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1
Hidayat, Nur Wahyu, Purwanto, and Fikri Budiman. "Whale Optimization Algorithm Bat Chaotic Map Multi Frekuensi for Finding Optimum Value." Journal of Applied Intelligent System 5, no. 2 (2021): 80–90. http://dx.doi.org/10.33633/jais.v5i2.4432.
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Optimization is one of the most interesting things in life. Metaheuristic is a method of optimization that tries to balance randomization and local search. Whale Optimization Algorithm (WOA) is a metaheuristic method that is inspired by the hunting behavior of humpback whales. WOA is very competitive compared to other metaheuristic algorithms, but WOA is easily trapped in a local optimum due to the use of encircling mechanism in its search space resulting in low performance. In this research, the WOA algorithm is combined with the BAT chaotic map multi-frequency (BCM) algorithm. This method is done by inserting the BCM algorithm in the WOA search phase. The experiment was carried out with 23 benchmarks test functions which were run 30 times continuously with the help of Matlab R2012a. The experimental results show that the WOABCM algorithm is able to outperform the WOA and WOABAT algorithms in most of the benchmark test functions. The increase of performance in the average of optimum value of WOABCM when compared to WOA is 2.27x10 ^ 3.
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Moqbel, Mohammed Ali Mohammed, Talal Ahmed Ali Ali, Zhu Xiao, and Amani Ali Ahmed Ali. "Design of efficient generalized digital fractional order differentiators using an improved whale optimization algorithm." PeerJ Computer Science 11 (July 1, 2025): e2971. https://doi.org/10.7717/peerj-cs.2971.
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This article proposes a new design and realization method for generalized digital fractional-order differentiator (GFOD) based on a composite structure of infinite impulse response (IIR) subfilters. The proposed method utilizes an improved whale optimization algorithm (IWOA) to compute the optimal coefficients of IIR subfilters of the realization structure. IWOA is developed by incorporating a piecewise linear chaotic mapping (PWLCM) and an adaptive inertia weight based on the hyperbolic tangent function (AIWHT) into the framework of original whale optimization algorithm (WOA). Simulation experiments are conducted to compare the performance of our method with that of well-known techniques, real-coded genetic algorithm (RCGA), particle swarm optimization (PSO), and original WOA. The results show that the new metaheuristic is superior to the other metaheuristics in terms of attaining the most accurate GFOD approximation. Moreover, the proposed IIR-based GFOD is compared with state-of-the-art GFOD, and observed to save about 50% of implementation complexity. Therefore, our method can be utilized in real-world digital signal processing applications.
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Sridhar, R., and Guruprasad N. "Energy efficient chaotic whale optimization technique for data gathering in wireless sensor network." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 4 (2020): 4176–88. https://doi.org/10.11591/ijece.v10i4.pp4176-4188.
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A Wireless Sensor Network includes the distributed sensor nodes using limited energy, to monitor the physical environments and forward to the sink node. Energy is the major resource in WSN for increasing the network lifetime. Several works have been done in this field but the energy efficient data gathering is still not improved. In order to amend the data gathering with minimal energy consumption, an efficient technique called chaotic whale metaheuristic energy optimized data gathering (CWMEODG) is introduced. The mathematical model called Chaotic tent map is applied to the parameters used in the CWMEODG technique for finding the global optimum solution and fast convergence rate. Simulation of the proposed CWMEODG technique is performed with different parameters such as energy consumption, data packet delivery ratio, data packet loss ratio and delay with deference to dedicated quantity of sensor nodes and number of packets. The consequences discussion shows that the CWMEODG technique progresses the data gathering and network lifetime with minimum delay as well as packet loss than the state-of-the-art methods.
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Xiaoming Shi, Xiaoming Shi, Kun Li Xiaoming Shi, and Liwei Jia Kun Li. "Improved Whale Optimization Algorithm via the Inertia Weight Method Based on the Cosine Function." 網際網路技術學刊 23, no. 7 (2022): 1623–32. http://dx.doi.org/10.53106/160792642022122307016.
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<p>Whale Optimization Algorithm (WOA) is a new meta-heuristic algorithm proposed by Australian scholar Mirjalili Seyedali in 2016 based on the feeding behavior of whales in the ocean. In response to the disadvantages of this algorithm, such as low solution accuracy, slow convergence speed and easy to fall into local optimum, an improved Whale Optimization Algorithm (IWOA) is proposed in this paper. We introduce chaotic mapping in the initialization of the algorithm to keep the whale population with diversity; introduce adaptive inertia weights in the spiral position update of humpback whales to prevent the algorithm from falling into local optimum; and introduce Levy flight in the random search for food of humpback whales to improve the global search ability of the algorithm. In the simulation experiments, we compare the algorithm of this paper with other metaheuristic algorithms in seven classical benchmark test functions, and the numerical results of four indexes, minimum, maximum, mean and standard deviation, in different dimensions, illustrate that the algorithm of this paper has better performance results.</p> <p>&nbsp;</p>
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Ridho, Akhmad, and Alamsyah Alamsyah. "Chaotic Whale Optimization Algorithm in Hyperparameter Selection in Convolutional Neural Network Algorithm." Journal of Advances in Information Systems and Technology 4, no. 2 (2023): 156–69. http://dx.doi.org/10.15294/jaist.v4i2.60595.
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In several previous studies, metaheuristic methods were used to search for CNN hyperparameters. However, this research only focuses on searching for CNN hyperparameters in the type of network architecture, network structure, and initializing network weights. Therefore, in this article, we only focus on searching for CNN hyperparameters with network architecture type, and network structure with additional regularization. In this article, the CNN hyperparameter search with regularization uses CWOA on the MNIST and FashionMNIST datasets. Each dataset consists of 60,000 training data and 10,000 testing data. Then during the research, the training data was only taken 50% of the total data, then the data was divided again by 10% for data validation and the rest for training data. The results of the research on the MNIST CWOA dataset have an error value of 0.023 and an accuracy of 99.63. Then the FashionMNIST CWOA dataset has an error value of 0.23 and an accuracy of 91.36.
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R., Sridhar, and N. Guruprasad. "Energy efficient chaotic whale optimization technique for data gathering in wireless sensor network." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 4 (2020): 4176. http://dx.doi.org/10.11591/ijece.v10i4.pp4176-4188.
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A Wireless Sensor Network includes the distributed sensor nodes using limited energy, to monitor the physical environments and forward to the sink node. Energy is the major resource in WSN for increasing the network lifetime. Several works have been done in this field but the energy efficient data gathering is still not improved. In order to amend the data gathering with minimal energy consumption, an efficient technique called chaotic whale metaheuristic energy optimized data gathering (CWMEODG) is introduced. The mathematical model called Chaotic tent map is applied to the parameters used in the CWMEODG technique for finding the global optimum solution and fast convergence rate. Simulation of the proposed CWMEODG technique is performed with different parameters such as energy consumption, data packet delivery ratio, data packet loss ratio and delay with deference to dedicated quantity of sensor nodes and number of packets. The consequences discussion shows that the CWMEODG technique progresses the data gathering and network lifetime with minimum delay as well as packet loss than the state-of-the-art methods.
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AlRijeb, Mothena Fakhri Shaker, Mohammad Lutfi Othman, Aris Ishak, Mohd Khair Hassan, and Baraa Munqith Albaker. "Whale Optimization Algorithm based on Tent Chaotic Map for Feature Selection in Soft Sensors." Engineering, Technology & Applied Science Research 15, no. 3 (2025): 23537–45. https://doi.org/10.48084/etasr.10965.
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Irrelevant features in data collected from oil refineries affect system performance due to conflicts between normal data and detected faults. Selecting the relevant features from the data leads to better classification results. Optimization algorithms are successfully applied in the feature selection task in many systems. One of the powerful optimization algorithms that is used for feature selection is the Whale Optimization Algorithm (WOA), which is a nature-inspired metaheuristic optimization algorithm that mimics the social behavior of humpback whales. This study presents an improvement to WOA using a tent chaotic map to select the most relevant features and enhance performance. The Tent map mainly applies randomness to generate diversification into the search process and escape from local optima in WOA. The tent map is used for generating the initial population, producing values in control parameters, and updating the position of search agents. The proposed approach combines the tent map with WOA, called TWOA, to enrich population diversity, prevent premature convergence, and speed up convergence. TWOA is applied in a soft sensor with actual data collected from the Salahuddin oil refinery in Iraq. The soft sensor was designed using several stages, including data collection, preprocessing, clustering, feature selection, and classification. The proposed TWOA achieved a higher fault classification result of 99.98% compared to other algorithms.
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Yildirim, Suna, and Bilal Alatas. "Increasing the explainability and success in classification: many-objective classification rule mining based on chaos integrated SPEA2." PeerJ Computer Science 10 (September 6, 2024): e2307. http://dx.doi.org/10.7717/peerj-cs.2307.
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Classification rule mining represents a significant field of machine learning, facilitating informed decision-making through the extraction of meaningful rules from complex data. Many classification methods cannot simultaneously optimize both explainability and different performance metrics at the same time. Metaheuristic optimization-based solutions, inspired by natural phenomena, offer a potential paradigm shift in this field, enabling the development of interpretable and scalable classifiers. In contrast to classical methods, such rule extraction-based solutions are capable of classification by taking multiple purposes into consideration simultaneously. To the best of our knowledge, although there are limited studies on metaheuristic based classification, there is not any method that optimize more than three objectives while increasing the explainability and interpretability for classification task. In this study, data sets are treated as the search space and metaheuristics as the many-objective rule discovery strategy and study proposes a metaheuristic many-objective optimization-based rule extraction approach for the first time in the literature. Chaos theory is also integrated to the optimization method for performance increment and the proposed chaotic rule-based SPEA2 algorithm enables the simultaneous optimization of four different success metrics and automatic rule extraction. Another distinctive feature of the proposed algorithm is that, in contrast to classical random search methods, it can mitigate issues such as correlation and poor uniformity between candidate solutions through the use of a chaotic random search mechanism in the exploration and exploitation phases. The efficacy of the proposed method is evaluated using three distinct data sets, and its performance is demonstrated in comparison with other classical machine learning results.
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Almotairi, Sultan, Elsayed Badr, Mustafa Abdul Salam, and Alshimaa Dawood. "Three Chaotic Strategies for Enhancing the Self-Adaptive Harris Hawk Optimization Algorithm for Global Optimization." Mathematics 11, no. 19 (2023): 4181. http://dx.doi.org/10.3390/math11194181.
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Harris Hawk Optimization (HHO) is a well-known nature-inspired metaheuristic model inspired by the distinctive foraging strategy and cooperative behavior of Harris Hawks. As with numerous other algorithms, HHO is susceptible to getting stuck in local optima and has a sluggish convergence rate. Several techniques have been proposed in the literature to improve the performance of metaheuristic algorithms (MAs) and to tackle their limitations. Chaos optimization strategies have been proposed for many years to enhance MAs. There are four distinct categories of Chaos strategies, including chaotic mapped initialization, randomness, iterations, and controlled parameters. This paper introduces SHHOIRC, a novel hybrid algorithm designed to enhance the efficiency of HHO. Self-adaptive Harris Hawk Optimization using three chaotic optimization methods (SHHOIRC) is the proposed algorithm. On 16 well-known benchmark functions, the proposed hybrid algorithm, authentic HHO, and five HHO variants are evaluated. The computational results and statistical analysis demonstrate that SHHOIRC exhibits notable similarities to other previously published algorithms. The proposed algorithm outperformed the other algorithms by 81.25%, compared to 18.75% for the prior algorithms, by obtaining the best average solutions for 13 benchmark functions. Furthermore, the proposed algorithm is tested on a real-life problem, which is the maximum coverage problem of Wireless Sensor Networks (WSNs), and compared with pure HHO, and two well-known algorithms, Grey Wolf Optimization (GWO) and Whale Optimization Algorithm (WOA). For the maximum coverage experiments, the proposed algorithm demonstrated superior performance, surpassing other algorithms by obtaining the best coverage rates of 95.4375% and 97.125% for experiments 1 and 2, respectively.
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Ayumi, Vina, L. M. Rasdi Rere, Mohamad Ivan Fanany, and Aniati Murni Arymurthy. "Random adjustment - based Chaotic Metaheuristic algorithms for image contrast enhancement." Jurnal Ilmu Komputer dan Informasi 10, no. 2 (2017): 67. http://dx.doi.org/10.21609/jiki.v10i2.375.
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Metaheuristic algorithm is a powerful optimization method, in which it can solve problemsby exploring the ordinarily large solution search space of these instances, that are believed tobe hard in general. However, the performances of these algorithms signicantly depend onthe setting of their parameter, while is not easy to set them accurately as well as completelyrelying on the problem's characteristic. To ne-tune the parameters automatically, manymethods have been proposed to address this challenge, including fuzzy logic, chaos, randomadjustment and others. All of these methods for many years have been developed indepen-dently for automatic setting of metaheuristic parameters, and integration of two or more ofthese methods has not yet much conducted. Thus, a method that provides advantage fromcombining chaos and random adjustment is proposed. Some popular metaheuristic algo-rithms are used to test the performance of the proposed method, i.e. simulated annealing,particle swarm optimization, dierential evolution, and harmony search. As a case study ofthis research is contrast enhancement for images of Cameraman, Lena, Boat and Rice. Ingeneral, the simulation results show that the proposed methods are better than the originalmetaheuristic, chaotic metaheuristic, and metaheuristic by random adjustment.
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Cisternas-Caneo, Felipe, Broderick Crawford, Ricardo Soto, Giovanni Giachetti, Álex Paz, and Alvaro Peña Fritz. "Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics." Mathematics 12, no. 2 (2024): 262. http://dx.doi.org/10.3390/math12020262.
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Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map.
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Akyol, Sinem, Muhammed Yildirim, and Bilal Alatas. "CIDO: Chaotically Initialized Dandelion Optimization for Global Optimization." International Journal of Advanced Networking and Applications 14, no. 06 (2023): 5696–704. http://dx.doi.org/10.35444/ijana.2023.14606.
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Metaheuristic algorithms are widely used for problems in many fields such as security, health, engineering. No metaheuristic algorithm can achieve the optimum solution for all optimization problems. For this, new metaheuristic methods are constantly being proposed and existing ones are being developed. Dandelion Optimizer, one of the most recent metaheuristic algorithms, is biology-based. Inspired by the wind-dependent long-distance flight of the ripening seed of the dandelion plant. It consists of three phases: ascending phase, descending phase and landing phase. In this study, the chaos-based version of Chaotically Initialized Dandelion Optimizer is proposed for the first time in order to prevent Dandelion Optimizer from getting stuck in local solutions and to increase its success in global search. In this way, it is aimed to increase global convergence and to prevent sticking to a local solution. While creating the initial population of the algorithm, six different Chaotically Initialized Dandelion Optimizer algorithms were presented using the Circle, Singer, Chebyshev, Gauss/Mouse, Iterative and Logistic chaotic maps. Two unimodal (Sphere and Schwefel 2.22), two multimodal (Schwefel and Rastrigin) and two fixed-dimension multimodal (Foxholes and Kowalik) quality test functions were used to compare the performances of the algorithms. When the experimental results were analyzed, it was seen that the Chaotically Initialized Dandelion Optimizer algorithms gave successful results compared to the classical Dandelion Optimizer.
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Shafique, Fizza, Muhammad Salman Fakhar, Akhtar Rasool, and Syed Abdul Rahman Kashif. "Analyzing the performance of metaheuristic algorithms in speed control of brushless DC motor: Implementation and statistical comparison." PLOS ONE 19, no. 10 (2024): e0310080. http://dx.doi.org/10.1371/journal.pone.0310080.
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A brushless DC (BLDC) motor is likewise called an electrically commutated motor; because of its long help life, high productivity, smaller size, and higher power output, it has numerous modern applications. These motors require precise rotor orientation for longevity, as they utilize a magnet at the shaft end, detected by sensors to maintain speed control for stability. In modern apparatuses, the corresponding, primary, and subsidiary (proportional-integral) regulator is broadly utilized in controlling the speed of modern machines; however, an ideal and effective controlling strategy is constantly invited. BLDC motor is a complex system having nonlinearity in its dynamic responses which makes primary controllers in efficient. Therefore, this paper implements metaheuristic optimization techniques such as Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Accelerated Particle Swarm Optimization (APSO), Levy Flight Trajectory-Based Whale Optimization Algorithm (LFWOA); moreover, a chaotic map and weight factor are also being applied to modify LFWOA (i.e., CMLFWOA) for optimizing the PI controller to control the speed of BLDC motor. Model of the brushless DC motor using a sensorless control strategy incorporated metaheuristic algorithms is simulated on MATLAB (Matrix Laboratory)/Simulink. The Integral Square Error (ISE) criteria is used to determine the efficiency of the algorithms-based controller. In the latter part of this article after implementing these mentioned techniques a comparative analysis of their results is presented through statistical tests using SPSS (Statistical Package for Social Sciences) software. The results of statistical and analytical tests show the significant supremacy of WOA on others.
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Wen, Xiaodong, Xiangdong Liu, Cunhui Yu, et al. "IOOA: A multi-strategy fusion improved Osprey Optimization Algorithm for global optimization." Electronic Research Archive 32, no. 3 (2024): 2033–74. http://dx.doi.org/10.3934/era.2024093.
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<abstract><p>With the widespread application of metaheuristic algorithms in engineering and scientific research, finding algorithms with efficient global search capabilities and precise local search performance has become a hot topic in research. The osprey optimization algorithm (OOA) was first proposed in 2023, characterized by its simple structure and strong optimization capability. However, practical tests have revealed that the OOA algorithm inevitably encounters common issues faced by metaheuristic algorithms, such as the tendency to fall into local optima and reduced population diversity in the later stages of the algorithm's iterations. To address these issues, a multi-strategy fusion improved osprey optimization algorithm is proposed (IOOA). First, the characteristics of various chaotic mappings were thoroughly explored, and the adoption of Circle chaotic mapping to replace pseudo-random numbers for population initialization improvement was proposed, increasing initial population diversity and improving the quality of initial solutions. Second, a dynamically adjustable elite guidance mechanism was proposed to dynamically adjust the position updating method according to different stages of the algorithm's iteration, ensuring the algorithm maintains good global search capabilities while significantly increasing the convergence speed of the algorithm. Lastly, a dynamic chaotic weight factor was designed and applied in the development stage of the original algorithm to enhance the algorithm's local search capability and improve the convergence accuracy of the algorithm. To fully verify the effectiveness and practical engineering applicability of the IOOA algorithm, simulation experiments were conducted using 21 benchmark test functions and the CEC-2022 benchmark functions, and the IOOA algorithm was applied to the LSTM power load forecasting problem as well as two engineering design problems. The experimental results show that the IOOA algorithm possesses outstanding global optimization performance in handling complex optimization problems and broad applicability in practical engineering applications.</p></abstract>
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Touabi, Cilina, Abderrahmane Ouadi, Hamid Bentarzi, and Abdelmadjid Recioui. "Photovoltaic Panel Parameter Estimation Enhancement Using a Modified Quasi-Opposition-Based Killer Whale Optimization Technique." Sustainability 17, no. 11 (2025): 5161. https://doi.org/10.3390/su17115161.
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Photovoltaic (PV) energy generation has seen rapid growth in recent years due to its sustainability and environmental benefits. However, accurately identifying PV panel parameters is crucial for enhancing system performance, especially under varying environmental conditions. This study presents an enhanced approach for estimating PV panel parameters using a Modified Quasi-Opposition-Based Killer Whale Optimization (MQOB-KWO) technique. The research aims to improve parameter extraction accuracy by optimizing the one-diode model (ODM), a widely used representation of PV cells, using a modified metaheuristic optimization technique. The proposed algorithm leverages a Quasi-Opposition-Based Learning (QOBL) mechanism to enhance search efficiency and convergence speed. The methodology involves implementing the MQOB-KWO in MATLAB R2021a and evaluating its effectiveness through experimental I-V data from two unlike photovoltaic panels. The findings are contrasted to established optimization techniques from the literature, such as the original Killer Whale Optimization (KWO), Improved Opposition-Based Particle Swarm Optimization (IOB-PSO), Improved Cuckoo Search Algorithm (ImCSA), and Chaotic Improved Artificial Bee Colony (CIABC). The findings demonstrate that the proposed MQOB-KWO achieves superior accuracy with the lowest Root Mean Square Error (RMSE) compared to other methods, and the lowest error rates (Root Mean Square Error—RMSE, and Integral Absolute Error—IAE) compared to the original KWO, resulting in a better value of the coefficient of determination (R2), hence effectively capturing PV module characteristics. Additionally, the algorithm shows fast convergence, making it suitable for real-time PV system modeling. The study confirms that the proposed optimization technique is a reliable and efficient tool for improving PV parameter estimation, contributing to better system efficiency and operational performance.
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Ramana, Ramana, K. Kavitha, Smita Rani Sahu, B. Manideep, T. Ravi Kumar, and Nibedan Panda. "An Improved Chaotic Grey Wolf Optimization Algorithm (CGWO)." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 11s (2023): 341–48. http://dx.doi.org/10.17762/ijritcc.v11i11s.8161.
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Grey Wolf Optimization (GWO) is a new type of swarm-based technique for dealing with realistic engineering design constraints and unconstrained problems in the field of metaheuristic research. Swarm-based techniques are a type of population-based algorithm inspired by nature that can produce low-cost, quick, and dependable solutions to a wider variety of complications. It is the best choice when it can achieve faster convergence by avoiding local optima trapping. This work incorporates chaos theory with the standard GWO to improve the algorithm's performance due to the ergodicity of chaos. The proposed methodology is referred to as Chaos-GWO (CGWO). The CGWO improves the search space's exploration and exploitation abilities while avoiding local optima trapping. Using different benchmark functions, five distinct chaotic map functions are examined, and the best chaotic map is considered to have great mobility and ergodicity characteristics. The results demonstrated that the best performance comes from using the suitable chaotic map function, and that CGWO can clearly outperform standard GWO.
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Shrestha, Keshika, H. M. Jabed Omur Rifat, Uzzal Biswas, Jun-Jiat Tiang, and Abdullah-Al Nahid. "Predicting the Recurrence of Differentiated Thyroid Cancer Using Whale Optimization-Based XGBoost Algorithm." Diagnostics 15, no. 13 (2025): 1684. https://doi.org/10.3390/diagnostics15131684.
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Background/Objectives: Differentiated Thyroid Cancer (DTC), comprising papillary and follicular carcinomas, is the most common type of thyroid cancer. This is highly infectious and increasing at a higher rate. Some patients experience recurrence even after undergoing successful treatment. Early signs of recurrence can be hard to identify, and the existing health care system cannot always identify it on time. Therefore, predicting its recurrence accurately and in its early stage is a significant clinical challenge. Numerous advanced technologies, such as machine learning, are being used to overcome this clinical challenge. Thus, this study presents a novel approach for predicting the recurrence of DTC. The key objective is to improve the prediction accuracy through hyperparameter optimization. Methods: In order to achieve this, we have used a metaheuristic algorithm, the whale optimization algorithm (WOA) and its modified version. The modifications that we introduced in the original WOA algorithm are a piecewise linear chaotic map for population initialization and inertia weight. Both of our algorithms optimize the hyperparameters of the Extreme Gradient Boosting (XGBoost) model to increase the overall performance. The proposed algorithms were applied to the dataset collected from the University of California, Irvine (UCI), Machine Learning Repository to predict the chances of recurrence for DTC. This dataset consists of 383 samples with a total of 16 features. Each feature captures the critical medical and demographic information. Results: The model has shown an accuracy of 99% when optimized with WOA and 97% accuracy when optimized with the modified WOA. Conclusions: Furthermore, we have compared our work with other innovative works and validated the performance of our model for the prediction of DTC recurrence.
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Assiri, Adel Saad. "On the performance improvement of Butterfly Optimization approaches for global optimization and Feature Selection." PLOS ONE 16, no. 1 (2021): e0242612. http://dx.doi.org/10.1371/journal.pone.0242612.
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Butterfly Optimization Algorithm (BOA) is a recent metaheuristics algorithm that mimics the behavior of butterflies in mating and foraging. In this paper, three improved versions of BOA have been developed to prevent the original algorithm from getting trapped in local optima and have a good balance between exploration and exploitation abilities. In the first version, Opposition-Based Strategy has been embedded in BOA while in the second Chaotic Local Search has been embedded. Both strategies: Opposition-based & Chaotic Local Search have been integrated to get the most optimal/near-optimal results. The proposed versions are compared against original Butterfly Optimization Algorithm (BOA), Grey Wolf Optimizer (GWO), Moth-flame Optimization (MFO), Particle warm Optimization (PSO), Sine Cosine Algorithm (SCA), and Whale Optimization Algorithm (WOA) using CEC 2014 benchmark functions and 4 different real-world engineering problems namely: welded beam engineering design, tension/compression spring, pressure vessel design, and Speed reducer design problem. Furthermore, the proposed approches have been applied to feature selection problem using 5 UCI datasets. The results show the superiority of the third version (CLSOBBOA) in achieving the best results in terms of speed and accuracy.
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Assiri, Adel Saad. "On the performance improvement of Butterfly Optimization approaches for global optimization and Feature Selection." PLOS ONE 16, no. 1 (2021): e0242612. http://dx.doi.org/10.1371/journal.pone.0242612.
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Butterfly Optimization Algorithm (BOA) is a recent metaheuristics algorithm that mimics the behavior of butterflies in mating and foraging. In this paper, three improved versions of BOA have been developed to prevent the original algorithm from getting trapped in local optima and have a good balance between exploration and exploitation abilities. In the first version, Opposition-Based Strategy has been embedded in BOA while in the second Chaotic Local Search has been embedded. Both strategies: Opposition-based & Chaotic Local Search have been integrated to get the most optimal/near-optimal results. The proposed versions are compared against original Butterfly Optimization Algorithm (BOA), Grey Wolf Optimizer (GWO), Moth-flame Optimization (MFO), Particle warm Optimization (PSO), Sine Cosine Algorithm (SCA), and Whale Optimization Algorithm (WOA) using CEC 2014 benchmark functions and 4 different real-world engineering problems namely: welded beam engineering design, tension/compression spring, pressure vessel design, and Speed reducer design problem. Furthermore, the proposed approches have been applied to feature selection problem using 5 UCI datasets. The results show the superiority of the third version (CLSOBBOA) in achieving the best results in terms of speed and accuracy.
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Abbassi, Rabeh, Salem Saidi, Shabana Urooj, Bilal Naji Alhasnawi, Mohamad A. Alawad, and Manoharan Premkumar. "An Accurate Metaheuristic Mountain Gazelle Optimizer for Parameter Estimation of Single- and Double-Diode Photovoltaic Cell Models." Mathematics 11, no. 22 (2023): 4565. http://dx.doi.org/10.3390/math11224565.
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Accurate parameter estimation is crucial and challenging for the design and modeling of PV cells/modules. However, the high degree of non-linearity of the typical I–V characteristic further complicates this task. Consequently, significant research interest has been generated in recent years. Currently, this trend has been marked by a noteworthy acceleration, mainly due to the rise of swarm intelligence and the rapid progress of computer technology. This paper proposes a developed Mountain Gazelle Optimizer (MGO) to generate the best values of the unknown parameters of PV generation units. The MGO mimics the social life and hierarchy of mountain gazelles in the wild. The MGO was compared with well-recognized recent algorithms, which were the Grey Wolf Optimizer (GWO), the Squirrel Search Algorithm (SSA), the Differential Evolution (DE) algorithm, the Bat–Artificial Bee Colony Optimizer (BABCO), the Bat Algorithm (BA), Multiswarm Spiral Leader Particle Swarm Optimization (M-SLPSO), the Guaranteed Convergence Particle Swarm Optimization algorithm (GCPSO), Triple-Phase Teaching–Learning-Based Optimization (TPTLBO), the Criss-Cross-based Nelder–Mead simplex Gradient-Based Optimizer (CCNMGBO), the quasi-Opposition-Based Learning Whale Optimization Algorithm (OBLWOA), and the Fractional Chaotic Ensemble Particle Swarm Optimizer (FC-EPSO). The experimental findings and statistical studies proved that the MGO outperformed the competing techniques in identifying the parameters of the Single-Diode Model (SDM) and the Double-Diode Model (DDM) PV models of Photowatt-PWP201 (polycrystalline) and STM6-40/36 (monocrystalline). The RMSEs of the MGO on the SDM and the DDM of Photowatt-PWP201 and STM6-40/36 were 2.042717 ×10−3, 1.387641 ×10−3, 1.719946 ×10−3, and 1.686104 ×10−3, respectively. Overall, the identified results highlighted that the MGO-based approach featured a fast processing time and steady convergence while retaining a high level of accuracy in the achieved solution.
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Nyandieka, Owen M., and Davies R. Segera. "A Chaotic Multi-Objective Runge–Kutta Optimization Algorithm for Optimized Circuit Design." Mathematical Problems in Engineering 2023 (December 7, 2023): 1–24. http://dx.doi.org/10.1155/2023/6691214.
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Circuit design plays a pivotal role in engineering, ensuring the creation of efficient, reliable, and cost-effective electronic devices. The complexity of modern circuit design problems has led to the exploration of multi-objective optimization techniques for circuit design optimization, as traditional optimization tools fall short in handling such problems. While metaheuristic algorithms, especially genetic algorithms, have demonstrated promise, their susceptibility to premature convergence poses challenges. This paper proposes a pioneering approach, the chaotic multi-objective Runge–Kutta algorithm (CMRUN), for circuit design optimization, building upon the Runge–Kutta optimization algorithm. By infusing chaos into the core RUN structure, a refined balance between exploration and exploitation is obtained, critical for addressing complex optimization landscapes, enabling the algorithm to navigate nonlinear and nonconvex optimization challenges effectively. This approach is extended to accommodate multiple objectives, ultimately generating Pareto Fronts for the multiple circuit design goals. The performance of CMRUN is rigorously evaluated against 11 multiobjective algorithms, encompassing 15 benchmark test functions and practical circuit design scenarios. The findings of this study underscore the efficiency and real-world applicability of CMRUN, offering valuable insights for tailoring optimization algorithms to the real-world circuit design challenges.
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Tang, Junjie, Huafei Wang, Mingyue Zhao, Ping Sun, Yutao Hao, and Zhiyuan Zhu. "Weed Detection in Lily Fields Using YOLOv7 Optimized by Chaotic Harris Hawks Algorithm for Underground Resource Competition." Symmetry 17, no. 3 (2025): 370. https://doi.org/10.3390/sym17030370.
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Lilies, a key cash crop in Lanzhou, China, widely planted in coal-based fields, cultivated fields, and gardens, face significant yield and quality reduction due to weed infestation, which competes for essential nutrients, water, and light. To address this challenge, we propose an advanced weed detection method that combines symmetry-based convolutional neural networks with metaheuristic optimization. A dedicated weed detection dataset is constructed through extensive field investigation, data collection, and annotation. To enhance detection efficiency, we introduce an optimized YOLOv7-Tiny model, integrating dynamic pruning and knowledge distillation, which reduces computational complexity while maintaining high accuracy. Additionally, a novel Chaotic Harris Hawks Optimization (CHHO) algorithm, incorporating chaotic mapping initialization and differential evolution, is developed to fine-tune YOLOv7-Tiny parameters and activation functions. Experimental results demonstrate that the optimized YOLOv7-Tiny achieves a detection accuracy of 92.53% outperforming traditional models while maintaining efficiency. This study provides a high-performance, lightweight, and scalable solution for real-time precision weed management in lily fields, offering valuable insights for agricultural automation and smart farming applications.
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Zhao, WanRu, Yan Liu, JianHui Li, TianNing Zhu, KunXia Zhao, and Kui Hu. "A Wild Horse Optimization algorithm with chaotic inertia weights and its application in linear antenna array synthesis." PLOS ONE 19, no. 7 (2024): e0304971. http://dx.doi.org/10.1371/journal.pone.0304971.
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Antennas play a crucial role in designing an efficient communication system. However, reducing the maximum sidelobe level (SLL) of the beam pattern is a crucial challenge in antenna arrays. Pattern synthesis in smart antennas is a major area of research because of its widespread application across various radar and communication systems. This paper presents an effective technique to minimize the SLL and thus improve the radiation pattern of the linear antenna array (LAA) using the chaotic inertia-weighted Wild Horse optimization (IERWHO) algorithm. The wild horse optimizer (WHO) is a new metaheuristic algorithm based on the social behavior of wild horses. The IERWHO algorithm is an improved Wild Horse optimization (WHO) algorithm that combines the concepts of chaotic sequence factor, nonlinear factor, and inertia weights factor. In this paper, the method is applied for the first time in antenna array synthesis by optimizing parameters such as inter-element spacing and excitation to minimize the SLL while keeping other constraints within the boundary limits, while ensuring that the performance is not affected. For performance evaluation, the simulation tests include 12 benchmark test functions and 12 test functions to verify the effectiveness of the improvement strategies. According to the encouraging research results in this paper, the IERWHO algorithm proposed has a place in the field of optimization.
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Zúñiga-Valenzuela, Pablo, Broderick Crawford, Felipe Cisternas-Caneo, et al. "Binary Chaotic White Shark Optimizer for the Unicost Set Covering Problem." Mathematics 13, no. 13 (2025): 2175. https://doi.org/10.3390/math13132175.
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The Unicost Set Covering Problem (USCP), an NP-hard combinatorial optimization challenge, demands efficient methods to minimize the number of sets covering a universe. This study introduces a binary White Shark Optimizer (WSO) enhanced with V3 transfer functions, elitist binarization, and chaotic maps. To evaluate algorithm performance, we employ the Relative Percentage Deviation (RPD), which measures the percentage difference between the obtained solutions and optimal values. Our approach achieves outstanding results on six benchmark instances: WSO-ELIT_CIRCLE delivers an RPD of 0.7% for structured instances, while WSO-ELIT_SINU attains an RPD of 0.96% in cyclic instances, showing empirical improvements over standard methods. Experimental results demonstrate that circle chaotic maps excel in structured problems, while sinusoidal maps perform optimally in cyclic instances, with observed improvements up to 7.31% over baseline approaches. Diversity and convergence analyses show structured instances favor exploitation-driven strategies, whereas cyclic instances benefit from adaptive exploration. This work establishes WSO as a robust metaheuristic for USCP, with applications in resource allocation and network design.
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Cicek, Orhan, Yusuf Bahri Özçelik, and Aytaç Altan. "A New Approach Based on Metaheuristic Optimization Using Chaotic Functional Connectivity Matrices and Fractal Dimension Analysis for AI-Driven Detection of Orthodontic Growth and Development Stage." Fractal and Fractional 9, no. 3 (2025): 148. https://doi.org/10.3390/fractalfract9030148.
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Accurate identification of growth and development stages is critical for orthodontic diagnosis, treatment planning, and post-treatment retention. While hand–wrist radiographs are the traditional gold standard, the associated radiation exposure necessitates alternative imaging methods. Lateral cephalometric radiographs, particularly the maturation stages of the second, third, and fourth cervical vertebrae (C2, C3, and C4), have emerged as a promising alternative. However, the nonlinear dynamics of these images pose significant challenges for reliable detection. This study presents a novel approach that integrates chaotic functional connectivity (FC) matrices and fractal dimension analysis to address these challenges. The fractal dimensions of C2, C3, and C4 vertebrae were calculated from 945 lateral cephalometric radiographs using three methods: fast Fourier transform (FFT), box counting, and a pre-processed FFT variant. These results were used to construct chaotic FC matrices based on correlations between the calculated fractal dimensions. To effectively model the nonlinear dynamics, chaotic maps were generated, representing a significant advance over traditional methods. Feature selection was performed using a wrapper-based approach combining k-nearest neighbors (kNN) and the Puma optimization algorithm, which efficiently handles the chaotic and computationally complex nature of cervical vertebrae images. This selection minimized the number of features while maintaining high classification performance. The resulting AI-driven model was validated with 10-fold cross-validation and demonstrated high accuracy in identifying growth stages. Our results highlight the effectiveness of integrating chaotic FC matrices and AI in orthodontic practice. The proposed model, with its low computational complexity, successfully handles the nonlinear dynamics in C2, C3, and C4 vertebral images, enabling accurate detection of growth and developmental stages. This work represents a significant step in the detection of growth and development stages and provides a practical and effective solution for future orthodontic diagnosis.
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Sulianto, Sulianto. "Kalibrasi Parameter Model Tangki Berbasis Metaheuristik untuk Transformasi Seri Data Hujan Menjadi Limpasan Periode Harian." JURNAL TEKNIK HIDRAULIK 15, no. 2 (2024): 113–28. https://doi.org/10.32679/jth.v15i2.789.
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The fundamental weakness of the Tank model are the large number of parameters and their continuous values, which make it ineffective for solving practical problems. This article proposes a metaheuristic-based automatic calibration method to enhance the Tank model’s performance and applicability in transforming rainfall data series into runoff in a watershed. The metaheuristic methods involved include the Differential Evolution (DE) algorithm, Particle Swam Optimization (PSO), synthesis of chaotic search-opposition based learning-differential evolution-quantum mechanism (CODEQ) algorithm and Shuffled Complex Evolution (SCE). The models resulting from the integration of the Tank model with these metaheuristic methods are called the Tank-DE, Tank-PSO, Tank-CODEQ and Tank-SCE models. The four models were tested in the Welang Watershed (473.39 Km2), located in Pasuruan Regency, East Java, using a 15-year hydroclimatology dataset from 2006 to 2020. The 2006-2010 dataset served as the training dataset forTank model parameter calibration, while the 2011-2020 dataset was used for model validation. Calibration results show that all models achieved an accuracy level equivalent to an average RMSE of 0.05 m3/s. However, during validation, there were slight differences in high flow response results. Compared to the training dataset, the model output responded effectively to both low and high flows but tended to produce slightly higher discharge at intermediate flows, with an average difference of 1.33 m3/s. When compared to the test dataset, the model outputs tended to overestimate high flow rates (average difference of 1.63 m3/s) and underestimated low flow rates, with minor deviations.Keywords: tank model, metaheuristic, transformation, rainfall-streamflow, Welang Watershed.
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Zhao, Jianping, Damin Zhang, Qing He, and Lun Li. "A Hybrid-Strategy-Improved Dragonfly Algorithm for the Parameter Identification of an SDM." Sustainability 15, no. 15 (2023): 11791. http://dx.doi.org/10.3390/su151511791.
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As primary components of solar power applications, photovoltaic cells have promising development prospects. Due to the characteristics of PV cells, the identification of parameters for circuit models has become a research focus. Among the various methods of parameter estimations, metaheuristic algorithms have attracted significant interest. In this paper, a hybrid-strategy-improved dragonfly algorithm (HIDA) is proposed to meet the demand for high parameter-identification accuracy. Tent chaotic mapping generates the initial position of individual dragonflies and aids in increasing the population diversity. Individual dragonflies can adapt their updated positions to various scenarios using the adjacent position decision approach. The whale optimization algorithm fusion strategy incorporates the spiral bubble-net attack mechanism into the dragonfly algorithm to improve the optimization-seeking precision. Moreover, the optimal position perturbation strategy reduces the frequency of the HIDA falling into local optima from the perspective of an optimal solution. The effectiveness of the HIDA was evaluated using function test experiments and engineering application experiments. Seven unimodal and five multimodal benchmark test functions in 50, 120, and 200 dimensions were used for the function test experiments, while five CEC2013 functions and seven CEC2014 functions were also selected for the experiments. In the engineering application experiments, the HIDA was applied to the single-diode model (SDM), engineering model, double-diode model (DDM), triple-diode model (TDM), and STM-40/36 parameter identification, as well as to the solution of seven classical engineering problems. The experimental results all verify the good performance of the HIDA with high stability, a wide application range, and high accuracy.
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Alanazi, Abdulaziz, and Tarek I. Alanazi. "Multi-Objective Framework for Optimal Placement of Distributed Generations and Switches in Reconfigurable Distribution Networks: An Improved Particle Swarm Optimization Approach." Sustainability 15, no. 11 (2023): 9034. http://dx.doi.org/10.3390/su15119034.
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Distribution network operators and planners face a significant challenge in optimizing planning and scheduling strategies to enhance distribution network efficiency. Using improved particle swarm optimization (IPSO), this paper presents an effective method for improving distribution system performance by concurrently deploying remote-controlled sectionalized switches, distributed generation (DG), and optimal network reconfiguration. The proposed optimization problem’s main objectives are to reduce switch costs, maximize reliability, reduce power losses, and enhance voltage profiles. An analytical reliability evaluation is proposed for DG-enhanced reconfigurable distribution systems, considering both switching-only and repairs and switching interruptions. The problem is formulated in the form of a mixed integer nonlinear programming problem, which is known as an NP-hard problem. To solve the problem effectively while improving conventional particle swarm optimization (PSO) exploration and exploitation capabilities, a novel chaotic inertia weight and crossover operation mechanism is developed here. It is demonstrated that IPSO can be applied to both single- and multi-objective optimization problems, where distribution systems’ optimization strategies are considered sequentially and simultaneously. Furthermore, IPSO’s effectiveness is validated and evaluated against well-known state-of-the-art metaheuristic techniques for optimizing IEEE 69-node distribution systems.
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Chhabra, Amit, Sudip Kumar Sahana, Nor Samsiah Sani, Ali Mohammadzadeh, and Hasmila Amirah Omar. "Energy-Aware Bag-Of-Tasks Scheduling in the Cloud Computing System Using Hybrid Oppositional Differential Evolution-Enabled Whale Optimization Algorithm." Energies 15, no. 13 (2022): 4571. http://dx.doi.org/10.3390/en15134571.
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Bag-of-Tasks (BoT) scheduling over cloud computing resources called Cloud Bag-of-Tasks Scheduling (CBS) problem, which is a well-known NP-hard optimization problem. Whale Optimization Algorithm (WOA) is an effective method for CBS problems, which still requires further improvement in exploration ability, solution diversity, convergence speed, and ensuring adequate exploration–exploitation tradeoff to produce superior scheduling solutions. In order to remove WOA limitations, a hybrid oppositional differential evolution-enabled WOA (called h-DEWOA) approach is introduced to tackle CBS problems to minimize workload makespan and energy consumption. The proposed h-DEWOA incorporates chaotic maps, opposition-based learning (OBL), differential evolution (DE), and a fitness-based balancing mechanism into the standard WOA method, resulting in enhanced exploration, faster convergence, and adequate exploration–exploitation tradeoff throughout the algorithm execution. Besides this, an efficient allocation heuristic is added to the h-DEWOA method to improve resource assignment. CEA-Curie and HPC2N real cloud workloads are used for performance evaluation of scheduling algorithms using the CloudSim simulator. Two series of experiments have been conducted for performance comparison: one with WOA-based heuristics and another with non-WOA-based metaheuristics. Experimental results of the first series of experiments reveal that the h-DEWOA approach results in makespan improvement in the range of 5.79–13.38% (for CEA-Curie workloads), 5.03–13.80% (for HPC2N workloads), and energy consumption in the range of 3.21–14.70% (for CEA-Curie workloads) and 10.84–19.30% (for HPC2N workloads) over well-known WOA-based metaheuristics. Similarly, h-DEWOA also resulted in significant performance in comparison with recent state-of-the-art non-WOA-based metaheuristics in the second series of experiments. Statistical tests and box plots also revealed the robustness of the proposed h-DEWOA algorithm.
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Liu, Xiang, Min Tian, Jie Zhou, and Jinyan Liang. "An efficient coverage method for SEMWSNs based on adaptive chaotic Gaussian variant snake optimization algorithm." Mathematical Biosciences and Engineering 20, no. 2 (2022): 3191–215. http://dx.doi.org/10.3934/mbe.2023150.
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<abstract> <p>Soil element monitoring wireless sensor networks (SEMWSNs) are widely used in soil element monitoring agricultural activities. SEMWSNs monitor changes in soil elemental content during agriculture products growing through nodes. Based on the feedback from the nodes, farmers adjust irrigation and fertilization strategies on time, thus promoting the economic growth of crops. The critical issue in SEMWSNs coverage studies is to achieve maximum coverage of the entire monitoring field by adopting a smaller number of sensor nodes. In this study, a unique adaptive chaotic Gaussian variant snake optimization algorithm (ACGSOA) is proposed for solving the above problem, which also has the advantages of solid robustness, low algorithmic complexity, and fast convergence. A new chaotic operator is proposed in this paper to optimize the position parameters of individuals, enhancing the convergence speed of the algorithm. Moreover, an adaptive Gaussian variant operator is also designed in this paper to effectively avoid SEMWSNs from falling into local optima during the deployment process. Simulation experiments are designed to compare ACGSOA with other widely used metaheuristics, namely snake optimizer (SO), whale optimization algorithm (WOA), artificial bee colony algorithm (ABC), and fruit fly optimization algorithm (FOA). The simulation results show that the performance of ACGSOA has been dramatically improved. On the one hand, ACGSOA outperforms other methods in terms of convergence speed, and on the other hand, the coverage rate is improved by 7.20%, 7.32%, 7.96%, and 11.03% compared with SO, WOA, ABC, and FOA, respectively.</p> </abstract>
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Li, Yonglin, Zhao Liu, Changtao Kan, Rongfei Qiao, Yue Yu, and Changgang Li. "A Virtual Power Plant-Integrated Proactive Voltage Regulation Framework for Urban Distribution Networks: Enhanced Termite Life Cycle Optimization Algorithm and Dynamic Coordination." Algorithms 18, no. 5 (2025): 251. https://doi.org/10.3390/a18050251.
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Amid global decarbonization mandates, urban distribution networks (UDNs) face escalating voltage volatility due to proliferating distributed energy resources (DERs) and emerging loads (e.g., 5G base stations and data centers). While virtual power plants (VPPs) and network reconfiguration mitigate operational risks, extant methods inadequately model load flexibility and suffer from algorithmic stagnation in non-convex optimization. This study proposes a proactive voltage control framework addressing these gaps through three innovations. First, a dynamic cyber-physical load model quantifies 5G/data centers’ demand elasticity as schedulable VPP resources. Second, an Improved Termite Life Cycle Optimizer (ITLCO) integrates chaotic initialization and quantum tunneling to evade local optima, enhancing convergence in high-dimensional spaces. Third, a hierarchical control architecture coordinates the VPP reactive dispatch and topology adaptation via mixed-integer programming. The effectiveness and economic viability of the proposed strategy are validated through multi-scenario simulations of the modified IEEE 33-bus system (represented by 12.66 kV, it is actually oriented to a broader voltage scene). These advancements establish a scalable paradigm for UDNs to harness DERs and next-gen loads while maintaining grid stability under net-zero transitions. The methodology bridges theoretical gaps in flexibility modeling and metaheuristic optimization, offering utilities a computationally efficient tool for real-world implementation.
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Khodadadi, Hamed, and Shima Nazem. "Improving cancer detection through computer-aided diagnosis: A comprehensive analysis of nonlinear and texture features in breast thermograms." PLOS One 20, no. 5 (2025): e0322934. https://doi.org/10.1371/journal.pone.0322934.
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Breast cancer is a significant health issue for women, characterized by its high rates of mortality and sickness. However, its early detection is crucial for improving patient outcomes. Thermography, which measures temperature variations between healthy and cancerous tissues, offers a promising approach for early diagnosis. This study proposes a novel method for analyzing breast thermograms. The method segments suspicious masses, extracts relevant features, and classifies them as benign or malignant. While the chaotic indices, including Lyapunov Exponent (LE), Fractal Dimension (FD), Kolmogorov–Sinai Entropy (KSE), and Correlation Dimension (CD), are employed for nonlinear analysis, the Gray-Level Co-occurrence Matrix (GLCM) method utilized for extracting the texture features. The effectiveness of the proposed approach is enhanced by integrating texture and complexity features. Besides, to optimize feature selection and reduce redundancy, a metaheuristic optimization technique called Non-Dominated Sorting Genetic Algorithm (NSGA III) is applied. The proposed method utilizes various machine learning algorithms, including Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Linear Discriminant Analysis (LDA), Pattern recognition Network (Pat net), and Fitting neural Network (Fit net), for classification. ten-fold cross-validation ensures robust performance evaluation. The achieved accuracy of 98.65%, emphasizes the superior performance of the proposed method in thermograms breast cancer diagnosis.
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El-Shorbagy, M. A., and Adel M. El-Refaey. "A hybrid genetic–firefly algorithm for engineering design problems." Journal of Computational Design and Engineering 9, no. 2 (2022): 706–30. http://dx.doi.org/10.1093/jcde/qwac013.
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Abstract Firefly algorithm (FA) is a new random swarm search optimization algorithm that is modeled after movement and the mutual attraction of flashing fireflies. The number of fitness comparisons and attractions in the FA varies depending on the attraction model. A large number of attractions can induce search oscillations, while a small number of attractions can cause early convergence and a large number of fitness comparisons that can add to the computational time complexity. This study aims to offer H-GA–FA, a hybrid algorithm that combines two metaheuristic algorithms, the genetic algorithm (GA) and the FA, to overcome the flaws of the FA and combine the benefits of both algorithms to solve engineering design problems (EDPs). In this hybrid system, which blends the concepts of GA and FA, individuals are formed in the new generation not only by GA processes but also by FA mechanisms to prevent falling into local optima, introduce sufficient diversity of the solutions, and make equilibrium between exploration/exploitation trends. On the other hand, to deal with the violation of constraints, a chaotic process was utilized to keep the solutions feasible. The proposed hybrid algorithm H-GA–FA is tested by well-known test problems that contain a set of 17 unconstrained multimodal test functions and 7 constrained benchmark problems, where the results have confirmed the superiority of H-GA–FA overoptimization search methods. Finally, the performance of the H-GA–FA is also investigated on many EDPs. Computational results show that the H-GA–FA algorithm is competitive and better than other optimization algorithms that solve EDPs.
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Kaur, Gaganpreet, and Sankalap Arora. "Chaotic whale optimization algorithm." Journal of Computational Design and Engineering 5, no. 3 (2018): 275–84. http://dx.doi.org/10.1016/j.jcde.2017.12.006.
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Abstract The Whale Optimization Algorithm (WOA) is a recently developed meta-heuristic optimization algorithm which is based on the hunting mechanism of humpback whales. Similarly to other meta-heuristic algorithms, the main problem faced by WOA is slow convergence speed. So to enhance the global convergence speed and to get better performance, this paper introduces chaos theory into WOA optimization process. Various chaotic maps are considered in the proposed chaotic WOA (CWOA) methods for tuning the main parameter of WOA which helps in controlling exploration and exploitation. The proposed CWOA methods are benchmarked on twenty well-known test functions. The results prove that the chaotic maps (especially Tent map) are able to improve the performance of WOA. Highlights Chaos has been introduced into WOA to improve its performance. Ten chaotic maps have been investigated to tune the key parameter ‘ p’ of WOA. The proposed CWOA is validated on a set of twenty benchmark functions. The proposed CWOA is validated on a set of twenty benchmark functions. Statistical results suggest that CWOA has better reliability of global optimality.
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Tian, Tao, Zhiwei Liang, Yuanfei Wei, Qifang Luo, and Yongquan Zhou. "Hybrid Whale Optimization with a Firefly Algorithm for Function Optimization and Mobile Robot Path Planning." Biomimetics 9, no. 1 (2024): 39. http://dx.doi.org/10.3390/biomimetics9010039.
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With the wide application of mobile robots, mobile robot path planning (MRPP) has attracted the attention of scholars, and many metaheuristic algorithms have been used to solve MRPP. Swarm-based algorithms are suitable for solving MRPP due to their population-based computational approach. Hence, this paper utilizes the Whale Optimization Algorithm (WOA) to address the problem, aiming to improve the solution accuracy. Whale optimization algorithm (WOA) is an algorithm that imitates whale foraging behavior, and the firefly algorithm (FA) is an algorithm that imitates firefly behavior. This paper proposes a hybrid firefly-whale optimization algorithm (FWOA) based on multi-population and opposite-based learning using the above algorithms. This algorithm can quickly find the optimal path in the complex mobile robot working environment and can balance exploitation and exploration. In order to verify the FWOA’s performance, 23 benchmark functions have been used to test the FWOA, and they are used to optimize the MRPP. The FWOA is compared with ten other classical metaheuristic algorithms. The results clearly highlight the remarkable performance of the Whale Optimization Algorithm (WOA) in terms of convergence speed and exploration capability, surpassing other algorithms. Consequently, when compared to the most advanced metaheuristic algorithm, FWOA proves to be a strong competitor.
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Manish, Chhabra Rajesh E. "Optimizing cloud tasks scheduling based on the hybridization of darts game hypothesis and beluga whale optimization technique." Indonesian Journal of Electrical Engineering and Computer Science 38, no. 2 (2025): 1195–207. https://doi.org/10.11591/ijeecs.v38.i2.pp1195-1207.
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This paper presents the hybridization of two metaheuristic algorithms which belongs to different categories, for optimizing the tasks scheduling in cloud environment. Hybridization of a game-based metaheuristic algorithm namely, darts game optimizer (DGO), with a swarm-based metaheuristic algorithm namely, beluga whale optimization (BWO), yields to the evolution of a new algorithm known as “hybrid darts game hypothesis – beluga whale optimization” (hybrid DGH-BWO) algorithm. Task scheduling optimization in cloud environment is a critical process and is determined as a non-deterministic polynomial (NP)-hard problem. Metaheuristic techniques are high-level optimization algorithms, designed to solve a wide range of complex, optimization problems. In the hybridization of DGO and BWO metaheuristic algorithms, expedition and convergence capabilities of both algorithms are combined together, and this enhances the chances of finding the higher-quality solutions compared to using a single algorithm alone. Other benefits of the proposed algorithm: increased overall efficiency, as “hybrid DGH-BWO” algorithm can exploit the complementary strengths of both DGO and BWO algorithms to converge to optimal solutions more quickly. Wide range of diversity is also introduced in the search space and this helps in avoiding getting trapped in local optima.
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Altay, Osman, and Elif Varol Altay. "A novel chaotic transient search optimization algorithm for global optimization, real-world engineering problems and feature selection." PeerJ Computer Science 9 (August 22, 2023): e1526. http://dx.doi.org/10.7717/peerj-cs.1526.
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Metaheuristic optimization algorithms manage the search process to explore search domains efficiently and are used efficiently in large-scale, complex problems. Transient Search Algorithm (TSO) is a recently proposed physics-based metaheuristic method inspired by the transient behavior of switched electrical circuits containing storage elements such as inductance and capacitance. TSO is still a new metaheuristic method; it tends to get stuck with local optimal solutions and offers solutions with low precision and a sluggish convergence rate. In order to improve the performance of metaheuristic methods, different approaches can be integrated and methods can be hybridized to achieve faster convergence with high accuracy by balancing the exploitation and exploration stages. Chaotic maps are effectively used to improve the performance of metaheuristic methods by escaping the local optimum and increasing the convergence rate. In this study, chaotic maps are included in the TSO search process to improve performance and accelerate global convergence. In order to prevent the slow convergence rate and the classical TSO algorithm from getting stuck in local solutions, 10 different chaotic maps that generate chaotic values instead of random values in TSO processes are proposed for the first time. Thus, ergodicity and non-repeatability are improved, and convergence speed and accuracy are increased. The performance of Chaotic Transient Search Algorithm (CTSO) in global optimization was investigated using the IEEE Congress on Evolutionary Computation (CEC)’17 benchmarking functions. Its performance in real-world engineering problems was investigated for speed reducer, tension compression spring, welded beam design, pressure vessel, and three-bar truss design problems. In addition, the performance of CTSO as a feature selection method was evaluated on 10 different University of California, Irvine (UCI) standard datasets. The results of the simulation showed that Gaussian and Sinusoidal maps in most of the comparison functions, Sinusoidal map in most of the real-world engineering problems, and finally the generally proposed CTSOs in feature selection outperform standard TSO and other competitive metaheuristic methods. Real application results demonstrate that the suggested approach is more effective than standard TSO.
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Gezici, Harun, and Haydar Livatyalı. "Chaotic Harris hawks optimization algorithm." Journal of Computational Design and Engineering 9, no. 1 (2022): 216–45. http://dx.doi.org/10.1093/jcde/qwab082.
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Abstract Harris hawks optimization (HHO) is a population-based metaheuristic algorithm, inspired by the hunting strategy and cooperative behavior of Harris hawks. In this study, HHO is hybridized with 10 different chaotic maps to adjust its critical parameters. Hybridization is performed using four different methods. First, 15 test functions with unimodal and multimodal features are used for the analysis to determine the most successful chaotic map and the hybridization method. The results obtained reveal that chaotic maps increase the performance of HHO and show that the piecewise map method is the most effective one. Moreover, the proposed chaotic HHO is compared to four metaheuristic algorithms in the literature using the CEC2019 set. Next, the proposed chaotic HHO is applied to three mechanical design problems, including pressure vessel, tension/compression spring, and three-bar truss system as benchmarks. The performances and results are compared with other popular algorithms in the literature. They show that the proposed chaotic HHO algorithm can compete with HHO and other algorithms on solving the given engineering problems very successfully.
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Chhabra, Manish, and Rajesh E. "Optimizing cloud tasks scheduling based on the hybridization of darts game hypothesis and beluga whale optimization technique." Indonesian Journal of Electrical Engineering and Computer Science 38, no. 2 (2025): 1195. https://doi.org/10.11591/ijeecs.v38.i2.pp1195-1207.
Full textAbstract:
<p>This paper presents the hybridization of two metaheuristic algorithms which belongs to different categories, for optimizing the tasks scheduling in cloud environment. Hybridization of a game-based metaheuristic algorithm namely, darts game optimizer (DGO), with a swarm-based metaheuristic algorithm namely, beluga whale optimization (BWO), yields to the evolution of a new algorithm known as “hybrid darts game hypothesis – beluga whale optimization” (hybrid DGH-BWO) algorithm. Task scheduling optimization in cloud environment is a critical process and is determined as a non-deterministic polynomial (NP)-hard problem. Metaheuristic techniques are high-level optimization algorithms, designed to solve a wide range of complex, optimization problems. In the hybridization of DGO and BWO metaheuristic algorithms, expedition and convergence capabilities of both algorithms are combined together, and this enhances the chances of finding the higher-quality solutions compared to using a single algorithm alone. Other benefits of the proposed algorithm: increased overall efficiency, as “hybrid DGH-BWO” algorithm can exploit the complementary strengths of both DGO and BWO algorithms to converge to optimal solutions more quickly. Wide range of diversity is also introduced in the search space and this helps in avoiding getting trapped in local optima.</p>
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Wei, Junhao, Yanzhao Gu, Baili Lu, and Ngai Cheong. "RWOA: A novel enhanced whale optimization algorithm with multi-strategy for numerical optimization and engineering design problems." PLOS One 20, no. 4 (2025): e0320913. https://doi.org/10.1371/journal.pone.0320913.
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Whale Optimization Algorithm (WOA) is a biologically inspired metaheuristic algorithm with a simple structure and ease of implementation. However, WOA suffers from issues such as slow convergence speed, low convergence accuracy, reduced population diversity in the later stages of iteration, and an imbalance between exploration and exploitation. To address these drawbacks, this paper proposed an enhanced Whale Optimization Algorithm (RWOA). RWOA utilized Good Nodes Set method to generate evenly distributed whale individuals and incorporated Hybrid Collaborative Exploration strategy, Spiral Encircling Prey strategy, and an Enhanced Spiral Updating strategy integrated with Levy flight. Additionally, an Enhanced Cauchy Mutation based on Differential Evolution was employed. Furthermore, we redesigned the update method for parameter a to better balance exploration and exploitation. The proposed RWOA was evaluated using 23 classical benchmark functions and the impact of six improvement strategies was analyzed. We also conducted a quantitative analysis of RWOA and compared its performance with other state-of-the-art (SOTA) metaheuristic algorithms. Finally, RWOA was applied to nine engineering design optimization problems to validate its ability to solve real-world optimization challenges. The experimental results demonstrated that RWOA outperformed other algorithms and effectively addressed the shortcomings of the canonical WOA.
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Wu, Tsu-Yang, Ankang Shao, and Jeng-Shyang Pan. "CTOA: Toward a Chaotic-Based Tumbleweed Optimization Algorithm." Mathematics 11, no. 10 (2023): 2339. http://dx.doi.org/10.3390/math11102339.
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Metaheuristic algorithms are an important area of research in artificial intelligence. The tumbleweed optimization algorithm (TOA) is the newest metaheuristic optimization algorithm that mimics the growth and reproduction of tumbleweeds. In practice, chaotic maps have proven to be an improved method of optimization algorithms, allowing the algorithm to jump out of the local optimum, maintain population diversity, and improve global search ability. This paper presents a chaotic-based tumbleweed optimization algorithm (CTOA) that incorporates chaotic maps into the optimization process of the TOA. By using 12 common chaotic maps, the proposed CTOA aims to improve population diversity and global exploration and to prevent the algorithm from falling into local optima. The performance of CTOA is tested using 28 benchmark functions from CEC2013, and the results show that the circle map is the most effective in improving the accuracy and convergence speed of CTOA, especially in 50D.
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Wei, Junhao, Yanzhao Gu, Yuzheng Yan, et al. "LSEWOA: An Enhanced Whale Optimization Algorithm with Multi-Strategy for Numerical and Engineering Design Optimization Problems." Sensors 25, no. 7 (2025): 2054. https://doi.org/10.3390/s25072054.
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The Whale Optimization Algorithm (WOA) is a bio-inspired metaheuristic algorithm known for its simple structure and ease of implementation. However, WOA suffers from issues such as premature convergence, low population diversity in the later stages of iteration, slow convergence rate, low convergence accuracy, and an imbalance between exploration and exploitation. In this paper, we proposed an enhanced whale optimization algorithm with multi-strategy (LSEWOA). LSEWOA employs Good Nodes Set Initialization to generate uniformly distributed whale individuals, a newly designed Leader-Followers Search-for-Prey Strategy, a Spiral-based Encircling Prey strategy inspired by the concept of Spiral flight, and an Enhanced Spiral Updating Strategy. Additionally, we redesigned the update mechanism for convergence factor a to better balance exploration and exploitation. The effectiveness of the proposed LSEWOA was evaluated using CEC2005, and the impact of each improvement strategy was analyzed. We also performed a quantitative analysis of LSEWOA and compare it with other state-of-art metaheuristic algorithms in 30/50/100 dimensions. Finally, we applied LSEWOA to nine engineering design optimization problems to verify its capability in solving real-world optimization challenges. Experimental results demonstrate that LSEWOA outperformed better than other algorithms and successfully addressed the shortcomings of the classic WOA.
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Liu, Lisang, and Rongsheng Zhang. "Multistrategy Improved Whale Optimization Algorithm and Its Application." Computational Intelligence and Neuroscience 2022 (May 27, 2022): 1–16. http://dx.doi.org/10.1155/2022/3418269.
Full textAbstract:
To address the shortcomings of the whale optimization algorithm (WOA) in terms of insufficient global search ability and slow convergence speed, a differential evolution chaotic whale optimization algorithm (DECWOA) is proposed in this paper. Firstly, the initial population is generated by introducing the Sine chaos theory at the beginning of the algorithm to increase the population diversity. Secondly, new adaptive inertia weights are introduced into the individual whale position update formula to lay the foundation for the global search and improve the optimization performance of the algorithm. Finally, the differential variance algorithm is fused to improve the global search speed and accuracy of the whale optimization algorithm. The impact of various improvement strategies on the performance of the algorithm is analyzed using different kinds of test functions that are randomly selected. The particle swarm optimization algorithm (PSO), butterfly optimization algorithm (BOA), WOA, chaotic feedback adaptive whale optimization algorithm (CFAWOA), and DECWOA algorithm are compared for the optimal search performance. Experimental simulations are performed using MATLAB software, and the results show that the improved whale optimization algorithm has a better global optimization-seeking capability. The improved whale optimization algorithm is applied to the distribution network fault location of IEEE-33 nodes, and the effectiveness and accuracy of the distribution network fault zone location based on the multistrategy improved whale optimization algorithm is verified.
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YILDIZDAN, Gülnur. "KAOTİK YILAN OPTİMİZE EDİCİ." Afyon Kocatepe University Journal of Sciences and Engineering 23, no. 5 (2023): 1122–41. http://dx.doi.org/10.35414/akufemubid.1263731.
Full textAbstract:
Metaheuristic algorithms provide approximate or optimal solutions for optimization problems in a 
 reasonable time. With this feature, metaheuristic algorithms have become an impressive research area 
 for solving difficult optimization problems. Snake Optimizer is a population-based metaheuristic 
 algorithm inspired by the mating behavior of snakes. In this study, different chaotic maps were 
 integrated into the parameters of the algorithm instead of random number sequences to improve the 
 performance of Snake Optimizer, and Snake Optimizer variants using four different chaotic mappings 
 were proposed. The performances of these proposed variants for eight different chaotic maps were 
 examined on classical and CEC2019 test functions. The results revealed that the proposed algorithms 
 contribute to the improvement of Snake Optimizer performance. In the comparison with the literature, 
 the proposed Chaotic Snake Optimizer algorithm found the best mean values in many functions and 
 took second place among the algorithms. As a result of the tests, Chaotic Snake Optimizer has been 
 shown to be a promising, successful, and preferable algorithm.
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Che, Yanhui, and Dengxu He. "A Hybrid Whale Optimization with Seagull Algorithm for Global Optimization Problems." Mathematical Problems in Engineering 2021 (January 28, 2021): 1–31. http://dx.doi.org/10.1155/2021/6639671.
Full textAbstract:
Seagull optimization algorithm (SOA) inspired by the migration and attack behavior of seagulls in nature is used to solve the global optimization problem. However, like other well-known metaheuristic algorithms, SOA has low computational accuracy and premature convergence. Therefore, in the current work, these problems are solved by proposing the modified version of SOA. This paper proposes a novel hybrid algorithm, called whale optimization with seagull algorithm (WSOA), for solving global optimization problems. The main reason is that the spiral attack prey of seagulls is very similar to the predation behavior of whale bubble net, and the WOA has strong global search ability. Therefore, firstly, this paper combines WOA’s contraction surrounding mechanism with SOA’s spiral attack behavior to improve the calculation accuracy of SOA. Secondly, the levy flight strategy is introduced into the search formula of SOA, which can effectively avoid premature convergence of algorithms and balance exploration and exploitation among algorithms more effectively. In order to evaluate the effectiveness of solving global optimization problems, 25 benchmark test functions are tested, and WSOA is compared with seven famous metaheuristic algorithms. Statistical analysis and results comparison show that WSOA has obvious advantages compared with other algorithms. Finally, four engineering examples are tested with the proposed algorithm, and the effectiveness and feasibility of WSOA are verified.
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Valencia-Ponce , Martín Alejandro, Esteban Tlelo-Cuautle, and Luis Gerardo de la Fraga. "Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators." Mathematics 9, no. 16 (2021): 1938. http://dx.doi.org/10.3390/math9161938.
Full textAbstract:
The execution time that takes to perform numerical simulation of a chaotic oscillator mainly depends on the time-step h. This paper shows that the optimization of chaotic oscillators can be enhanced by estimating the highest h in either one-step or multi-step methods. Four chaotic oscillators are used as a case study, and the optimization of their Kaplan-Yorke dimension (DKY) is performed by applying three metaheuristics, namely: particle swarm optimization (PSO), many optimizing liaison (MOL), and differential evolution (DE) algorithms. Three representative one-step and three multi-step methods are used to solve the four chaotic oscillators, for which the estimation of the highest h is obtained from their stability analysis. The optimization results show the effectiveness of using a high h value for the six numerical methods in reducing execution time while maximizing the positive Lyapunov exponent (LE+) and DKY of the chaotic oscillators by applying PSO, MOL, and DE algorithms.
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Dong, Yingchao, Shaohua Zhang, Hongli Zhang, Xiaojun Zhou, and Jiading Jiang. "Chaotic evolution optimization: A novel metaheuristic algorithm inspired by chaotic dynamics." Chaos, Solitons & Fractals 192 (March 2025): 116049. https://doi.org/10.1016/j.chaos.2025.116049.
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TATSUMI, KEIJI, and TETSUZO TANINO. "A SUFFICIENT CONDITION FOR CHAOS IN THE GRADIENT MODEL WITH PERTURBATION METHOD FOR GLOBAL OPTIMIZATION." International Journal of Bifurcation and Chaos 23, no. 06 (2013): 1350102. http://dx.doi.org/10.1142/s0218127413501022.
Full textAbstract:
The chaotic system has been exploited in metaheuristic methods of solving global optimization problems having a large number of local minima. In those methods, the selection of chaotic system is significantly important to search for solutions extensively. Recently, a novel chaotic system, the gradient model with perturbation methods (GP), was proposed, which can be regarded as the steepest descent method for minimizing an objective function with additional perturbation terms, and it is reported that chaotic metaheuristic method with the GP model has a good performance of solving some benchmark problems through numerical experiments. Moreover, a sufficient condition of parameter was theoretically shown for chaoticity in a simplified GP model where the descent term for the objective function is removed from the original model. However, the shown conditions does not provide enough information to select parameter values in the GP model for metaheuristic methods. Therefore, in this paper, we theoretically derive a sufficient condition under which the original GP model is chaotic, which can be usefully exploited for an appropriate selection of parameter values. In addition, we examine the derived sufficient condition by calculating the Lyapunov exponents of the GP model, and analyze its bifurcation structure through numerical experiments.
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UZER, Mustafa Serter, and Onur İNAN. "COMBINING GREY WOLF OPTIMIZATION AND WHALE OPTIMIZATION ALGORITHM FOR BENCHMARK TEST FUNCTIONS." Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi 26, no. 2 (2023): 462–75. http://dx.doi.org/10.17780/ksujes.1213693.
Full textAbstract:
Many optimization problems have been successfully addressed using metaheuristic approaches. These approaches are frequently able to choose the best answer fast and effectively. Recently, the use of swarm-based optimization algorithms, a kind of metaheuristic approach, has become more common. In this study, a hybrid swarm-based optimization method called WOAGWO is proposed by combining the Whale Optimization Algorithm (WOA) and Grey Wolf Optimization (GWO). This method aims to realize a more effective hybrid algorithm by using the positive aspects of the two algorithms. 23 benchmark test functions were utilized to assess the WOAGWO. By running the proposed approach 30 times, the mean fitness and standard deviation values were computed. These results were compared to WOA, GWO, Ant Lion Optimization algorithm (ALO), Particle Swarm Optimization (PSO), and Improved ALO (IALO) in the literature. The WOAGWO algorithm, when compared to these algorithms in the literature, produced the optimal results in 5 of 7 unimodal benchmark functions, 4 of 6 multimodal benchmark functions, and 9 of 10 fixed-dimension multimodal benchmark functions. Therefore, the suggested approach generally outperforms the findings in the literature. The proposed WOAGWO seems to be promising and it has a wide range of uses.
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Zhang, Yixuan, Fuzhong Li, Yihe Zhang, Svitlana Pavlova, and Zhou Zhang. "Enhanced Whale Optimization Algorithm for Fuzzy Proportional–Integral–Derivative Control Optimization in Unmanned Aerial Vehicles." Machines 12, no. 5 (2024): 295. http://dx.doi.org/10.3390/machines12050295.
Full textAbstract:
The traditional PID controller in quadrotor UAVs has poor performance, a large overshoot, and a long adjustment time, which limit its stability and accuracy in practical applications. In order to solve this problem, an improved whale optimization fuzzy PID control strategy based on CRICLE chaos map initialization is proposed, and a detailed simulation analysis was carried out using MATLAB software (MATLAB R2022B). Firstly, to more realistically reflect quadrotor UAVs’ flight behavior, a dynamic simulation model was established, and the dynamics and kinematic characteristics of the aircraft were considered. Then, CRICLE chaotic mapping initialization was introduced to improve the global search ability of the whale optimization algorithm and to effectively initialize the parameters of the fuzzy PID controller. This improved initialization method helped to speed up the convergence process and improve the stability of the control system. In the simulation experiments, we compared the performance indicators of the improved CRICLE chaotic mapping initialization whale optimization fuzzy PID controller to the traditional PID and fuzzy PID controllers, including overshoot, adjustment time, etc. The results show that the proposed control strategy has better performance than the traditional PID and fuzzy PID controllers, significantly reduces overshoot, and achieves a significant improvement in adjustment time. Therefore, the improved CRICLE chaotic mapping initialization whale optimization fuzzy PID control strategy proposed in this study provides an effective solution for improving the performance of the quadrotor control system and has practical application potential.