<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332015000200341</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[SC - system of convergence: theory and foundations]]></article-title>
<article-title xml:lang="es"><![CDATA[SC - sistema de convergencia: teoría y fundamentos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[De-Los-Cobos-Silva]]></surname>
<given-names><![CDATA[Sergio G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma Metropolitana Departamento de Ingeniería Eléctrica ]]></institution>
<addr-line><![CDATA[Iztapalapa México D.F.]]></addr-line>
<country>MX</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2015</year>
</pub-date>
<volume>22</volume>
<numero>2</numero>
<fpage>341</fpage>
<lpage>367</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332015000200341&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332015000200341&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332015000200341&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractIn this paper a novel system of convergence (SC) is presented as well as its fundamentals and computing experience. An implementation using a novel mono-objetive particle swarm optimization (PSO) algorithm with three phases (PSO-3P): stabilization, generation with broad-ranging exploration and generation with in-depth exploration, is presented and tested in a diverse benchmark problems. Evidence shows that the three-phase PSO algoritm along with the SC criterion (SC-PSO-3P)can converge to the global optimum in several difficult test functions for multiobjective optimization problems, constrained optimization problems and unconstrained optimization problems with 2 until 120,000 variables.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEn este trabajo se presenta un novedoso sistema de convergencia (SC), sus fundamentos y la experiencia computacional. Se implementó en un algoritmo PSO monoobjetivo de tres fases (PSO-3P): Estabilización, generación y búsqueda en amplitud, generación y búsqueda a profundidad, el cual se probó con diversos problemas benchmark. La evidencia muestra que el algoritmo PSO de 3 fases junto con el criterio SC (SC-PSO-3P) convergen al óptimo global para diversas funciones consideradas como difíciles para problemas de optimización multiobjetivo, para problemas de optimización con restricciones y para problemas de optimización sin restricciones que van desde 2 hasta 120,000 variables.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[particle swarm optimization]]></kwd>
<kwd lng="en"><![CDATA[unconstrained optimization]]></kwd>
<kwd lng="en"><![CDATA[constrained optimization]]></kwd>
<kwd lng="en"><![CDATA[multiobjective optimization]]></kwd>
<kwd lng="en"><![CDATA[fuzzy numbers]]></kwd>
<kwd lng="es"><![CDATA[optimización por enjambres de partículas]]></kwd>
<kwd lng="es"><![CDATA[optimización sin restricciones]]></kwd>
<kwd lng="es"><![CDATA[optimización con restricciones]]></kwd>
<kwd lng="es"><![CDATA[optimización multiobjetivo]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coello Coello]]></surname>
<given-names><![CDATA[C.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lamont]]></surname>
<given-names><![CDATA[G.B.]]></given-names>
</name>
<name>
<surname><![CDATA[Veldhuizen]]></surname>
<given-names><![CDATA[D.A. van]]></given-names>
</name>
</person-group>
<source><![CDATA[Evolutionary Algorithms for Solving Multi-Objective Problems]]></source>
<year>2007</year>
<edition>2d</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Ed. Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[de-los-Cobos-Silva]]></surname>
<given-names><![CDATA[S.G.]]></given-names>
</name>
</person-group>
<source><![CDATA["SC: sistema de convergencia: Condiciones y propiedades"]]></source>
<year>2014</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Instituto Nacional del Derecho de Autor, Secretaria de Educación Pública]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Deb]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Thiele]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Laumanns]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Zitzler]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA["Scalable multiobjective optimization test problems"]]></source>
<year>2002</year>
<conf-name><![CDATA[ Proceedings of the Congress on Evolutionary Computation]]></conf-name>
<conf-loc> </conf-loc>
<page-range>825-30</page-range><publisher-loc><![CDATA[Honolulu ]]></publisher-loc>
<publisher-name><![CDATA[IEEE Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA["Operations on fuzzy numbers"]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dubois]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Prade]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[International Journal of Systems Science]]></source>
<year>1978</year>
<volume>9</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>613-26</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gavana]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA["Global optimization benchmarks and AMPGO. Test functions"]]></source>
<year>2007</year>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hedar]]></surname>
<given-names><![CDATA[A.R.]]></given-names>
</name>
</person-group>
<source><![CDATA["Global optimization test problems"]]></source>
<year>2007</year>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kalami Heris]]></surname>
<given-names><![CDATA[S.M.]]></given-names>
</name>
</person-group>
<source><![CDATA[]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kennedy]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Eberhart]]></surname>
<given-names><![CDATA[R.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Shi]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Swarm Intelligence]]></source>
<year>2001</year>
<publisher-loc><![CDATA[San Francisco ]]></publisher-loc>
<publisher-name><![CDATA[Morgan Kaufmann]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Liang]]></surname>
<given-names><![CDATA[J.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Runarsson]]></surname>
<given-names><![CDATA[T.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mezura-Montes]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Clerc]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Suganthan]]></surname>
<given-names><![CDATA[P.N.]]></given-names>
</name>
<name>
<surname><![CDATA[Coello Coello]]></surname>
<given-names><![CDATA[C.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Deb]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA["Problem definitions and evaluation criteria for the CEC 2006, special session on constrained realparameter optimization"]]></source>
<year>2006</year>
<conf-name><![CDATA[ IEEE Congress on Evolutionary Computation]]></conf-name>
<conf-loc> </conf-loc>
<page-range>24</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA["Ranking fuzzy numbers with integral value"]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Liou]]></surname>
<given-names><![CDATA[T.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[M.J.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Fuzzy Sets and Systems]]></source>
<year>1992</year>
<volume>50</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>247-55</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Michalewicz]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Fogel]]></surname>
<given-names><![CDATA[D.B.]]></given-names>
</name>
</person-group>
<source><![CDATA[How to Solve It: Modern Heuristics]]></source>
<year>1998</year>
<edition>2nd</edition>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Surjanovic]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Bingham]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA["Virtual library of simulation experiments: test functions and datasets"]]></source>
<year>2013</year>
<publisher-name><![CDATA[Simon Fraser University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA["Comparison of multiobjective evolutionary algorithm: Empirical results"]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zitzler]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Deb]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Thiele]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Evolutionary Computation]]></source>
<year>2000</year>
<volume>8</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>173-95</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
