The Convergence Basis of Particle Swarm Optimization

The general mathematical description of the Particle Swarm Optimization is given in this paper. Also has proved that the solution space of PSO is Normed Space, the iterative relations of PSO are contraction mapping. Using the theorem of Banach space and contraction mapping principle prove the existe...

Full description

Saved in:
Bibliographic Details
Published in2012 International Conference on Industrial Control and Electronics Engineering pp. 63 - 66
Main Authors Wang Kan, Shen Jihong
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.08.2012
Subjects
Banach space
contraction mapping principle
convergence
Industrial control
parameter selection
stability
Online AccessGet full text
ISBN1467314501
9781467314503
DOI10.1109/ICICEE.2012.25

Cover

More Information
Summary:The general mathematical description of the Particle Swarm Optimization is given in this paper. Also has proved that the solution space of PSO is Normed Space, the iterative relations of PSO are contraction mapping. Using the theorem of Banach space and contraction mapping principle prove the existence and uniqueness of the convergence position. And summary the mathematical description of the convergence, using the theory of probability and stochastic process give the parameter condition that influences the stability of PSO. At last proves that if parameter satisfying the condition the probability that Particle Swarm Optimization converging the best position is one.
ISBN:1467314501
9781467314503
DOI:10.1109/ICICEE.2012.25