Document Type : Research Paper


1 Department of Mechanical Engineering, University of Huddersfield, Huddersfield, UK

2 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran

3 Department of Mechanical Engineering, University of Thi-qar, Nasiriyah, Iraq

4 Department of Computer Science and Systems Engineering, Ayandegan University, Tonekabon, Iran


Optimization of noisy non-linear problems plays a key role in engineering and design problems. These optimization problems can't be solved effectively by using conventional optimization methods. However, metaheuristic algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) seem very efficient to approach in these problems and became very popular. The efficiency of these methods against many new metaheuristic optimization algorithms has been proved in previous works, however a robust comparison between GA and PSO to solve noisy nonlinear problems has not been reported yet. Therefore, in this paper GA and PSO are adapted to find optimal solutions of some noisy mathematical models. Based on the obtained results, GA shows a promising potential in terms of number of iteration to converge and solutions found so far for either for optimization of low or elevated levels of noise.


Main Subjects

Azimi, M., Kolahdooz, A., & Eftekhari, S. A. (2017). An Optimization on the DIN1. 2080 Alloy in the Electrical Discharge Machining Process Using ANN and GA. Journal of Modern Processes in Manufacturing and Production, 6(1), 33-47.
Chai-ead, N., Aungkulanon, P., Luangpaiboon, P. (2011). Bees and Firefly Algorithms for Noisy Non-Linear Optimisation Problems. Proceeding of the International Multiconference of Engineering and Computer Scientists, Vol II, IMECS 2011, March 16-18, Hong Kong.
Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. In Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on (pp. 39-43). IEEE.
Elbeltagi, E., Hegazy, T., & Grierson, D. (2007). A modified shuffled frog-leaping optimization algorithm: applications to project management. Structure and Infrastructure Engineering, 3(1), 53-60.
Holland, J. H. (1975). Adaptation in natural and artificial systems. An introductory analysis with application to biology, control, and artificial intelligence. Ann Arbor, MI: University of Michigan Press, 439-444.
Kennedy, J. (2010). Particle swarm optimization Encyclopedia of Machine Learning, Springer, 760-766.
Lin, W. Y., Lee, W. Y., & Hong, T. P. (2003). Adapting crossover and mutation rates in genetic algorithms. J. Inf. Sci. Eng., 19(5), 889-903.
Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.
modeFRONTIER, (2008). modeFRONTIER v4.0 User manual. Trierste, Italy: ESTECO srl.
Molga, M., & Smutnicki, C. (2005). Test functions for optimization needs. Test functions for optimization needs, 101.
Pal, S.K., Rai,  C.S., Singh A.P. (2017). Comparative Study of Firefly Algorithm and Particle Swarm Optimization for Noisy Non-Linear Optimization Problems.  International Journal of Intelligent Systems and Applications, 4(10), 50-57.
Picheny, V., Wagner, T., & Ginsbourger, D. (2013). A benchmark of kriging-based infill criteria for noisy optimization. Structural and Multidisciplinary Optimization, 48(3), 60.
Sai, V. O., Shieh, C. S., Lin, Y. C., Horng, M. F., Nguyen, T. T., Le, Q. D., & Jiang, J. Y. (2016, May). Comparative Study on Recent Development of Heuristic Optimization Methods. In Computing Measurement Control and Sensor Network (CMCSN), 2016 Third International Conference on (pp. 68-71). IEEE.
Towsyfyan, H., Salehi, S.A.A., Davoudi, GH., Bahmanpour M. (2013). A new approach to solve differential equations arising in fluid mechanics, International Journal of Mathematical Modelling & Computation,   3(2), 115-124.
Yang, X. S., & He, X. (2013). Firefly algorithm: recent advances and applications. International Journal of Swarm Intelligence, 1(1), 36-50.
Yazdi, M.S., Latifi Rostami, S.A., Kolahdooz, A. (2016). Optimization of geometrical parameters in a specific composite lattice structure using neural networks and ABC algorithm, Journal of Mechanical Science & Technology, 30(4), 1763-1771.
Zhan, Z. H., Zhang, J., Shi, Y. H., & Liu, H. L. (2012). A modified brain storm optimization. In Evolutionary Computation (CEC), 2012 IEEE Congress on (pp. 1-8). IEEE.