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Mathematical Problems in Engineering
Volume 2015, Article ID 178545, 17 pages
Research Article

An Efficient Algorithm for Unconstrained Optimization

1Departamento de Ingeniería Eléctrica, Universidad Autónoma Metropolitana-Iztapalapa, Avenida San Rafael Atlixco 186, Colonia Vicentina, Delegación Iztapalapa, 09340 México, DF, Mexico
2Departamento de Sistemas, Universidad Autónoma Metropolitana-Azcapotzalco, Avenida San Pablo 180, Colonia Reynosa Tamaulipas, 02200 México, DF, Mexico

Received 29 April 2015; Revised 4 August 2015; Accepted 6 August 2015

Academic Editor: Peide Liu

Copyright © 2015 Sergio Gerardo de-los-Cobos-Silva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an original and efficient PSO algorithm, which is divided into three phases: (1) stabilization, (2) breadth-first search, and (3) depth-first search. The proposed algorithm, called PSO-3P, was tested with 47 benchmark continuous unconstrained optimization problems, on a total of 82 instances. The numerical results show that the proposed algorithm is able to reach the global optimum. This work mainly focuses on unconstrained optimization problems from 2 to 1,000 variables.