Synthesis of the parameters of a nonlinear predictive model using a genetic algorithm
DOI:
https://doi.org/10.34185/1562-9945-2-145-2023-07Keywords:
Genetic algorithm, least squares method, nonlinear model, Richard's function, model parametersAbstract
The article deals with the definition and estimation of the parameters of a nonlinear regression model using a genetic algorithm. Parameter estimation is a type of optimization problem that can be solved using stochastic algorithms, which presents the possibility of using such algorithms to fit nonlinear regression models. The trees data set, which displays the non-linear relationship between traits, was investigated. The nonlinear method of least squares (NLS) was used to find the coefficients of the regression equation using a genetic algorithm on the trees data set belonging to the spuRs library. The set contains 1200 observations and three variables: tree ID; age of the tree; volume of wood. Visual analysis revealed the presence of additional signs that affect the volume of wood. Only data for trees with a certain location are selected for further work. As a result, the sample has 12 observations and two variables. The dependence of the volume of wood (Vol) on the age of the tree (Age) was analyzed. Attention to tree locations made it possible to choose the Richards logistic function as a functional dependence, nonlinear both in terms of parameters and variables. A genetic algorithm was used to estimate the parameters of the Richards function. The result of the work of the genetic algorithm depends on how its parameters are configured. When implementing the genetic algorithm, the following parameters were set: population size; the maximum number of iterations after which the work of the genetic algorithm stops; the number of consecutive generations without any improvement in the value of the fitness function before stopping the algorithm. A random scheme was used for the selection operation. A mutation operation involves changing a randomly selected bit. The type of crossover operation is one-point. Coefficients of nonlinear models were calculated for randomly selected tree locations. The coefficient of determination R2 was used to assess the quality of the models.
References
Бідюк П.І., Гожий О.П. Ймовірнісно-статистичні методи моделювання і про-гнозування: [монографія] . – Миколаїв: Вид-во ЧДУ ім. Петра Могили, 2014. – 440 с.
De Gooijer J.G. Elements of Nonlinear Time Series Analysis and Forecasting. Springer Series in Statistics. Library of Congress Control Number: 2017935720. 2017, 620 p. DOI 10.1007/978-3-319-43252-6/
Bidyuk P., Gozhyj A., Kalinina I., Vysotska V. (2020) Methods for Forecasting Nonline-ar Non-stationary Processes in Machine Learning. Communications in Computer and Information Science. – Volume 1158. – Springer, Cham, 2020. – pp. 470-485. - Print ISBN978-3-030-61655-7, Online ISBN978-3-030-61656-4. DOI: https://doi.org/10.1007/ 978-3-030-61656-4_32.
Gen M., Cheng R. (2000), Genetic Algorithms and Engineering Optimization (New York: John Wiley &Sons Inc).
Kapanoglu M., Koc I.O., Erdogmus S., Genetic algorithms in parameter estimation for nonlinear regression models: an experimental approach, Journal of Statistical Computation and Simulation, 77(10):851-867, (2007).
Haj Seyed Hadi M.R., Gonzalez-Andujar J.L. Comparison of Fitting Weed Seedling Emergence Models with Nonlinear Regression and Genetic Algorithm. Comput. Electron. Agric. 2009, 65, pp. 19–25.
Mitra S., Mitra A., Kundu D. Genetic algorithm and M-estimator based robust se-quential estimation of parameters of nonlinear sinusoidal signals. Communications in Nonlinear Science and Numerical Simulation. Vol. 16, Issue 7, 2011, pp. 2796-2809. https://doi.org/10.1016/j.cnsns. 2010.10.005.
Paterakis E., Petridis V., Kehagias A. Genetic algorithm in parameter estimation of nonlinear dynamic systems. International Conference on Parallel Problem Solving from Nature, 2006, 171 Accesses, 2 Citations, pp. 1008–1017.
DOI: 10.1007/BFb0056942.
Monti C.A.U., Oliveira R.M., Roise J.P., Scolforo H.F., Gomide L.R. Hybrid Method for Fitting Nonlinear Height–Diameter Functions. Journals “Forests”, Vol. 13, Issue 11, 2022. https://doi.org/10.3390/f13111783.
Leehter, Y., Sethares, W.A. Nonlinear Parameter Estimation via the Genetic Al-gorithm. IEEE Trans. Signal Process. 1994, 42, pp. 927–935.
Chatterjee, S., Laudato M., Lynch, L.A. Genetic Algorithms and Their Statistical Applications: An Introduction. Comput. Stat. Data Anal. 1996, 22, pp. 633–651.
Jin Y.-F., Yin Z.-Y., Shen S.-L., Hicher, P.-Y. Selection of Sand Models and Iden-tification of Parameters Using an Enhanced Genetic Algorithm. Int. J. Numer. Anal. Methods Geomech. 2016, 40, pp. 1219–1240.
VanderNoot T.J. Abrahams I. The Use of Genetic Algorithms in the Non-Linear Regression of Immittance Data. J. Electroanal. Chem. 1998, 448, pp. 17–23.
Lacerda T.H.S., Miranda E.N., E Lopes I.L., Fonseca G.R., França L.C., de Jesus França L.C., Gomide L.R. Feature Selection by Genetic Algorithm in Nonlinear Taper Model. Can. J. For. Res. 2022, 52, pp. 769–779.
Zhou X., Wang J., (2005) A genetic method of LAD estimation for models with censored data. Computational Statistics and Data Analysis,48(3), pp. 451–466.
