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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.22 n.2 San José Jul./Dec. 2015



SC - system of convergence: theory and foundations

SC - sistema de convergencia: teoría y fundamentos

Sergio G. De-Los-Cobos-Silva 1  

1Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, México. EMail:


In 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.

Keywords: particle swarm optimization; unconstrained optimization; constrained optimization; multiobjective optimization; fuzzy numbers


En 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.

Palabras clave:  optimización por enjambres de partículas; optimización sin restricciones; optimización con restricciones; optimización multiobjetivo

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The author would like to thank to D.Sto., and to P.V.Gpe. for their inspiration, and his family: Ma, Ser, Mon, Chema, and to his Flaquita for all their support.


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1Mathematics Subject Classification: 90C26, 90C29, 90C59.

Received: February 25, 2014; Revised: May 11, 2015; Accepted: May 20, 2015

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