Open Access

REVIEW

Stochastic Fractal Search: A Decade Comprehensive Review on Its Theory, Variants, and Applications

Mohammed A. El-Shorbagy¹, Anas Bouaouda^2,*, Laith Abualigah^3,4, Fatma A. Hashim^5,6

1 Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia
2 Faculty of Science and Technology, Hassan II University of Casablanca, Mohammedia, 28806, Morocco
3 School of Engineering and Technology, Sunway University Malaysia, Petaling Jaya, 27500, Malaysia
4 Centre for Research Impact & Outcome, Chitkara University Institute of Engineering and Technology, Chitkara University, Rajpura, 140401, Punjab, India
5 Faculty of Engineering, Helwan University, Cairo, 11792, Egypt
6 Applied Science Research Center, Applied Science Private University, Amman, 11937, Jordan

* Corresponding Author: Anas Bouaouda. Email:

(This article belongs to the Special Issue: Swarm and Metaheuristic Optimization for Applied Engineering Application)

Computer Modeling in Engineering & Sciences 2025, 142(3), 2339-2404. https://doi.org/10.32604/cmes.2025.061028

Received 15 November 2024; Accepted 10 February 2025; Issue published 03 March 2025

Abstract

With the rapid advancements in technology and science, optimization theory and algorithms have become increasingly important. A wide range of real-world problems is classified as optimization challenges, and meta-heuristic algorithms have shown remarkable effectiveness in solving these challenges across diverse domains, such as machine learning, process control, and engineering design, showcasing their capability to address complex optimization problems. The Stochastic Fractal Search (SFS) algorithm is one of the most popular meta-heuristic optimization methods inspired by the fractal growth patterns of natural materials. Since its introduction by Hamid Salimi in 2015, SFS has garnered significant attention from researchers and has been applied to diverse optimization problems across multiple disciplines. Its popularity can be attributed to several factors, including its simplicity, practical computational efficiency, ease of implementation, rapid convergence, high effectiveness, and ability to address single- and multi-objective optimization problems, often outperforming other established algorithms. This review paper offers a comprehensive and detailed analysis of the SFS algorithm, covering its standard version, modifications, hybridization, and multi-objective implementations. The paper also examines several SFS applications across diverse domains, including power and energy systems, image processing, machine learning, wireless sensor networks, environmental modeling, economics and finance, and numerous engineering challenges. Furthermore, the paper critically evaluates the SFS algorithm’s performance, benchmarking its effectiveness against recently published meta-heuristic algorithms. In conclusion, the review highlights key findings and suggests potential directions for future developments and modifications of the SFS algorithm.

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