Analysis of stability, local convergence, and transformation sensitivity of a variant of the particle swarm optimization algorithm

Bonyadi, Mohammad Reza and Michalewicz, Zbigniew (2016) Analysis of stability, local convergence, and transformation sensitivity of a variant of the particle swarm optimization algorithm. IEEE Transactions on Evolutionary Computation, 20 3: 370-385. doi:10.1109/TEVC.2015.2460753


Author Bonyadi, Mohammad Reza
Michalewicz, Zbigniew
Title Analysis of stability, local convergence, and transformation sensitivity of a variant of the particle swarm optimization algorithm
Journal name IEEE Transactions on Evolutionary Computation   Check publisher's open access policy
ISSN 1089-778X
1941-0026
Publication date 2016-06-01
Year available 2015
Sub-type Article (original research)
DOI 10.1109/TEVC.2015.2460753
Open Access Status Not Open Access
Volume 20
Issue 3
Start page 370
End page 385
Total pages 16
Place of publication Piscataway, United States
Publisher Institute of Electrical and Electronics Engineers
Collection year 2017
Language eng
Formatted abstract
In this paper, we investigate three important properties (stability, local convergence, and transformation invariance) of a variant of particle swarm optimization (PSO) called standard PSO 2011 (SPSO2011). Through some experiments, we identify boundaries of coefficients for this algorithm that ensure particles converge to their equilibrium. Our experiments show that these convergence boundaries for this algorithm are: 1) dependent on the number of dimensions of the problem; 2) different from that of some other PSO variants; and 3) not affected by the stagnation assumption. We also determine boundaries for coefficients associated with different behaviors, e.g., nonoscillatory and zigzagging, of particles before convergence through analysis of particle positions in the frequency domain. In addition, we investigate the local convergence property of this algorithm and we prove that it is not locally convergent. We provide a sufficient condition and related proofs for local convergence for a formulation that represents updating rules of a large class of PSO variants. We modify the SPSO2011 in such a way that it satisfies that sufficient condition; hence, the modified algorithm is locally convergent. Also, we prove that the original standard PSO algorithm is not sensitive to rotation, scaling, and translation of the search space.
Keyword Local convergence
Particle swarm optimization (PSO)
Stability analysis
Transformation invariance
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: HERDC Pre-Audit
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