Convergence and Stability Analysis of Particle Swarm Optimization Using The Fixed Point Method

Subject Areas : International Journal of Mathematical Modelling & Computations

H Akewe ^{1 *} , E. P.Fasina ² , B. A.Sawyerr ³

1 - Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria.
2 - Department of Computer Sciences, University of Lagos, Lagos, Nigeria.
3 - Department of Computer Sciences, University of Lagos, Lagos, Nigeria.

Received: 2023-07-10 Accepted : 2025-05-21 Published : 2025-05-30

Keywords: Fixed point, Banach space, Particle Swarm Optimization, iteration algorithm,

Abstract :

This paper presents a fixed point analytical approach to one of the most commonly used optimization techniques known as particle swarm optimization (PSO) and established that the solution space of PSO is a Banach space. With the help of well constructed fixed point theorem, the iterative intelligence algorithm of the PSO was shown to converge to the unique global fixed point. The PSO iterative algorithm was further proven to be $T$-stable. An example was provided and used to demonstrate the applicablity of the stability result. Our results complement other methods of obtaining solutions for PSO in the literature.

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