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Journal of Applied Mathematics
Volume 2014, Article ID 293087, 10 pages
Research Article

A Comparison of Selected Modifications of the Particle Swarm Optimization Algorithm

Department of Water Resources and Environmental Modeling, Faculty of Environmental Sciences, Czech University of Life Sciences Prague, Kamýcká 1176, Prague 6, 165 21 Suchdol, Czech Republic

Received 10 October 2013; Accepted 24 March 2014; Published 15 June 2014

Academic Editor: Nan-Jing Huang

Copyright © 2014 Michala Jakubcová 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.


We compare 27 modifications of the original particle swarm optimization (PSO) algorithm. The analysis evaluated nine basic PSO types, which differ according to the swarm evolution as controlled by various inertia weights and constriction factor. Each of the basic PSO modifications was analyzed using three different distributed strategies. In the first strategy, the entire swarm population is considered as one unit (OC-PSO), the second strategy periodically partitions the population into equally large complexes according to the particle’s functional value (SCE-PSO), and the final strategy periodically splits the swarm population into complexes using random permutation (SCERand-PSO). All variants are tested using 11 benchmark functions that were prepared for the special session on real-parameter optimization of CEC 2005. It was found that the best modification of the PSO algorithm is a variant with adaptive inertia weight. The best distribution strategy is SCE-PSO, which gives better results than do OC-PSO and SCERand-PSO for seven functions. The sphere function showed no significant difference between SCE-PSO and SCERand-PSO. It follows that a shuffling mechanism improves the optimization process.