@misc{10481/72771,
year = {2021},
month = {12},
url = {http://hdl.handle.net/10481/72771},
abstract = {Function interpolation and approximation are classical problems of vital importance in
many science/engineering areas and communities. In this paper, we propose a powerful methodology
for the optimal placement of centers, when approximating or interpolating a curve or surface to
a data set, using a base of functions of radial type. In fact, we chose a radial basis function under
tension (RBFT), depending on a positive parameter, that also provides a convenient way to control
the behavior of the corresponding interpolation or approximation method. We, therefore, propose
a new technique, based on multi-objective genetic algorithms, to optimize both the number of
centers of the base of radial functions and their optimal placement. To achieve this goal, we use
a methodology based on an appropriate modification of a non-dominated genetic classification
algorithm (of type NSGA-II). In our approach, the additional goal of maintaining the number of
centers as small as possible was also taken into consideration. The good behavior and efficiency of
the algorithm presented were tested using different experimental results, at least for functions of one
independent variable.},
organization = {Junta de Andalucía-Consejería de Transformación Econímica, Industria, Conocimiento y Universidades

A-FQM-76-UGR20},
organization = {Universidad de Granada},
organization = {European Regional Development Fund},
organization = {Junta de Andalucía

	FQM191},
publisher = {MDPI},
keywords = {Approximation},
keywords = {Interpolation},
keywords = {RBFs},
keywords = {Centers’ allocation},
keywords = {MOGA},
keywords = {NSGA-II algorithms},
title = {Optimal Centers’ Allocation in Smoothing or Interpolating with Radial Basis Functions},
doi = {10.3390/math10010059},
author = {González Rodelas, Pedro and Idais, Hasan M. H. and Yasin, Mohammed and Pasadas Fernández, Miguel},
}