In this contribution, an interpolation problem using radial basis functions is considered. A recently proposed approach for the search of the optimal value of the shape parameter is studied. The approach consists of using global optimization algorithms to minimize the error function obtained using a leave-one-out cross validation (LOOCV) technique, which is commonly used for solving machine learning problems. In this paper, the proposed approach is studied experimentally on classes of randomly generated test problems using the GKLS-generator, which is widely used for testing global optimization algorithms. The experimental study on classes of randomly generated test problems is very important from the practical point of view, since results show the behavior of the algorithms for solving not a single test problem, but the whole class with controllable difficulty, which is the main property of the GKLS-generator. The obtained results are relevant, since the experiments have been carried out on 200 randomized test problems, and show that the algorithms are efficient for solving difficult real-life problems demonstrating a promising behavior.

An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions

Cavoretto R.;De Rossi A.
2020-01-01

Abstract

In this contribution, an interpolation problem using radial basis functions is considered. A recently proposed approach for the search of the optimal value of the shape parameter is studied. The approach consists of using global optimization algorithms to minimize the error function obtained using a leave-one-out cross validation (LOOCV) technique, which is commonly used for solving machine learning problems. In this paper, the proposed approach is studied experimentally on classes of randomly generated test problems using the GKLS-generator, which is widely used for testing global optimization algorithms. The experimental study on classes of randomly generated test problems is very important from the practical point of view, since results show the behavior of the algorithms for solving not a single test problem, but the whole class with controllable difficulty, which is the main property of the GKLS-generator. The obtained results are relevant, since the experiments have been carried out on 200 randomized test problems, and show that the algorithms are efficient for solving difficult real-life problems demonstrating a promising behavior.
10th International Conference on Optimization and Applications (OPTIMA)
Petrovac, MONTENEGRO
SEP 30-OCT 04, 2019
OPTIMIZATION AND APPLICATIONS, OPTIMA 2019
SPRINGER INTERNATIONAL PUBLISHING AG
1145
326
339
978-3-030-38602-3
978-3-030-38603-0
http://www.springer.com/series/7899
Global optimization algorithms; Radial basis functions; Shape parameter
Mukhametzhanov M.S.; Cavoretto R.; De Rossi A.
File in questo prodotto:
File Dimensione Formato  
P35.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 684.09 kB
Formato Adobe PDF
684.09 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
paper_optima19_UniTO.pdf

Accesso aperto

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 703.21 kB
Formato Adobe PDF
703.21 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1730688
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 2
social impact