On Trajectories of Particles in PSO

The moving behaviour of the particles in particle swarm optimization (PSO) algorithms is studied in this paper. It is shown that particles in standard PSO have a clear bias in their movement direction that depends on the direction of the coordinate axes. This has the effect that the optimization behaviour of standard PSO is not invariant to rotations of the optimization function. A second problem of standard PSO is that non-oscillatory trajectories can quickly cause a particle to stagnate. A sidestep mechanism is proposed to improve the movement of the particles. A particle performs a sidestep with respect to a certain dimension when stagnation of movement along this dimension is observed. It is shown for simple test functions that the movement behaviour of sidestep PSO can prevent the unwanted bias and makes PSO less dependent on rotations of the optimization function. It is also shown for standard benchmark functions that sidestep PSO outperforms standard PSO