Analyzing Convergence and Rates of Convergence of Particle Swarm Optimization Algorithms Using Stochastic Approximation Methods

Recently, much progress has been made on particle swarm optimization (PSO). A number of works have been devoted to analyzing the convergence of the underlying algorithms. Nevertheless, in most cases, rather simplified hypotheses are used. For example, it often assumes that the swarm has only one par...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:IEEE transactions on automatic control Jg. 60; H. 7; S. 1760 - 1773
Hauptverfasser: Quan Yuan, Yin, George
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.07.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithm design and analysis
Algorithms
Approximation algorithms
Approximation methods
Convergence
Optimization
Particle swarm optimization
Queuing theory
rate of convergence
stochastic approximation
Stochastic processes
weak convergence
rate of convergence
stochastic approximation
weak convergence
Particle swarm optimization (PSO)
ISSN:0018-9286, 1558-2523
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Recently, much progress has been made on particle swarm optimization (PSO). A number of works have been devoted to analyzing the convergence of the underlying algorithms. Nevertheless, in most cases, rather simplified hypotheses are used. For example, it often assumes that the swarm has only one particle. In addition, more often than not, the variables and the points of attraction are assumed to remain constant throughout the optimization process. In reality, such assumptions are often violated. Moreover, there are no rigorous rates of convergence results available to date for the particle swarm, to the best of our knowledge. In this paper, we consider a general form of PSO algorithms, and analyze asymptotic properties of the algorithms using stochastic approximation methods. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence method. A centered and scaled sequence of the estimation errors is shown to have a diffusion limit.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2014.2381454