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

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dc.contributor.authorChaquet, José M.
dc.contributor.authorCarmona, Enrique J.
dc.date.accessioned2024-08-21T12:13:35Z
dc.date.available2024-08-21T12:13:35Z
dc.date.issued2019-03-15
dc.description.abstractA 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.en
dc.description.versionversión final
dc.identifier.doihttps://doi.org/10.1007/s00500-017-2888-9
dc.identifier.issn1433-7479
dc.identifier.urihttps://hdl.handle.net/20.500.14468/23292
dc.journal.titleSoft Computing
dc.journal.volume23
dc.language.isoen
dc.publisherSpringer
dc.relation.centerFacultades y escuelas::E.T.S. de Ingeniería Informática
dc.relation.departmentInteligencia Artificial
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject.keywordsDifferential equations
dc.subject.keywordsCovariance Matrix
dc.subject.keywordsAdaptation Evolution Strategies
dc.subject.keywordsGaussian kernel
dc.subject.keywordsDownhill Simplex algorithm
dc.titleUsing covariance matrix adaptation evolution strategies for solving different types of differential equationses
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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