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 observer dependence. 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.
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