Using covariance matrix adaptation evolution strategies for solving different types of differential equations

Chaquet, José M. y Carmona, Enrique J. . (2019) Using covariance matrix adaptation evolution strategies for solving different types of differential equations. Soft Computing, 23, 1643-1666, 2019

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Título Using covariance matrix adaptation evolution strategies for solving different types of differential equations
Autor(es) Chaquet, José M.
Carmona, Enrique J.
Materia(s) Informática
Ingeniería Informática
Abstract A novel mesh-free heuristic method for solving differential equations is proposed. The new approach can cope with linear, nonlinear, and partial differential equations (DE), and systems of DEs. Candidate solutions are expressed using a linear combination of kernel functions. Thus, the original problem is transformed into an optimization problem that consists in finding the parameters that define each kernel. The new optimization problem is solved applying a Covariance Matrix Adaptation Evolution Strategy. To increase the accuracy of the results, a Downhill Simplex local search is applied to the best solution found by the mentioned evolutionary algorithm. Our method is applied to 32 differential equations extracted from the literature. All problems are successfully solved, achieving competitive accuracy levels when compared to other heuristic methods. A simple comparison with numerical methods is performed using two partial differential equations to show the pros and cons of the proposed algorithm. To verify the potential of this approach with a more practical problem, an electric circuit is analyzed in depth. The method can obtain the dynamic behavior of the circuit in a parametric way, taking into account different component values.
Palabras clave Differential equations
Covariance Matrix
Adaptation Evolution Strategies
Gaussian kernel
Downhill Simplex algorithm
Editor(es) Springer
Fecha 2019-03-15
Identificador bibliuned:95-Ejcarmona-0006
http://e-spacio.uned.es/fez/view/bibliuned:95-Ejcarmona-0006
DOI - identifier https://doi.org/10.1007/s00500-017-2888-9
ISSN - identifier 1433-7479
Nombre de la revista Soft Computing
Número de Volumen 23
Página inicial 1643
Página final 1666
Publicado en la Revista Soft Computing, 23, 1643-1666, 2019
Idioma eng
Versión de la publicación acceptedVersion
Tipo de recurso Article
Derechos de acceso y licencia http://creativecommons.org/licenses/by-nc-nd/4.0
info:eu-repo/semantics/openAccess
Tipo de acceso Acceso abierto
Notas adicionales This is an Accepted Manuscript of an article published by Springer in "Soft Computing, 23, 1643-1666, (2019)", available at: https://doi.org/10.1007/s00500-017-2888-9
Notas adicionales Este es el manuscrito aceptado del artículo publicado por Springer en "Soft Computing, 23, 1643-1666, (2019)", disponible en línea: https://doi.org/10.1007/s00500-017-2888-9

 
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