Particle swarm optimizer: The impact of unstable particles on performance

There exists a wealth of theoretical analysis on particle swarm optimization (PSO), specifically the conditions needed for stable particle behavior are well studied. This paper investigates the effect that the stability of the particle has on the PSO's actually ability to optimize. It is shown empirically that a majority of PSO parameters that are theoretically unstable perform worse than a trivial random search across 28 objective functions, and across various dimensionalities. It is also noted that there exists a number of parameter configurations just outside the stable-2 region which did not exhibit poor performance, implying that a minor violation of the conditions for order-2 stability is still acceptable in terms of overall performance of the PSO.