### Journals Information

Mathematics and Statistics Vol. 9(3), pp. 273 - 277
DOI: 10.13189/ms.2021.090307
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## Volume Minimization of a Closed Coil Helical Spring Using ALO, GWO, DA, FA, FPA, WOA, CSO. BA, PSO and GSA

Rejula Mercy. J 1,2, S. Elizabeth Amudhini Stephen 3,*
1 Karunya Institute of Technology and Sciences, Coimbatore, India
2 Department of Mathematics, PSGR Krishnammal College for Women, Coimbatore, India
3 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, India

ABSTRACT

Springs are important members often used in machines to exert force, absorb energy and provide flexibility. In mechanical systems, wherever flexibility or relatively a large load under the given circumstances is required, some form of spring is used. In this paper, non-traditional optimization algorithms, namely, Ant Lion Optimizer, Grey Wolf Optimizer, Dragonfly optimization algorithm, Firefly algorithm, Flower Pollination Algorithm, Whale Optimization Algorithm, Cat Swarm Optimization, Bat Algorithm, Particle Swarm Optimization, Gravitational Search Algorithm are proposed to get the global optimal solution for the closed coil helical spring design problem. The problem has three design variables and eight inequality constraints and three bounds. The mathematical formulation of the objective function U is to minimize the volume of closed coil helical spring subject to constraints. The design variables considered are Wire diameter d, Mean coil diameter D, Number of active coils N of the spring. The proposed methods are tested and the performance is evaluated. Ten non-traditional optimization methods are used to find the minimum volume. The problem is computed in the MATLAB environment. The experimental results show that Particle Swarm Optimization outperforms other methods. The results show that PSO gives better results in terms of consistency and minimum value in terms of time and volume of a closed coil helical spring compared to other methods. When compared to other Optimization methods, PSO has few advantages like simplicity and efficiency. In the future, PSO could be extended to solve other mechanical element problems.

KEYWORDS
Non-traditional Optimization, Closed Coil Helical Spring, Volume Minimization

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Rejula Mercy. J , S. Elizabeth Amudhini Stephen , "Volume Minimization of a Closed Coil Helical Spring Using ALO, GWO, DA, FA, FPA, WOA, CSO. BA, PSO and GSA," Mathematics and Statistics, Vol. 9, No. 3, pp. 273 - 277, 2021. DOI: 10.13189/ms.2021.090307.

(b). APA Format:
Rejula Mercy. J , S. Elizabeth Amudhini Stephen (2021). Volume Minimization of a Closed Coil Helical Spring Using ALO, GWO, DA, FA, FPA, WOA, CSO. BA, PSO and GSA. Mathematics and Statistics, 9(3), 273 - 277. DOI: 10.13189/ms.2021.090307.