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Enhanced zebra optimization algorithm for reliability redundancy allocation and engineering optimization problems

CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2025年第4期28卷 1-55页

作者： Punia, Parul Raj, Amit Kumar, Pawan Cent Univ Haryana Dept Math Mahendergarh 123031 Haryana India

In this study, an enhanced version of the recently developed zebra optimization algorithm (ZOA) is introduced, which takes inspiration from the foraging and defensive behaviors of zebras. ZOA is an efficient metaheuristic algorithm that has been used to solve various complex optimization problems. However, there is potential for further enhancement in preventing premature convergence, addressing local optima stagnation, and improving solution quality. To address these issues, two key strategies are integrated into the Enhanced zebra optimization algorithm (EZOA): Levy flight and lens opposition-based learning. The Levy flight strategy promotes effective exploration in the initial foraging stage, thus preventing premature convergence to sub-optimal solutions. Next, the lens opposition-based learning strategy is introduced to improve diversity and ensure convergence towards higher-quality solutions. The proposed approach is evaluated on three test cases of optimization problems, including twenty-three classical benchmark functions, a set of CEC-2019 functions, four mixed-integer reliability optimization benchmark problems, and four constrained engineering design optimization problems. The results of EZOA are compared against several well-performing metaheuristic algorithms from the literature, along with some champion algorithms of IEEE CEC competitions. Additionally, Friedman's rank, Wilcoxon signed-rank test, and Mann-Whitney U test are employed to analyze the simulation results, providing statistical validation of the robustness and significance of the proposed EZOA, which ranks first across all test cases. Furthermore, a comprehensive evaluation of time complexity, along with boxplot and convergence analysis, conducted provides insights into the effectiveness and stability of EZOA.

关键词： Metaheuristic optimization zebra optimization algorithm Reliability optimization Engineering design optimization Constrained optimization

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A path planning method in three-dimensional complex space based on Bézier curves and a hybrid zebra optimization algorithm

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2025年第2期28卷 1-20页

作者： Huang, Hanqiao Du, Bo Zhou, Huan Wang, Meng Ming, Yufei Hu, Gang Northwestern Polytech Univ Unmanned Syst Res Inst Xian 710072 Shaanxi Peoples R China AF Engn Univ Aviat Engn Sch Xian 710038 Shaanxi Peoples R China Shanghai Electromech Engn Inst Shanghai 200000 Peoples R China Harbin Engn Univ Coll Underwater Acoust Engn Harbin 150000 Peoples R China Xian Univ Technol Dept Appl Math Xian 710054 Shaanxi Peoples R China

For the safety and efficiency of aircraft executing tasks in complex environments, this paper presents a path planning method in three-dimensional space based on B & eacute;zier curve and a hybrid zebra optimization algorithm. Firstly, a path planning model using curves to directly generate flight paths is developed, by taking three kinds of flight costs as an objective function and control points as decision variables. To solve the established model with higher accuracy, a hybrid zebra optimization algorithm (HZOA) is constructed. It incorporates the hierarchical system of grey wolf optimization algorithm to form habitat searching strategy, which guides candidate solutions to approach better solutions by integrating information from the three pioneer zebras. Experimental results on CEC2019 test suite illustrate that the HZOA can get solutions with higher accuracy and faster convergence rate, especially in the late stage of searching. Meanwhile, its significantly superior performance to other comparison algorithms on more than half of all test functions is proved by the p values of the Kruskal-Wallis test. Finally, solving the path planning model through the HZOA, the results on three given simulated cases indicate paths obtained by HZOA have smaller total flight costs than those of other comparison algorithms for all simulated scenes. For the three sub-indicators, the approach based on HZOA ranks at least second to others, which proves it performs better in optimizing the flight distance, altitude and path smoothness.

关键词： Path planning B & eacute zier curve zebra optimization algorithm Social hierarchical structure Flight cost

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Characteristic wavelength selection based on multi-strategy fusion zebra optimization algorithm for PLSR

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MEASUREMENT 2025年 253卷

作者： Liu, Yu Tong, Chenqing Wu, Simin Shang, Weiwei Xing, Xiaoxue Yuan, Weixiang Changchun Univ Coll Elect Informat Engn Changchun 130012 Peoples R China COFCO Nutr & Hlth Res Inst Beijing 102209 Peoples R China

Wavelength selection plays a key role in near-infrared spectral analysis, because it can significantly enhance the generalization capability of multivariate models while simultaneously reducing their complexity. Scholars have proposed many wavelength selection methods based on different strategies, among which the swarm intelligence optimization algorithm is one of the most widely applied. The zebra optimization algorithm (ZOA) is a novel algorithm, which iteratively searches for the optimal solution by mimicking zebra foraging and defense behavior. In this work, the ZOA is first applied to the wavelength selection of near-infrared spectra. And a new wavelength selection method, multi-strategy fusion of zebra optimization algorithm (MFZOA), for spectral variable selection in the partial least squares regression (PLSR) model is proposed. MFZOA consists of three strategies. First, the population initialization strategy incorporates the good point set method to ensure a more uniform distribution of the initial population. Second, the dynamic convergence strategy employs a nonlinear convergence factor to further balance the algorithm's exploitation and exploration capabilities. Third, an adaptive Gaussian mutation strategy is introduced to help the algorithm escape local optima. The interpretability of the selected wavelengths is assessed on five public NIR datasets (corn, marzipan, soil, grain and wheat kernels datasets). The experimental results show that, compared to other wavelength selection algorithms, MFZOA can identify a smaller set of characteristic wavelengths while achieving superior predictive performance.

关键词： Near-infrared spectral analysis zebra optimization algorithm Wavelength selection Partial Least Squares Regression

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DDoS Attack Autonomous Detection Model Based on Multi-Strategy Integrate zebra optimization algorithm

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Computers, Materials & Continua 2025年第1期82卷 645-674页

作者： Chunhui Li Xiaoying Wang Qingjie Zhang Jiaye Liang Aijing Zhang School of Information Engineering Institute of Disaster PreventionLangfang065201China Langfang Key Laboratory of Network Emergency Protection and Network Security Langfang065201China

Previous studies have shown that deep learning is very effective in detecting known ***,when facing unknown attacks,models such as Deep Neural Networks(DNN)combined with Long Short-Term Memory(LSTM),Convolutional Neural Networks(CNN)combined with LSTM,and so on are built by simple stacking,which has the problems of feature loss,low efficiency,and low ***,this paper proposes an autonomous detectionmodel for Distributed Denial of Service attacks,Multi-Scale Convolutional Neural Network-Bidirectional Gated Recurrent Units-Single Headed Attention(MSCNN-BiGRU-SHA),which is based on a Multistrategy Integrated zebra optimization algorithm(MI-ZOA).The model undergoes training and testing with the CICDDoS2019 dataset,and its performance is evaluated on a new GINKS2023 *** hyperparameters for Conv_filter and GRU_unit are optimized using the Multi-strategy Integrated zebra optimization algorithm(MIZOA).The experimental results show that the test accuracy of the MSCNN-BiGRU-SHA model based on the MIZOA proposed in this paper is as high as 0.9971 in the CICDDoS 2019 *** evaluation accuracy of the new dataset GINKS2023 created in this paper is *** to the MSCNN-BiGRU-SHA model based on the zebra optimization algorithm(ZOA),the detection accuracy on the GINKS2023 dataset has improved by 5.81%,precisionhas increasedby 1.35%,the recallhas improvedby 9%,and theF1scorehas increasedby 5.55%.Compared to the MSCNN-BiGRU-SHA models developed using Grid Search,Random Search,and Bayesian optimization,the MSCNN-BiGRU-SHA model optimized with the MI-ZOA exhibits better performance in terms of accuracy,precision,recall,and F1 score.

关键词： Distributed denial of service attack intrusion detection deep learning zebra optimization algorithm multi-strategy integrated zebra optimization algorithm

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Drilling characteristics optimization of polymer composite fortified with eggshells using box-Behnken design and zebra optimization algorithm

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RESULTS IN ENGINEERING 2025年 25卷

作者： Deepanraj, B. Saravanan, A. M. Senthilkumar, N. Afzal, Abdul Aziz Afzal, Abdul Rahman Prince Mohammad Bin Fahd Univ Coll Engn Dept Mech Engn Al khobar 31952 Saudi Arabia Natl Univ Sci & Technol Dept Mech & Ind Engn Muscat 111 Oman Saveetha Inst Med & Tech Sci Saveetha Sch Engn Chennai 602105 Tamil Nadu India Univ Business & Technol UBT Dahban Dept Ind Engn North Jeddah 21448 Saudi Arabia

This study investigates the drilling characteristics of eggshell powders (ESPs) reinforced in delrin polymer composite. ESPs are obtained from the waste shells of eggs that are crushed, ground, and sieved to obtain a uniform size of 100 mu m. ESPs are added to the delrin polymer in varying proportions (10-30 %) by weight, and the polymer composite is fabricated using injection molding. Box-Behnken design (BBD) is adopted for planning the experiments for varying values of rotational speed (RS), feed rate (FR), and % ESP. Drilling studies on the fabricated delrin+ESPs (DESP) are carried out using an uncoated carbide drill bit in a vertical machining center (VMC), and the surface roughness (SR) and material removal rate (MRR) are measured for further analysis. Observation shows that with higher RS and FR, the MRR and SR increase. With higher inclusion of ESP, the mechanical strength increases, which lowers the MRR and produces better SR. Desirability analysis provides the multi-criteria optimization, making an ideal condition of 912.14 rpm of RS, 0.054 mm/rev of FS, and 24.25 % ESP addition, which predicts an MRR of 0.274 mm3/min and SR of 3.102 mu m. A bio-inspired metaheuristic algorithm, zebra optimization algorithm (ZOA), is adopted to maximize MRR and minimize SR, producing an ideal condition of 1000 rpm of RS, 0.02 mm/rev of FS, and 30 % ESP addition. The confirmation experiment with RSM-based optimal conditions presents an improvement in MRR of 2.46 % and an SR reduction of 23.25 %. In contrast, ZOA ideal conditions provide an increase in MRR by 1.06 % and a decrease in SR by 28.62 %.

关键词： Delrin Eggshell particles Surface roughness Environmental sustainability Box-Behnken design zebra optimization algorithm

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Chaotic zebra optimization algorithm for Increasing the Lifetime of Wireless Sensor Network

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JOURNAL OF NETWORK AND SYSTEMS MANAGEMENT 2024年第4期32卷 85页

作者： El-Hageen, Hazem M. Alfaifi, Yousef H. Albalawi, Hani Alzahmi, Ahmed Alatwi, Aadel M. Ali, Ahmed F. Mead, Mohamed A. Univ Tabuk Fac Engn Elect Engn Dept Tabuk 47913 Saudi Arabia Univ Tabuk Renewable Energy & Environm Technol Ctr Tabuk 47913 Saudi Arabia Egyptian Atom Energy Author Cairo 47913 Egypt Univ Tabuk Fac Comp & Informat Technol Tabuk 47913 Saudi Arabia Suez Canal Univ Fac Comp & Informat Dept Comp Sci Ismailia Egypt Sinai Univ Fac Informat Technol & Comp Sci Dept Informat Technol Arish Egypt

A wireless sensor network (WSN) is made up of one or more sink nodes, also known as base stations, and spatially dispersed sensors. Real-time monitoring of physical parameters like temperature, vibration, and motion is done using sensors, which also provide sensory data. A sensor node may act as a data router in addition to an originator of data. However, there are a number of issues with these sensors, including a high rate of energy consumption and a short network lifetime. One of the greatest ways to handle this problem is to use the clustering technique. In the WSN, selecting the optimal Cluster Heads (CHs) helps save energy consumption. algorithms for Swarm Intelligence (SI) can assist in resolving challenging issues. We present a novel algorithm in this research to choose the top CHs in the WSN. A Chaotic zebra optimization algorithm (CZOA) is the name of the new algorithm. We integrate the chaotic map and the zebra optimization algorithm (ZOA) in the CZOA. By doing so, the suggested algorithm's processes of diversification can help to prevent the possibility of being trapped in local minima. Different SI algorithms are compared with the CZOA. The suggested algorithm's results demonstrate that it can use less energy than the other algorithms and that more nodes are still alive for it than for the other algorithms combined. As a result, the CZOA demonstrated its superiority in lowering energy consumption and lengthening network lifetime.

关键词： Cluster head selection Wireless sensor network Chaotic map Network lifetime zebra optimization algorithm

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Hybrid Chaotic zebra optimization algorithm and Long Short-Term Memory for Cyber Threats Detection

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IEEE ACCESS 2024年 12卷 93235-93260页

作者： Amin, Reham El-Taweel, Ghada Ali, Ahmed F. Tahoun, Mohamed Suez Canal Univ Fac Comp & Informat Ismailia 8366004 Egypt Sinai Univ Fac Informat Technol & Comp Sci Kantara 8392130 Egypt

Cyber Threat Detection (CTD) is subject to complicated and rapidly accelerating developments. Poor accuracy, high learning complexity, limited scalability, and a high false positive rate are problems that CTD encounters. Deep Learning defense mechanisms aim to build effective models for threat detection and protection allowing them to adapt to the complex and ever-accelerating changes in the field of CTD. Furthermore, swarm intelligence algorithms have been developed to tackle the optimization challenges. In this paper, a Chaotic zebra optimization Long-Short Term Memory (CZOLSTM) algorithm is proposed. The proposed algorithm is a hybrid between Chaotic zebra optimization algorithm (CZOA) for feature selection and LSTM for cyber threat classification in the CSE-CIC-IDS2018 dataset. Invoking the chaotic map in CZOLSTM can improve the diversity of the search and avoid trapping in a local minimum. In evaluating the effectiveness of the newly proposed CZOLSTM, binary and multi-class classifications are considered. The acquired outcomes demonstrate the efficiency of implemented improvements across many other algorithms. When comparing the performance of the proposed CZOLSTM for cyber threat detection, it outperforms six innovative deep learning algorithms for binary classification and five of them for multi-class classification. Other evaluation criteria such as accuracy, recall, F1 score, and precision have been also used for comparison. The results showed that the best accuracy was achieved using the proposed algorithm for binary is 99.83%, with F1-score of 99.82%, precision of 99.83%, and recall of 99.82%. The proposed CZOLSTM algorithm also achieved the best performance for multi-class classification among other compared algorithms.

关键词： Classification algorithms optimization methods Feature extraction Particle swarm optimization Machine learning algorithms Long short term memory Threat assessment Computer security Deep learning Intrusion detection Cyber security deep learning feature selection long short-term memory intrusion detection swarm intelligence zebra optimization algorithm

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UAV Obstacle Avoidance Trajectory Planning Based on Improved zebra optimization algorithm 43

UAV Obstacle Avoidance Trajectory Planning Based on Improved...

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43rd Chinese Control Conference (CCC)

作者： Liang, Qing Niu, Miao Xu, Xinyuan Hu, Yue Xian Univ Posts & Telecommun Sch Elect Engn Xian 710121 Shaanxi Peoples R China

ISBN: (纸本)9798350366907;9789887581581

An upgraded zebra optimization algorithm (GSZOA) is presented to solve the issues of slow convergence speed and easy fall into local optimum of zebra optimization algorithm (ZOA) in obstacle avoidance trajectory planning of Unmanned aerial vehicle (UAV). In order to solve the problem of slow convergence, chaotic mapping is invoked for ZOA to enhance the population diversity and accelerate the convergence speed. The golden sine algorithm is integrated to improve the zebra position update formula, which effectively coordinates the global search and local mining ability. Aiming at the problem of easily falling into local optimization, a cycle mutation strategy is introduced to reduce the probability of this problem. Finally, the improved algorithm is compared with the other five algorithms on the classical benchmark function to verify the superiority of the GSZOA algorithm. It is also applied to UAV obstacle avoidance trajectory planning, and the simulation results show that show that the GSZOA algorithm has better optimization seeking ability and faster convergence.

关键词： Unmanned Aerial Vehicle zebra optimization algorithm Bernoulli Chaos Mapping Golden Sine Obstacle Avoidance Trajectory Planning

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Passive Localization using TDOA Based on Improved zebra optimization algorithm 9

Passive Localization using TDOA Based on Improved Zebra Opti...

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9th International Conference on Electronic Technology and Information Science (ICETIS)

作者： Liao, Yanping Wang, Yongpeng Harbin Engn Univ Sch Informat & Commun Engn Harbin Peoples R China

ISBN: (纸本)9798350388350;9798350388343

In passive localization, the time difference of arrival (TDOA) measurement model is commonly used for source location estimation. Methods for TDOA based estimation can be categorized into two main groups: closed-form algebraic solutions and iterative approaches. Algebraic solutions circumvent convergence issues and achieve global optima, but are usually sensitive to TDOA measurement inaccuracies. Iterative methods include deterministic iterative methods and stochastic optimization methods. The deterministic iterative methods suffer from the risk of not converging and require initial values. In this paper, a stochastic optimization algorithm named zebra optimization algorithm (ZOA) is used to solve the TDOA localization problem. Improvements are made to the defensive strategies of zebras in the improved ZOA (IZOA), adjusting the proportion of predators at different stages of the algorithm to optimize the balance between exploration and exploitation. Simulation results show that IZOA performs excellently in TDOA localization, exhibiting rapid convergence. It efficiently and accurately solves the TDOA equations to obtain the source position, outperforming comparative algorithms in terms of localization accuracy.

关键词： passive localization time difference of arrival zebra optimization algorithm

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Research and application of improved zebra optimization algorithm 5

Research and application of improved Zebra optimization algo...

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5th International Conference on Computer Engineering and Application (ICCEA)

作者： Sun, Yige Wu, Changyou Cong, Min Yan, Beibei Shandong Coll Business & Technol Sch Management Sci & Engn Yantai Shandong Peoples R China

ISBN: (纸本)9798350386783;9798350386776

To solve the problems of slow convergence of zebra optimization algorithm (ZOA), limited accuracy and prone to local optimality, a novel zebra optimization algorithm (TLZOA) combining Tent chaos mapping, Levy flight strategy and adaptive T-distribution was proposed. Firstly, the population is initialized using Tent chaotic mapping, which effectively solves the problem of insufficient population diversity and lack of information exchange among populations. Secondly, Levi's flight strategy makes the algorithm to depart from the local optimal;to enhance the algorithm's capacity for global search, disturbances are added to the population's late update using the adaptive *** testing on 6 different test functions, Other swarm intelligence algorithms are compared with the suggested TLZOA. The results show that TLZOA has superior performance in terms of convergence and optimization accuracy, which is feasible.

关键词： zebra optimization algorithm Tent Chaotic mapping Levy flight strategy Adaptive T distribution

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