CLFOX: A Cubic–Lévy Flight Enhanced FOX Optimizer for Global Numerical Optimization and Engineering Design Problems

Sima Abdulla Salih; Hardi Mohammed Mohammed; Zrar Khalid Abdul

doi:10.24017/science.2026.2.3

Authors

Sima Abdulla Salih Department of Computer Science, College of Science, Charmo University, 46023 Chamchamal, Sulaimani, Kurdistan Region, Iraq. Author
Hardi Mohammed Mohammed Department of Computer Science, College of Science, Charmo University, 46023 Chamchamal, Sulaimani, Kurdistan Region, Iraq. Author
Zrar Khalid Abdul Department of Computer Science, College of Science, Charmo University, 46023 Chamchamal, Sulaimani, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.24017/science.2026.2.3

Keywords:

Engineering design optimiza-tion, Chaotic maps, Exploration enhancement, Lévy flight, Metaheuristic optimization, Three-bar truss

Abstract

FOX is a recent powerful metaheuristic optimization algorithm, motivated by a red fox’s behavior inside snow for catching prey. Although FOX is one of the more powerful algorithms, it has some limitations, including weak exploration, getting trapped inside local optima, and having unbalanced exploration and exploitation. This study proposes a Cubic–Lévy flight enhanced FOX optimizer (CLFOX), which is an improved version of FOX, to overcome its limitations. Four new techniques have been added to CLFOX to improve FOX’s performance. The first technique is initializing the population using a chaotic map. Second is introducing Lévy flight as another exploration strategy. Third is increasing the main condition of the algorithm to keep the balance between each strategy that happens inside the algorithm. Finally, an interval-based operator is added that runs once every 10 iterations. To show the importance of CLFOX, three sets of benchmark test functions are used: the classical benchmark function set, the CEC2019 set, and the CEC2022 set. The results show that CLFOX can outperform FOX in 42 out of 45 benchmark testing functions. CLFOX was also compared to nine competitive algorithms, including FOX. The results show that CLFOX outperforms almost all the other algorithms and takes the first rank among them. The statistical results show that 88% of the improved values are significant. CLFOX is also used to solve real-world engineering challenges, including pressure vessel design, tension/string design, three-bar truss design, gear train design, cantilever beam design, and welded beam design, to show its performance in comparison to the other algorithms.

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