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Chapter 18
Dario Schor
University of Manitoba, Canada
Witold Kinsner
University of Manitoba, Canada
Time and Frequency Analysis
of Particle Swarm Trajectories
for Cognitive Machines
ABSTRACT
This paper examines the inherited persistent behavior of particle swarm optimization and its implica-
tions to cognitive machines. The performance of the algorithm is studied through an average particle’s
trajectory through the parameter space of the Sphere and Rastrigin function. The trajectories are decom-
posed into position and velocity along each dimension optimized. A threshold is defned to separate the
transient period, where the particle is moving towards a solution using information about the position of
its best neighbors, from the steady state reached when the particles explore the local area surrounding
the solution to the system. Using a combination of time and frequency domain techniques, the inherited
long-term dependencies that drive the algorithm are discerned. Experimental results show the particles
balance exploration of the parameter space with the correlated goal oriented trajectory driven by their
social interactions. The information learned from this analysis can be used to extract complexity mea-
sures to classify the behavior and control of particle swarm optimization, and make proper decisions on
what to do next. This novel analysis of a particle trajectory in the time and frequency domains presents
clear advantages of particle swarm optimization and inherent properties that make this optimization
algorithm a suitable choice for use in cognitive machines.
DOI: 10.4018/978-1-4666-2476-4.ch018