Optimization of coefficients of lists of polynomials by evolutionary algorithms

Authors
Sendra Pons, Juan RafaelUniversity of Alcalá Author; Winkler, Stephan M.
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/22340
ISSN: 1787-6117
Publisher
Líceum University Press
Date
2015
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Annales Mathematicae et Informaticae, 2015, v. 44, p. 177-185
Keywords
Optimization of parametrizations
symbolic computation
evolutionary computation
evolution strategies
Project
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
http://ami.ektf.hu
Rights
(c) Annales Mathematicae et Informaticae, 2015
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We here discuss the optimization of coefficients of lists of polynomials using evolutionary computation. The given polynomials have 5 variables, namely t, a1, a2, a3, a4, and integer coefficients. The goal is to find integer values i, with i 2 {1, 2, 3, 4}, substituting ai such that, after crossing out the gcd (greatest common divisor) of all coefficients of the polynomials, the resulting integers are minimized in absolute value. Evolution strategies, a special class of heuristic, evolutionary algorithms, are here used for solving this problem. In this paper we describe this approach in detail and analyze test results achieved for two benchmark problem instances; we also show a visual analysis of the fitness landscapes of these problem instances
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