier system. Moreover, it achieves a 1.19% reduction in electricity cost over a system with fixed control parameters, while maintaining rail potential and catenary voltage within safe limits. These findings demonstrate that the proposed method strikes an effective balance between initial investment and long-term operational benefits, contributing to improved energy efficiency and economic performance. Full article
(This article belongs to the Special Issue Stability, Operation, and Control in Power Systems)
Show Figures

Figure 1

38 pages, 9863 KB  
Article
Fog Task Scheduling Using Quality-Source-Driven Multi-Anchor Synchronized Search Algorithm
by Haitao Xie, Zhuo Luo, Zhiwei Ye, Wen Zhou, Xianjing Zhou, Donglei Xu and Mingming Zhao
Biomimetics 2026, 11(6), 392; https://doi.org/10.3390/biomimetics11060392 - 3 Jun 2026
Viewed by 378
Abstract
Efficient task scheduling in heterogeneous IoT–Fog environments is challenging due to limited fog resources, diverse task demands, and conflicting QoS objectives. This paper proposes ASQS, a Quality-Source-driven Multi-Anchor Synchronized Search algorithm for IoT–Fog task scheduling. ASQS is biomimetically motivated by collective search behaviors [...] Read more.
Efficient task scheduling in heterogeneous IoT–Fog environments is challenging due to limited fog resources, diverse task demands, and conflicting QoS objectives. This paper proposes ASQS, a Quality-Source-driven Multi-Anchor Synchronized Search algorithm for IoT–Fog task scheduling. ASQS is biomimetically motivated by collective search behaviors in natural systems, where distributed exploration, collective memory, and probabilistic cooperation support an exploration–exploitation balance. Specifically, ASQS constructs quality layers from candidate schedules, extracts representative quality-source anchors, and reuses them through an ACO-inspired probabilistic synchronization mechanism, thereby improving the utilization of high-quality historical search information. FNO-based search and Lévy-flight perturbation are further incorporated to enhance directional guidance and long-range exploration. Experiments on 33 benchmark functions, ablation studies, sensitivity analysis, standard fog scheduling scenarios, and large-scale task-intensive scenarios were conducted to evaluate ASQS. The results show that ASQS achieves competitive optimization accuracy, stable convergence, and superior comprehensive scheduling performance in terms of fitness, makespan, latency, load balance, and constraint handling. In particular, the large-scale experiment with 100 fog nodes and up to 8000 IoT tasks verifies the scalability of ASQS under heavy workload pressure. Statistical tests further confirm the reliability of the observed improvements. These results demonstrate that ASQS is an effective, scalable, and biomimetically motivated optimizer for IoT–Fog task scheduling. Full article
(This article belongs to the Section Biological Optimisation and Management)
Show Figures

Figure 1

26 pages, 3664 KB  
Article
A Hybrid ISSA-XGBoost Model for Predicting Wellbore Leakage
by Kai Bai, Jiaqi Chen, Senlin Yin, Chaojie Wei, Yuzhou Yan and Junjie Liu
Sensors 2026, 26(11), 3526; https://doi.org/10.3390/s26113526 - 2 Jun 2026
Viewed by 296
Abstract
As critical underground engineering structures, wellbores may suffer complex structural deterioration and hidden safety hazards may be encountered during drilling. Multi-source sensor monitoring data provides an effective data basis for structural health perception and early warnings for wellbore structures at risk. The inherent [...] Read more.
As critical underground engineering structures, wellbores may suffer complex structural deterioration and hidden safety hazards may be encountered during drilling. Multi-source sensor monitoring data provides an effective data basis for structural health perception and early warnings for wellbore structures at risk. The inherent diversity of formation conditions and the dynamic disturbances during drilling jointly lead to the differentiated presentation of drilling loss types, among which fractured, permeable, and vuggy losses are the most typical. This paper focuses on fractured wellbore leakage, regards wellbore leakage as an important structural failure form of underground drilling engineering structures. In-depth analysis and research on the structural deterioration mechanism of wellbore leakage were conducted, and we propose a wellbore leakage prediction method based on the improved sparrow search algorithm (ISSA) optimized gradient boosting decision tree (XGBoost). First, the Sobol sequence is adopted to replace the random initialization strategy, combined with the opposition-based learning mechanism; then, an adaptive Levy flight search mechanism is introduced to dynamically adjust the population ratio of discoverers and vigilantes; finally, intelligent optimization technologies are integrated to reconstruct the position update strategies of discoverers, followers, and vigilantes, enhancing the optimization adaptability of the algorithm. Relying on multi-field sensor monitoring datasets collected from actual drilling engineering, this paper compares the proposed model with wellbore leakage prediction models built by classical machine learning algorithms, and verifies its generalization ability on different datasets. Experimental data indicate that the improved algorithm exhibits significant advantages in optimization accuracy, enabling the proposed model to achieve an AUC improvement of 4.46%, along with accuracy (95.1%), precision (94.9%), recall (94.7%), and F1-score (94.2%). On this basis, the ISSA was applied to the hyperparameter optimization of XGBoost, constructing the ISSA-XGBoost prediction model. The method has high accuracy and good generalization ability in fractured wellbore leakage prediction, and it can realize intelligent health monitoring of underground wellbore structures, including early warnings. This study provides a reliable sensing data analysis scheme and technical support for structural health monitoring and hazard prevention in drilling engineering. Full article
(This article belongs to the Special Issue Novel Sensors for Structural Health Monitoring: 2nd Edition)
Show Figures

Figure 1

62 pages, 12401 KB  
Article
A Multi-Strategy Enhanced Bionic-Inspired Secretary Bird Optimization Algorithm for Numerical Optimization and Artistic Image Segmentation
by Xuanqi Yuan, Jinlu Qin and Xiaohan Zhong
Biomimetics 2026, 11(6), 385; https://doi.org/10.3390/biomimetics11060385 - 1 Jun 2026
Viewed by 335
Abstract
To address the limitations of the original Secretary Bird Optimization Algorithm (SBOA), such as insufficient population diversity, weak local exploitation ability, and a tendency to become trapped in local optima when solving complex optimization problems, this paper proposes a Multi-Strategy Improved Secretary Bird [...] Read more.
To address the limitations of the original Secretary Bird Optimization Algorithm (SBOA), such as insufficient population diversity, weak local exploitation ability, and a tendency to become trapped in local optima when solving complex optimization problems, this paper proposes a Multi-Strategy Improved Secretary Bird Optimization Algorithm (MISBOA). First, a chaotic elite initialization strategy is introduced to improve the quality and diversity of the initial population. Second, an adaptive spiral Lévy flight strategy is designed to enhance the balance between global exploration and local exploitation during the iterative process. Third, a dynamic neighborhood-guided mutation strategy is incorporated to maintain population diversity and improve convergence accuracy in the later search stage. To validate the effectiveness of the proposed algorithm, MISBOA is comprehensively evaluated on the IEEE CEC2014, CEC2017, and CEC2020 benchmark suites. Experimental results demonstrate that MISBOA achieves superior convergence speed, optimization accuracy, and robustness compared with several representative metaheuristic algorithms. Furthermore, MISBOA is applied to Otsu-based multilevel threshold image segmentation. The segmentation performance is assessed using PSNR, FSIM, SSIM, and visual quality comparisons. The results indicate that MISBOA can generate more accurate and stable segmentation outcomes, demonstrating its strong potential for solving complex numerical optimization and artistic image segmentation problems. Full article
(This article belongs to the Special Issue Advances in Biological and Bio-Inspired Algorithms: 2nd Edition)
Show Figures

Figure 1

21 pages, 14353 KB  
Article
Research on Three-Layer Cooperative Robust Optimal Scheduling of Rural Integrated Energy System Based on Potential Game Information Gap
by Fangjie Gao, Congyi Ding, Yubin Wang, Qinqing Zhang and Yin Zhao
Systems 2026, 14(6), 621; https://doi.org/10.3390/systems14060621 - 1 Jun 2026
Viewed by 181
Abstract
A clean and efficient rural energy system is essential for building a modern energy system and for accelerating the transition to renewable energy in rural areas. Therefore, a robust collaborative optimal scheduling method for rural integrated energy systems is proposed, incorporating multi-agent gaming. [...] Read more.
A clean and efficient rural energy system is essential for building a modern energy system and for accelerating the transition to renewable energy in rural areas. Therefore, a robust collaborative optimal scheduling method for rural integrated energy systems is proposed, incorporating multi-agent gaming. First, a three-layer cooperative structure is developed based on current rural energy consumption patterns. Second, a scheduling model is formulated using potential game theory, with the objective of maximizing the overall benefits of all parties. The model also accounts for multi-energy complementarity, demand response, and multiple uncertainties, leading to a robust optimal scheduling framework based on information gap decision theory. The resulting problem is solved using a chicken swarm optimization algorithm improved by Lévy flight. Finally, a case study of the three-layer cooperative optimization model is presented. The results show that multi-energy complementarity can increase local renewable energy consumption and improve the economic efficiency of diverse energy use for rural consumers. Information gap decision theory helps balance economic and uncertain factors and supports decision-making for agents with different risk preferences. Full article
Show Figures

Figure 1

49 pages, 3442 KB  
Article
Optimal FACTS Placement in Power Systems with Load Uncertainty Using a Lévy Flight and Chaotic Search-Based Whale Optimization Algorithm
by Ashish Tripathi, Mohd Tauseef Khan and Anurag Tripathi
Sustainability 2026, 18(11), 5400; https://doi.org/10.3390/su18115400 - 27 May 2026
Viewed by 736
Abstract
The Balanced Whale Optimization Algorithm (BWOA) is proposed to address the optimal power flow (OPF) problem in grids incorporating flexible AC transmission systems (FACTS) and renewable energy sources. The standard Whale Optimization Algorithm (WOA) is enhanced through the integration of Lévy Flight (LF) [...] Read more.
The Balanced Whale Optimization Algorithm (BWOA) is proposed to address the optimal power flow (OPF) problem in grids incorporating flexible AC transmission systems (FACTS) and renewable energy sources. The standard Whale Optimization Algorithm (WOA) is enhanced through the integration of Lévy Flight (LF) dynamics for global exploration and Chaotic Local Search (CLS) for refined exploitation, producing a balanced search that mitigates premature convergence and local-optima stagnation typical of metaheuristic OPF solvers. The BWOA is benchmarked on the modified IEEE 30-bus system under both fixed and dynamic loading conditions and against five state-of-the-art metaheuristics (ALCPSO, CLPSO, MFO, SaDE, and the standard WOA) across eight study cases. Across the full set of cases, the BWOA delivers, on average, lower gross cost (mean reduction of approximately 1.3–6.8% relative to the comparators), lower active power loss (mean reduction of 6–22%), and lower expected gross cost under load and renewable uncertainty (mean reduction of 0.5–4.9%). The BWOA additionally attains the leading or co-leading position in the Friedman rank test (FRT) in the majority of cases, while incurring only a marginal runtime overhead (≤1% over the next-fastest comparator). The algorithm shows slightly higher voltage deviations in some scenarios, which is discussed as a controllable trade-off. The results indicate that the BWOA is a robust and cost-effective solver for OPF in grids with FACTS devices and stochastic renewable generation. Full article
Show Figures

Figure 1

29 pages, 6477 KB  
Article
Multi-Strategy Enhanced White Shark Optimizer for Solving Job Shop Scheduling Problem
by Li Cao, Meng Li, Ken Chen, Yinggao Yue, Yang Qiu and Zihao Cheng
Biomimetics 2026, 11(6), 372; https://doi.org/10.3390/biomimetics11060372 - 27 May 2026
Viewed by 204
Abstract
Aiming at the inherent limitations of the basic White Shark Optimizer (WSO), such as insufficient population diversity, unbalanced global and local search mechanisms, and weak convergence in the later stage, this paper proposes an Improved White Shark Optimizer (IWSO). The algorithm is improved [...] Read more.
Aiming at the inherent limitations of the basic White Shark Optimizer (WSO), such as insufficient population diversity, unbalanced global and local search mechanisms, and weak convergence in the later stage, this paper proposes an Improved White Shark Optimizer (IWSO). The algorithm is improved from the following three aspects: Firstly, the Tent chaotic map is introduced to replace the traditional random initialization in the population initialization stage. Secondly, an adaptive nonlinear convergence factor and a dynamic inertia weight adjustment strategy are designed to focus on the fine search in the neighborhood of the optimal solution. Thirdly, the Levy flight perturbation mechanism and the elite opposition-based learning strategy are integrated to expand the search range and further accelerate the convergence speed. To verify the effectiveness and superiority of the IWSO algorithm, the CEC2017 test suite is selected for simulation experiments, and the IWSO is systematically compared with seven other representative swarm intelligence algorithms. The experimental results show that the IWSO is significantly superior to all comparison algorithms in multiple evaluation indicators, including minimum makespan, average convergence value, standard deviation, and successful convergence rate, on scheduling instances of different scales and difficulties. The convergence curve remains leading throughout the iteration process and shows a smoother convergence trend. The multi-strategy enhanced white shark optimizer proposed in this paper effectively overcomes the inherent defects of the basic algorithm, significantly improves the solution accuracy and convergence efficiency of the job shop scheduling problem, and has high theoretical research value and practical engineering application prospects. In the future, the multi-strategy improved White Shark Optimizer will be extended to multi-objective job shop scheduling, dynamic disturbance job shop scheduling, and large-scale production scheduling scenarios with numerous workpieces and machines. Full article
(This article belongs to the Section Biological Optimisation and Management)
Show Figures

Figure 1

Back to TopTop