ESTIMATING NONLINEAR REGRESSION PARAMETERS USING PARTICLE SWARM OPTIMIZATION AND GENETIC ALGORITHM
Abstract
Obtaining parameter estimates for nonlinear regression model using gauss-newton and gradient-based methods present some complex analytical challenges. In this paper we investigated the effectiveness and simplicity of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) on five nonlinear regression models with varying level of complexities. We developed function in R-programming for each models and performed 30 independent runs for at least 100 iterations for both PSO and GA. We evaluated PSO and GA performance in view of computation time, residual error produced and compared our results with values published online. Based on the results obtained, PSO significantly outperform GA in view of computation time and quality of parameter estimates. Even so, GA required fewer iterations and produced fairly accurate results. Further investigation shows that PSO and GA are both competitive, effective, simple to implement, and can be considered reliable for obtaining the parameter estimates of different nonlinear regression tasks.
References
Adeniyi, I. A., Yahya, W. B., & Ezenweke, C.P. (2018). A Note on Pharmacokinetics Modelling of Theophylline Concentration Data on Patients with Respiratory Diseases. Turkiye Klinikleri Journal of Biostatistics, 10(1), 27-45. doi:10.5336/biostatic.2017-58451. DOI: https://doi.org/10.5336/biostatic.2017-58451
Adjad H., Baba YF., Mers A. A., Merron O., Bouatern A., Boutmmachte N. (2019). Particle swarm optimization for optimal-geometric optimization of linear Fresnel solar concentrations. Renewable Energy, 130, 992-1001. DOI: https://doi.org/10.1016/j.renene.2018.07.001
Ajay S. & Ausif M. (2016). Improving Genetic Algorithm with fine-tuned Crossover and Scaled Architecture. Journal of Mathematics, 2016. DOI: https://doi.org/10.1155/2016/4015845
Archontoulis, S. V., & Miguez, F. E. (2015). Nonlinear regression models and applications in agricultural research. Agronomy Journal, 107(2), 786-798. DOI: https://doi.org/10.2134/agronj2012.0506
Bates, D. M. & D. G. Watts. (2007). Nonlinear Regression and its Applications. John Wiley and Sons, New York.
Belhocine, A., Shinde, D., & Patil, R. (2021). Thermo-mechanical coupled analysis based design of ventilated brake disc using genetic algorithm and particle swarm optimization. JMST Advances, 3(3), 41-54. DOI: https://doi.org/10.1007/s42791-021-00040-0
Bulent, A., & Alptekin E. (2004). The genetic algorithm method for estimation in nonlinear regression. G.U Journal of Science 17(2), 43-51.
Chandrashaker R. B., Venkat Prasad, Reddy P., & Rajeshwari M., Kavya Y. Sai (2017). Correlation of GA and PSO for Analysis of Efficient optimization. International Journal of Advance Research and Development, 2(4).
Chicco, G., & Mazza, A. (2020). Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the ‘Rush to Heuristics.’ Energies, 13(19), 5097. http://dx.doi.org/10.3390/en13195097 DOI: https://doi.org/10.3390/en13195097
de Almeida, B. S. G., & Leite, V. C. (2019). Particle swarm optimization: A powerful technique for solving engineering problems. Swarm intelligence-recent advances, new perspectives and applications, 1-21.
Desale, S.A., Rasool, A., Andhale, S., & Rane, P.V. (2015). Heuristic and Meta-Heuristic Algorithms and Their Relevance to the Real World: A Survey. International journal of computer engineering in research trends, 351. 2349-7084.
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