Multiple Response Optimization: Comparative Analysis Between Models Obtained by Ordinary Least Method and Genetic Programming

• Autores: Nilo Antonio de Souza Sampaio, José Salvador da Motta Reis, José Glenio Medeiros de Barros, Cleginaldo Pereira de Carvalho, Fabricio Maciel Gomes, Luís César Ferreira Motta Barbosa, Messias Borges da Silva
• Localización: International Journal of Professional Business Review: Int. J. Prof.Bus. Rev., ISSN 2525-3654, ISSN-e 2525-3654, Vol. 8, Nº. 8, 2023 (Ejemplar dedicado a: Continuous publication; e02907)
• Idioma: inglés
• DOI: 10.26668/businessreview/2023.v8i8.3131
• Enlaces
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• Resumen

  • Purpose: This work aims to analyze and compare the performance between the Ordinary Least Squares (OLS) method executed in Minitab (v. 17) and the genetic programming performed in Eureqa Formulize (v. 1.24.0).

      Theoretical reference: Obtaining a model that mathematically describes the relationship between the independent variable and the response variable is essential to optimizing the process. The model can be described as an approximate representation of the real system or process, while the modeling process is a balance between simplicity and accuracy (X. Chen et al., 2018; Gomes et al., 2019; Sampaio et al., 2022; A. R. S. Silva et al., 2021).

      Method: An Evaluation of the best method for constructing mathematical models was performed using the Adjusted Coefficient of Determination (Radj2) and Akaike's Information Criterion   Results and conclusion: The comparison between the use of the methods showed the superiority of genetic programming over OLS in the construction of mathematical models.

      Originality/Value: Genetic Programming produces mathematical models that are sometimes differentiated when several replicates are performed, but always with similar explanatory power and with biased characteristic that does not affect in any way the quality of prediction of the dependent variable being studied.

• Referencias bibliográficas
  • Alrubaie, K., Godefroid, L., & Lopes, J. (2007). Statistical modeling of fatigue crack growth rate in Inconel alloy 600. International...
  • Amir Haeri, M., Ebadzadeh, M. M., & Folino, G. (2017). Statistical genetic programming for symbolic regression. Applied Soft Computing,...
  • Araujo, M. J. F. de, Araújo, M. V. F. de, Araujo Jr, A. H. de, Barros, J. G. M. de, Almeida, M. da G. de, Fonseca, B. B. da, Reis, J. S. D....
  • Beena, V. T., & Kumaran, M. (2010). Measuring inequality and social welfare from any arbitrary distribution. Brazilian Journal of Probability...
  • Box, G. E. P., & Wilson, K. B. (1951). On the Experimental Attainment of Optimum Conditions. Journal of the Royal Statistical Society....
  • Burnham, K. P., & Anderson, D. R. (2004). Model Selection and Multimodel Inference. In K. P. Burnham & D. R. Anderson (Eds.), Springer...
  • Ch’ng, C. K., Quah, S. H., & Low, H. C. (2005). A New Approach for Multiple-Response Optimization. Quality Engineering, 17(4), 621–626....
  • Chau, K. (2017). Use of Meta-Heuristic Techniques in Rainfall-Runoff Modelling. Water, 9(3), 186. https://doi.org/10.3390/w9030186
  • Chen, V. C. P., Tsui, K.-L., Barton, R. R., & Meckesheimer, M. (2006). A review on design, modeling and applications of computer experiments....
  • Chen, X., Mei, C., Xu, B., Yu, K., & Huang, X. (2018). Quadratic interpolation based teaching-learning-based optimization for chemical...
  • Cribari-Neto, F., & Lima, M. da G. A. (2014). New heteroskedasticity-robust standard errors for the linear regression model. Brazilian...
  • Derringer, G., & Suich, R. (1980). Simultaneous Optimization of Several Response Variables. Journal of Quality Technology, 12(4), 214–219....
  • Diniz, C. A. R., Louzada-Neto, F., & Morita, L. H. M. (2012). The multiplicative heteroscedastic Von Bertalanffy model. Brazilian Journal...
  • Draper, N. R., & Smith, H. (1998). Applied Regression Analysis. In Wiley-Interscience (3a). Wiley-Interscience.
  • Dubčáková, R. (2011). Eureqa: software review. Genetic Programming and Evolvable Machines, 12(2), 173–178. https://doi.org/10.1007/s10710-010-9124-z
  • Garg, A., & Lam, J. S. L. (2015). Improving environmental sustainability by formulation of generalized power consumption models using...
  • Gomes, F. M., Pereira, F. M., Silva, A. F., & Silva, M. B. (2019). Multiple response optimization: Analysis of genetic programming for...
  • Gonçalves, K. C. M., & Ghosh, M. (2022). Unit level model for small area estimation with count data under square root transformation....
  • Ivanov, D., Dolgui, A., Sokolov, B., Werner, F., & Ivanova, M. (2016). A dynamic model and an algorithm for short-term supply chain scheduling...
  • Kalra, M., & Singh, S. (2015). A review of metaheuristic scheduling techniques in cloud computing. Egyptian Informatics Journal, 16(3),...
  • Katebi, M., Seif, A., & Faraz, A. (2017). Economic and economic-statistical designs of the T 2 control charts with SVSSI sampling scheme....
  • Khuri, A. I., & Conlon, M. (1981). Simultaneous Optimization of Multiple Responses Represented by Polynomial Regression Functions. Technometrics,...
  • Kilmer, J. T., & Rodríguez, R. L. (2017). Ordinary least squares regression is indicated for studies of allometry. Journal of Evolutionary...
  • Lakshmi, K., Mahaboob, B., Rajaiah, M., & Narayana, C. (2021). Ordinary least squares estimation of parameters of linear model. Journal...
  • Liu, G., & Piantadosi, S. (2017). Ridge estimation in generalized linear models and proportional hazards regressions. Communications in...
  • Naderi, M., & Khamehchi, E. (2017). Application of DOE and metaheuristic bat algorithm for well placement and individual well controls...
  • Pang, S., Zhang, X., & Zhang, Q. (2020). The Hamming distances of saturated asymmetrical orthogonal arrays with strength 2. Communications...
  • Pinto, E. R., & Pereira, L. A. (2021). On variable selection in joint modeling of mean and dispersion. Brazilian Journal of Probability...
  • Pitt, M. A., & Myung, I. J. (2002). When a good fit can be bad. Trends in Cognitive Sciences, 6(10), 421–425. https://doi.org/10.1016/S1364-6613(02)01964-2
  • Poli, R., Langdon, W. B., McPhee, N. F., & Koza, J. R. (2008). A Field Guide to Genetic Programming. In Lulu Enterprises (1o). Lulu Enterprises.
  • Qasim, M., Amin, M., & Omer, T. (2020). Performance of some new Liu parameters for the linear regression model. Communications in Statistics...
  • Salido, M. A., Escamilla, J., Giret, A., & Barber, F. (2016). A genetic algorithm for energy-efficiency in job-shop scheduling. The International...
  • Salmeron, R., Garcia, C., Garcia, J., & Lopez, M. del M. (2017). The raise estimator estimation, inference, and properties. Communications...
  • Sampaio, N. A. de S., Reis, J. S. da M., Espuny, M., Cardoso, R. P., Gomes, F. M., Pereira, F. M., Ferreira, L. C., Barbosa, M., Santos, G.,...
  • Sathiya, P., Abdul Jaleel, M. Y., Katherasan, D., & Shanmugarajan, B. (2011). Optimization of laser butt welding parameters with multiple...
  • Silva, A. R. S., Azevedo, C. L. N., Bazán, J. L., & Nobre, J. S. (2021). Bayesian inference for zero-and/or-one augmented beta rectangular...
  • Silva, H. de O. G. da, Costa, M. C. M., Aguilera, M. V. C., Almeida, M. da G. D. de, Fonseca, B. B. da, Reis, J. S. da M., Barbosa, L. C....
  • Wan, Q., Wu, Y., Zhou, W., & Chen, X. (2018). Economic design of an integrated adaptive synthetic chart and maintenance management system....
  • Wang, X., & Leng, C. (2016). High dimensional ordinary least squares projection for screening variables. Journal of the Royal Statistical...
  • Wilcox, R. R. (2007). On Flexible Tests of Independence and homoscedasticity. Journal of Modern Applied Statistical Methods, 6(1), 30–35....
  • Will M. Bertrand, J., & Fransoo, J. C. (2002). Operations management research methodologies using quantitative modeling. International...
  • Wu, X., & Yang, Z. (2013). Nonlinear speech coding model based on genetic programming. Applied Soft Computing, 13(7), 3314–3323. https://doi.org/10.1016/j.asoc.2013.02.008
  • Zhang, J., Gai, Y., Cui, X., & Li, G. (2020). Measuring symmetry and asymmetry of multiplicative distortion measurement errors data. Brazilian...