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Mathematical Problems in Engineering
Volume 2014, Article ID 762015, 9 pages
Research Article

Analysis of Population Diversity of Dynamic Probabilistic Particle Swarm Optimization Algorithms

1School of Computer Science and Engineering, Southeast University, Nanjing 211189, China
2Laboratory of Military Network Technology, PLA University of Science and Technology, Nanjing 210007, China

Received 6 September 2013; Revised 24 December 2013; Accepted 26 December 2013; Published 3 February 2014

Academic Editor: Shuping He

Copyright © 2014 Qingjian Ni and Jianming Deng. 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.


In evolutionary algorithm, population diversity is an important factor for solving performance. In this paper, combined with some population diversity analysis methods in other evolutionary algorithms, three indicators are introduced to be measures of population diversity in PSO algorithms, which are standard deviation of population fitness values, population entropy, and Manhattan norm of standard deviation in population positions. The three measures are used to analyze the population diversity in a relatively new PSO variant—Dynamic Probabilistic Particle Swarm Optimization (DPPSO). The results show that the three measure methods can fully reflect the evolution of population diversity in DPPSO algorithms from different angles, and we also discuss the impact of population diversity on the DPPSO variants. The relevant conclusions of the population diversity on DPPSO can be used to analyze, design, and improve the DPPSO algorithms, thus improving optimization performance, which could also be beneficial to understand the working mechanism of DPPSO theoretically.