S. Kok, D.N. Wilke, and A.A. Groenwold (South Africa)
Particle swarm optimization, observer independence, invari
ance, diversity, line search, trajectory collapse
We present a detailed analysis of the particle swarm opti
mization algorithm (PSOA). We show that implementation
subtleties due to ambiguous notation have resulted in two
distinctly different implementations of the PSOA, both of
which have been used unknowingly within the optimization
community. However, discerning between these two imple
mentations is shown to be of crucial importance.
We also investigate the ability of the particle swarm
optimization algorithm (PSOA) to satisfy objectivity, also
called observer independence or frame indifference.
The ﬁrst implementation is shown to be observer inde
pendent, but the search trajectories in this implementation
suffer from a collapse to line searches. In turn, we show that
the second implementation of the PSOA, for which the par
ticle trajectories are shown to be space ﬁlling, suffers from
We then introduce a novel formulation of the PSOA,
in which the particle trajectories do not collapse to line
searches, while observer independence is preserved. In this
formulation a new parameter is introduced, and the effect
thereof is investigated.
We quantify the three different formulations using a
popular test set in both the unrotated reference frame, and
an arbitrary rotated reference frame.