Particle swarm stability: a theoretical extension using the non-stagnate distribution assumption

This paper presents an extension of the state of the art theoretical model utilized for understanding the stability criteria of the particles in particle swarm optimization algorithms. Conditions for order-1 and order-2 stability are derived by modeling, in the simplest case, the expected value and...

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Bibliographic Details
Published in:Swarm intelligence 2018-03, Vol.12 (1), p.1-22
Main Authors: Cleghorn, Christopher W., Engelbrecht, Andries P.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Communications Engineering
Computer Communication Networks
Computer Science
Computer Systems Organization and Communication Networks
Expected values
Mathematical and Computational Engineering
Networks
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Summary:This paper presents an extension of the state of the art theoretical model utilized for understanding the stability criteria of the particles in particle swarm optimization algorithms. Conditions for order-1 and order-2 stability are derived by modeling, in the simplest case, the expected value and variance of a particle’s personal and neighborhood best positions as convergent sequences of random variables. Furthermore, the condition that the expected value and variance of a particle’s personal and neighborhood best positions are convergent sequences is shown to be a necessary condition for order-1 and order-2 stability. The theoretical analysis presented is applicable to a large class of particle swarm optimization variants.
ISSN:1935-3812
1935-3820
DOI:10.1007/s11721-017-0141-x