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Journal articles on the topic 'Stochastic fractal search'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

Lagunes, Marylu L., Oscar Castillo, Fevrier Valdez, Jose Soria, and Patricia Melin. "A New Approach for Dynamic Stochastic Fractal Search with Fuzzy Logic for Parameter Adaptation." Fractal and Fractional 5, no. 2 (2021): 33. http://dx.doi.org/10.3390/fractalfract5020033.

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Stochastic fractal search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic stochastic diffusion property, an improved dynamic stochastic fractal search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid, and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuz

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2

Juybari, Mohammad N., Mostafa Abouei Ardakan, and Hamed Davari-Ardakani. "A penalty-guided fractal search algorithm for reliability–redundancy allocation problems with cold-standby strategy." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 233, no. 5 (2019): 775–90. http://dx.doi.org/10.1177/1748006x19825707.

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This article addresses the system reliability optimization problem as reliability–redundancy allocation problem, aiming to maximize the system reliability through a trade-off between redundancy levels and the reliability of the components. In this study, cold-standby strategy has been considered for the redundant components, and a population-based meta-heuristic algorithm, called stochastic fractal search, is applied to solve different benchmark problems. Using the proposed stochastic fractal search algorithm, all the benchmark problems are improved and new structures with higher reliability v

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3

Salimi, Hamid. "Stochastic Fractal Search: A powerful metaheuristic algorithm." Knowledge-Based Systems 75 (February 2015): 1–18. http://dx.doi.org/10.1016/j.knosys.2014.07.025.

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4

Luo, Qifang, Sen Zhang, and Yongquan Zhou. "Stochastic Fractal Search Algorithm for Template Matching with Lateral Inhibition." Scientific Programming 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/1803934.

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Template matching is a basic and crucial process for image processing. In this paper, a hybrid method of stochastic fractal search (SFS) and lateral inhibition (LI) is proposed to solve complicated template matching problems. The proposed template matching technique is called LI-SFS. SFS is a new metaheuristic algorithm inspired by random fractals. Furthermore, lateral inhibition mechanism has been verified to have good effects on image edge extraction and image enhancement. In this work, lateral inhibition is employed for image preprocessing. LI-SFS takes both the advantages of SFS and latera

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Alomoush, Muwaffaq I., and Zaid B. Oweis. "Environmental-economic dispatch using stochastic fractal search algorithm." International Transactions on Electrical Energy Systems 28, no. 5 (2018): e2530. http://dx.doi.org/10.1002/etep.2530.

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6

Pham, Ly Huu, Thang Trung Nguyen, Lam Duc Pham, and Nam Hoang Nguyen. "Stochastic fractal search based method for economic load dispatch." TELKOMNIKA (Telecommunication Computing Electronics and Control) 17, no. 5 (2019): 2535. http://dx.doi.org/10.12928/telkomnika.v17i5.12539.

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7

Chen, Xu, Hong Yue, and Kunjie Yu. "Perturbed stochastic fractal search for solar PV parameter estimation." Energy 189 (December 2019): 116247. http://dx.doi.org/10.1016/j.energy.2019.116247.

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8

Ly, Huu Pham, Trung Nguyen Thang, Duc Pham Lam, and Hoang Nguyen Nam. "Stochastic fractal search based method for economic load dispatch." TELKOMNIKA Telecommunication, Computing, Electronics and Control 17, no. 5 (2019): 2535–46. https://doi.org/10.12928/TELKOMNIKA.v17i5.12539.

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This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are introduced in the paper by employing two different random walk generators for diffusion process in which SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from three test system. These systems with 6, 10, and 20 units with different objective function forms and diffe

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Sun, Xiaohan, Anlin Li, Shaoxiang Zhu, and Feng Zhu. "Random Walk on T-Fractal with Stochastic Resetting." Entropy 26, no. 12 (2024): 1034. https://doi.org/10.3390/e26121034.

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In this study, we explore the impact of stochastic resetting on the dynamics of random walks on a T-fractal network. By employing the generating function technique, we establish a recursive relation between the generating function of the first passage time (FPT) and derive the relationship between the mean first passage time (MFPT) with resetting and the generating function of the FPT without resetting. Our analysis covers various scenarios for a random walker reaching a target site from the starting position; for each case, we determine the optimal resetting probability γ* that minimizes the

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10

M. Eid, Marwa, Fawaz Alassery, Abdelhameed Ibrahim, Bandar Abdullah Aloyaydi, Hesham Arafat Ali, and Shady Y. El-Mashad. "Hybrid Sine Cosine and Stochastic Fractal Search for Hemoglobin Estimation." Computers, Materials & Continua 72, no. 2 (2022): 2467–82. http://dx.doi.org/10.32604/cmc.2022.025220.

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11

Dhal, Krishna Gopal, Jorge Gálvez, Swarnajit Ray, Arunita Das, and Sanjoy Das. "Acute lymphoblastic leukemia image segmentation driven by stochastic fractal search." Multimedia Tools and Applications 79, no. 17-18 (2020): 12227–55. http://dx.doi.org/10.1007/s11042-019-08417-z.

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12

Betka, Abir, Nadjiba Terki, Abida Toumi, Madina Hamiane, and Amina Ourchani. "A new block matching algorithm based on stochastic fractal search." Applied Intelligence 49, no. 3 (2018): 1146–60. http://dx.doi.org/10.1007/s10489-018-1312-1.

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13

Nguyen, Thang Trung, Dieu Ngoc Vo, Hai Van Tran, and Le Van Dai. "Optimal Dispatch of Reactive Power Using Modified Stochastic Fractal Search Algorithm." Complexity 2019 (May 28, 2019): 1–28. http://dx.doi.org/10.1155/2019/4670820.

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This paper applies a proposed modified stochastic fractal search algorithm (MSFS) for dealing with all constraints of optimal reactive power dispatch (ORPD) and finding optimal solutions for three different cases including power loss optimization, voltage deviation optimization, and L-index optimization. The proposed MSFS method is newly constructed in the paper by modifying three new solution update mechanisms on standard stochastic fractal search algorithm (SSFS). The first modification is to keep only one formula and abandon one formula in the diffusion process while the second modification

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14

Mellal, Mohamed Arezki, and Enrico Zio. "A penalty guided stochastic fractal search approach for system reliability optimization." Reliability Engineering & System Safety 152 (August 2016): 213–27. http://dx.doi.org/10.1016/j.ress.2016.03.019.

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15

Lin, Jian, and Zhou-Jing Wang. "Multi-area economic dispatch using an improved stochastic fractal search algorithm." Energy 166 (January 2019): 47–58. http://dx.doi.org/10.1016/j.energy.2018.10.065.

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16

Pham, Ly Huu, Minh Quan Duong, Van-Duc Phan, Thang Trung Nguyen, and Hoang-Nam Nguyen. "A High-Performance Stochastic Fractal Search Algorithm for Optimal Generation Dispatch Problem." Energies 12, no. 9 (2019): 1796. http://dx.doi.org/10.3390/en12091796.

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This paper proposes applications of a modified stochastic fractal search algorithm (MSFS) to solve the economic load dispatch problem (ELD) in which valve-point effects, prohibited operating zones, power losses in all conductors, multi-fuel sources and other constraints of power system are taken into consideration. The proposed method is first developed in the study by performing two modifications on two procedures of new solution generation from conventional stochastic fractal search (SFS). The first modification is used to change the strategy of producing new solutions of the first and the s

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17

Zhang, Qingsong, Yibo He, Meng Shu, et al. "A Level-Based Learning Swarm Optimizer with Stochastic Fractal Search for Parameters Identification of Solar Photovoltaic Models." Mathematical Problems in Engineering 2023 (February 22, 2023): 1–16. http://dx.doi.org/10.1155/2023/3397430.

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As the most popular renewable energy, solar energy could be converted into electricity by photovoltaic (PV) systems directly. To maximize the effectiveness of the conversion, it is critical to find the precise and accurate parameters of the PV model. In this paper, we propose a level-based learning swarm optimizer with stochastic fractal search (LLSOF) to tackle the parameter estimation of several kinds of solar PV models. The population is separated into multiple levels according to their fitness at first. The individuals at the lower levels evolve through learning from the individuals at the

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18

I. Alomoush, Muwaffaq. "Optimal Combined Heat and Power Economic Dispatch Using Stochastic Fractal Search Algorithm." Journal of Modern Power Systems and Clean Energy 8, no. 2 (2020): 276–86. http://dx.doi.org/10.35833/mpce.2018.000753.

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19

Hinojosa, Salvador, Krishna Gopal Dhal, Mohamed Abd Elaziz, Diego Oliva, and Erik Cuevas. "Entropy-based imagery segmentation for breast histology using the Stochastic Fractal Search." Neurocomputing 321 (December 2018): 201–15. http://dx.doi.org/10.1016/j.neucom.2018.09.034.

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20

Tran, Tung The, Khoa Hoang Truong, and Dieu Ngoc Vo. "Stochastic fractal search algorithm for reconfiguration of distribution networks with distributed generations." Ain Shams Engineering Journal 11, no. 2 (2020): 389–407. http://dx.doi.org/10.1016/j.asej.2019.08.015.

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21

Bhatt, Rajesh, Girish Parmar, Rajeev Gupta, and Afzal Sikander. "Application of stochastic fractal search in approximation and control of LTI systems." Microsystem Technologies 25, no. 1 (2018): 105–14. http://dx.doi.org/10.1007/s00542-018-3939-6.

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22

Dang, Yinglong, Xiaoguang Gao, and Zidong Wang. "Stochastic Fractal Search for Bayesian Network Structure Learning Under Soft/Hard Constraints." Fractal and Fractional 9, no. 6 (2025): 394. https://doi.org/10.3390/fractalfract9060394.

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A Bayesian network (BN) is an uncertainty processing model that simulates human cognitive thinking on the basis of probability theory and graph theory. Its network topology is a directed acyclic graph (DAG) that can be manually constructed through expert knowledge or automatically generated through data learning. However, the acquisition of expert knowledge faces problems such as excessively high labor costs, limited expert experience, and the inability to solve large-scale and highly complex DAGs. Moreover, the current data learning methods also face the problems of low computational efficien

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23

Hai, Van Tran, Van Pham Thanh, Huu Pham Ly, Trong Le Nghia, and Trung Nguyen Thang. "Finding optimal reactive power dispatch solutions by using a novel improved stochastic fractal search optimization algorithm." TELKOMNIKA Telecommunication, Computing, Electronics and Control 17, no. 5 (2019): 2517–26. https://doi.org/10.12928/TELKOMNIKA.v17i5.10767.

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In this paper, a novel improved Stochastic Fractal Search optimization algorithm (ISFSOA) is proposed for finding effective solutions of a complex optimal reactive power dispatch (ORPD) problem with consideration of all constraints in transmission power network. Three different objectives consisting of total power loss (TPL), total voltage deviation (TVD) and voltage stabilization enhancement index are independently optimized by running the proposed ISFSOA and standard Stochastic Fractal Search optimization algorithm (SFSOA). The potential search of the proposed ISFSOA can be highly improved s

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24

SUN, Mei-yu. "Approach for effective fractal-based similarity search of stochastic non-stationary time series." Journal of Computer Applications 28, no. 6 (2008): 1431–34. http://dx.doi.org/10.3724/sp.j.1087.2008.01431.

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25

Khalilpourazari, Soheyl, and Saman Khalilpourazary. "A Robust Stochastic Fractal Search approach for optimization of the surface grinding process." Swarm and Evolutionary Computation 38 (February 2018): 173–86. http://dx.doi.org/10.1016/j.swevo.2017.07.008.

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26

Nguyen, Thang Trung, Thuan Thanh Nguyen, Minh Quan Duong, and Anh Tuan Doan. "Optimal operation of transmission power networks by using improved stochastic fractal search algorithm." Neural Computing and Applications 32, no. 13 (2019): 9129–64. http://dx.doi.org/10.1007/s00521-019-04425-0.

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27

El-Shorbagy, Mohammed A., Anas Bouaouda, Laith Abualigah, and Fatma A. Hashim. "Stochastic Fractal Search: A Decade Comprehensive Review on Its Theory, Variants, and Applications." Computer Modeling in Engineering & Sciences 142, no. 3 (2025): 2339–404. https://doi.org/10.32604/cmes.2025.061028.

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28

Wanliss, J. A., K. Shiokawa, and K. Yumoto. "Latitudinal variation of stochastic properties of the geomagnetic field." Nonlinear Processes in Geophysics 21, no. 2 (2014): 347–56. http://dx.doi.org/10.5194/npg-21-347-2014.

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Abstract. We explore the stochastic fractal qualities of the geomagnetic field from 210 mm ground-based magnetometers during quiet and active magnetospheric conditions. We search through 10 yr of these data to find events that qualify as quiet intervals, defined by Kp ≤ 1 for 1440 consecutive minutes. Similarly, active intervals require Kp ≥ 4 for 1440 consecutive minutes. The total for quiet intervals is ~ 4.3 x 106 and 2 x 108 min for active data points. With this large number of data we characterize changes in the nonlinear statistics of the geomagnetic field via measurements of a fractal s

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29

Rezk, Hegazy, and Ahmed Fathy. "Stochastic Fractal Search Optimization Algorithm Based Global MPPT for Triple-Junction Photovoltaic Solar System." Energies 13, no. 18 (2020): 4971. http://dx.doi.org/10.3390/en13184971.

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A significant growth in PV (photovoltaic) system installations have been observed during the last decade. The PV array has a nonlinear output characteristic because of weather intermittency. Partial shading is an environmental phenomenon that causes multiple peaks in the power curve and has a negative effect on the efficiency of the conventional maximum power point tracking (MPPT) methods. This tends to have a substantial effect on the overall performance of the PV system. Therefore, to enhance the performance of the PV system under shading conditions, the global MPPT technique is mandatory to

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30

Pang, Bizhao, Kin Huat Low, and Chen Lv. "Adaptive conflict resolution for multi-UAV 4D routes optimization using stochastic fractal search algorithm." Transportation Research Part C: Emerging Technologies 139 (June 2022): 103666. http://dx.doi.org/10.1016/j.trc.2022.103666.

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31

Das, Arunita, Krishna Gopal Dhal, Swarnajit Ray, and Jorge Gálvez. "Histogram-based fast and robust image clustering using stochastic fractal search and morphological reconstruction." Neural Computing and Applications 34, no. 6 (2021): 4531–54. http://dx.doi.org/10.1007/s00521-021-06610-6.

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32

Aras, Sefa, Eyüp Gedikli, and Hamdi Tolga Kahraman. "A novel stochastic fractal search algorithm with fitness-Distance balance for global numerical optimization." Swarm and Evolutionary Computation 61 (March 2021): 100821. http://dx.doi.org/10.1016/j.swevo.2020.100821.

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33

Lin, Jian, and Zhou-Jing Wang. "Parameter identification for fractional-order chaotic systems using a hybrid stochastic fractal search algorithm." Nonlinear Dynamics 90, no. 2 (2017): 1243–55. http://dx.doi.org/10.1007/s11071-017-3723-7.

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34

Rahman, Tuan A. Z., N. A. Abdul Jalil, A. As’arry, and R. K. Raja Ahmad. "Chaos-enhanced Stochastic Fractal Search algorithm for Global Optimization with Application to Fault Diagnosis." IOP Conference Series: Materials Science and Engineering 210 (June 2017): 012060. http://dx.doi.org/10.1088/1757-899x/210/1/012060.

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35

Hasan, Faraz, Mohammad Imran, Mohammad Shahid, Faisal Ahmad, and Mohammad Sajid. "Load balancing strategy for workflow tasks using stochastic fractal search (SFS) in Cloud Computing." Procedia Computer Science 215 (2022): 815–23. http://dx.doi.org/10.1016/j.procs.2022.12.084.

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36

Mohammad, Shahid, Shamim Mohd, Ashraf Zubair, and Shamim Ansari Mohd. "A novel evolutionary optimization algorithm based solution approach for portfolio selection problem." International Journal of Artificial Intelligence (IJ-AI) 11, no. 3 (2022): 843–50. https://doi.org/10.11591/ijai.v11.i3.pp843-850.

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The portfolio selection problem is one of the most common problems which drawn the attention of experts of the field in recent decades. The mean variance portfolio optimization aims to minimize variance (risk) and maximize the expected return. In case of linear constraints, the problem can be solved by variants of Markowitz. But many constraints such as cardinality, and transaction cost, make the problem so vital that conventional techniques are not good enough in giving efficient solutions. Stochastic fractal search (SFS) is a strong population based meta-heuristic approach that has derived f

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37

BARTUMEUS, FREDERIC. "LÉVY PROCESSES IN ANIMAL MOVEMENT: AN EVOLUTIONARY HYPOTHESIS." Fractals 15, no. 02 (2007): 151–62. http://dx.doi.org/10.1142/s0218348x07003460.

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The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems, fractal patterns show up in many subtle ways and have been interpreted as emergent phenomena related to some universal principles of complex systems. Recently, Lévy-type processes have been pointed out as relevant in large-scale animal movements. The existence of Lévy probability distributions in the behavior of relevant variables of movement, introduces new potential diffusive properties and optimization mechanisms in animal foraging processes. In particular, it has been shown that Lévy pr

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38

Xu, Ailing, Li Mo, and Qi Wang. "Research on Operation Mode of the Yalong River Cascade Reservoirs Based on Improved Stochastic Fractal Search Algorithm." Energies 15, no. 20 (2022): 7779. http://dx.doi.org/10.3390/en15207779.

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With the completion of the Lianghekou Reservoir, with a multiyear regulation capacity, the operation relationship of the cascade reservoirs in the Yalong River is becoming increasingly complex. In order to study an optimal operation mode of the cascade reservoirs in the Yalong River under different inflow frequencies, based on the shortcomings of the existing single reservoir operation mode and the local joint operation mode of the cascade reservoirs, this paper first proposed a global joint operation mode for the cascade reservoirs to develop the power generation potential of daily regulating

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39

Kien, Le Chi, Thuan Thanh Nguyen, Bach Hoang Dinh, and Thang Trung Nguyen. "Optimal Reactive Power Generation for Radial Distribution Systems Using a Highly Effective Proposed Algorithm." Complexity 2021 (February 2, 2021): 1–36. http://dx.doi.org/10.1155/2021/2486531.

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In this paper, a proposed modified stochastic fractal search algorithm (MSFS) is applied to find the most appropriate site and size of capacitor banks for distribution systems with 33, 69, and 85 buses. Two single-objective functions are considered to be reduction of power loss and reduction of total cost of energy loss and capacitor investment while satisfying limit of capacitors, limit of conductor, and power balance of the systems. MSFS was developed by performing three new mechanisms including new diffusion mechanism and two new update mechanisms on the conventional stochastic fractal sear

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40

Tran The, Tung, Bao-Huy Truong, Khanh Dang Tuan, and Dieu Vo Ngoc. "A Nondominated Sorting Stochastic Fractal Search Algorithm for Multiobjective Distribution Network Reconfiguration with Distributed Generations." Mathematical Problems in Engineering 2021 (February 11, 2021): 1–20. http://dx.doi.org/10.1155/2021/6638559.

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This paper aims to propose a new multiobjective algorithm for multiobjective distributed network reconfiguration (DNR) with the placements of distributed generation (DG) in radial distribution networks (RDNs). The new proposed algorithm, called the nondominated sorting stochastic fractal search (NSSFS), is a new multiobjective version of the original SFS algorithm. NSSFS incorporated fast nondominated sorting strategies, crowding distance computation, and selection mechanism into SFS to find and maintain the best nondominated solutions. The proposed NSSFS algorithm was tested with eight multio

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41

Xu, Shuhui, and Huadong Qiu. "A modified stochastic fractal search algorithm for parameter estimation of solar cells and PV modules." Energy Reports 8 (November 2022): 1853–66. http://dx.doi.org/10.1016/j.egyr.2022.01.008.

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42

Mai, The Anh, and Thai Son Dang. "Optimal fuzzy PD control for a two-link robot manipulator based on stochastic fractal search." European Physical Journal Special Topics 230, no. 21-22 (2021): 3935–45. http://dx.doi.org/10.1140/epjs/s11734-021-00339-y.

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43

Khalilpourazari, Soheyl, Bahman Naderi, and Saman Khalilpourazary. "Multi-Objective Stochastic Fractal Search: a powerful algorithm for solving complex multi-objective optimization problems." Soft Computing 24, no. 4 (2019): 3037–66. http://dx.doi.org/10.1007/s00500-019-04080-6.

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44

El-Kenawy, El-Sayed M., Marwa Metwally Eid, Mohamed Saber, and Abdelhameed Ibrahim. "MbGWO-SFS: Modified Binary Grey Wolf Optimizer Based on Stochastic Fractal Search for Feature Selection." IEEE Access 8 (2020): 107635–49. http://dx.doi.org/10.1109/access.2020.3001151.

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45

El-Fergany, Attia A., and Hany M. Hasanien. "Optimized settings of directional overcurrent relays in meshed power networks using stochastic fractal search algorithm." International Transactions on Electrical Energy Systems 27, no. 11 (2017): e2395. http://dx.doi.org/10.1002/etep.2395.

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46

Sami Khafaga, Doaa, El-Sayed M. El-kenawy, Amel Ali Alhussan, and Marwa M. Eid. "Forecasting Energy Consumption Using a Novel Hybrid Dipper Throated Optimization and Stochastic Fractal Search Algorithm." Intelligent Automation & Soft Computing 37, no. 2 (2023): 2117–32. http://dx.doi.org/10.32604/iasc.2023.038811.

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47

Gonzalez, Francisco, Ricardo Soto, and Broderick Crawford. "Stochastic Fractal Search Algorithm Improved with Opposition-Based Learning for Solving the Substitution Box Design Problem." Mathematics 10, no. 13 (2022): 2172. http://dx.doi.org/10.3390/math10132172.

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The main component of a cryptographic system that allows us to ensure its strength against attacks, is the substitution box. The strength of this component can be validated by various metrics, one of them being the nonlinearity. To this end, it is essential to develop a design for substitution boxes that allows us to guarantee compliance with this metric. In this work, we implemented a hybrid between the stochastic fractal search algorithm in conjunction with opposition-based learning. This design is supported by sequential model algorithm configuration for the proper parameters configuration.

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48

Tyagi, Tushar, Hari Mohan Dubey, and Manjaree Pandit. "Multi-Objective Optimal Dispatch Solution of Solar-Wind-Thermal System Using Improved Stochastic Fractal Search Algorithm." International Journal of Information Technology and Computer Science 8, no. 11 (2016): 61–73. http://dx.doi.org/10.5815/ijitcs.2016.11.08.

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49

Tran, Hai Van, Thanh Van Pham, Ly Huu Pham, Nghia Trong Le, and Thang Trung Nguyen. "Finding optimal reactive power dispatch solutions by using a novel improved stochastic fractal search optimization algorithm." TELKOMNIKA (Telecommunication Computing Electronics and Control) 17, no. 5 (2019): 2517. http://dx.doi.org/10.12928/telkomnika.v17i5.10767.

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Nguyen, Tri Phuoc, and Dieu Ngoc Vo. "A novel stochastic fractal search algorithm for optimal allocation of distributed generators in radial distribution systems." Applied Soft Computing 70 (September 2018): 773–96. http://dx.doi.org/10.1016/j.asoc.2018.06.020.

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