It is known that the most common versions of particle swarm optimization (PSO) algorithms are rotationally variant. It has also been pointed out that PSO algorithms can concentrate particles along paths parallel to the coordinate axes. In this paper we explicitly connect these two observations, by showing that the rotational variance is related to the concentration along lines parallel to the coordinate axes. We then clarify the nature of this connection. Based on this explicit connection we create fitness functions that are easy or hard for PSO to solve, depending on the rotation of the function.
William M. Spears, Derek T. Green, Diana F. Spears