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Mathematical Problems in Engineering
Volume 2017, Article ID 6129865, 14 pages
Research Article

A Study on the Convergence of Family Particle Swarm Optimization

1Yuxi Normal University, Yuxi 653100, China
2Yunnan University, Yunnan 650091, China

Correspondence should be addressed to Zhenzhou An; moc.anis@uohznehzna

Received 31 August 2016; Revised 18 October 2016; Accepted 30 November 2016; Published 31 January 2017

Academic Editor: Bing Wang

Copyright © 2017 Zhenzhou An 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.


The sociological concept of family has been introduced in the particle swarm optimization (PSO) and the family PSO (FPSO) has been proposed, in which the particle swarm consisted of different families, each family consisted of different members, and there were different constraint relationships between family members. To further study the sensitivity of FPSO to the control parameters, this paper proposed a special model of FPSO and analyzed the convergence of FPSO theoretically. This model offered a new view to research the particle trajectory and divided the position sequence of particle into the even and odd subsequences. By mathematical analysis, the condition of two subsequences convergence was obtained and the related convergent theories and corollaries were proved. Simulations for benchmark functions showed that the convergence behavior of model and experimental results provided a valuable guideline for selecting control parameters.