Optimal Centers’ Allocation in Smoothing or Interpolating with Radial Basis Functions

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-01, Vol.10 (1), p.59
Main Authors: González-Rodelas, Pedro, Idais, Hasan M. H., Yasin, Mohammed, Pasadas, Miguel
Format: Article
Language:English
Subjects:
Approximation
centers’ allocation
Food science
Genetic algorithms
Independent variables
Interpolation
Mathematical analysis
MOGA
Multiple objective analysis
Neural networks
NSGA-II algorithms
Optimization
Ordinary differential equations
Placement
Radial basis function
RBFs
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10010059