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Shape and Size Optimization of Truss Structures under Frequency Constraints Based on Hybrid Sine Cosine Firefly Algorithm

Ran Tao, Xiaomeng Yang, Huanlin Zhou*, Zeng Meng*
School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China
* Corresponding Authors: Huanlin Zhou. Email: ; Zeng Meng. Email:
(This article belongs to this Special Issue: New Trends in Structural Optimization)

Computer Modeling in Engineering & Sciences 2023, 134(1), 405-428.

Received 14 December 2021; Accepted 09 February 2022; Issue published 24 August 2022


Shape and size optimization with frequency constraints is a highly nonlinear problem with mixed design variables, non-convex search space, and multiple local optima. Therefore, a hybrid sine cosine firefly algorithm (HSCFA) is proposed to acquire more accurate solutions with less finite element analysis. The full attraction model of firefly algorithm (FA) is analyzed, and the factors that affect its computational efficiency and accuracy are revealed. A modified FA with simplified attraction model and adaptive parameter of sine cosine algorithm (SCA) is proposed to reduce the computational complexity and enhance the convergence rate. Then, the population is classified, and different populations are updated by modified FA and SCA respectively. Besides, the random search strategy based on Lévy flight is adopted to update the stagnant or infeasible solutions to enhance the population diversity. Elitist selection technique is applied to save the promising solutions and further improve the convergence rate. Moreover, the adaptive penalty function is employed to deal with the constraints. Finally, the performance of HSCFA is demonstrated through the numerical examples with nonstructural masses and frequency constraints. The results show that HSCFA is an efficient and competitive tool for shape and size optimization problems with frequency constraints.


Firefly algorithm; sine cosine algorithm; frequency constraints; structural optimization

Cite This Article

Tao, R., Yang, X., Zhou, H., Meng, Z. (2023). Shape and Size Optimization of Truss Structures under Frequency Constraints Based on Hybrid Sine Cosine Firefly Algorithm. CMES-Computer Modeling in Engineering & Sciences, 134(1), 405–428.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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