Comparison of linear and classical velocity update rules in particle swarm optimization: notes on scale and frame invariance

In this paper we investigate whether the particle swarm optimization (PSO) algorithm is invariant of the scale and frame (i.e. translation and rotation) in which an objective function is posed. To do so, we study the linear and classical velocity update rules. We will show that the linear velocity update rule is scale and frame invariant, but that the classical velocity update rule lacks rotational invariance.

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