SPSO 2011: analysis of stability; local convergence; and rotation sensitivity

Abstract

In a particle swarm optimization algorithm (PSO) it is essential to guarantee convergence of particles to a point in the search space (this property is called stability of particles). It is also important that the PSO algorithm converges to a local optimum (this is called the local convergence property). Further, it is usually expected that the performance of the PSO algorithm is not affected by rotating the search space (this property is called the rotation sensitivity). In this paper, these three properties, i.e. stability of particles, local convergence, and rotation sensitivity are investigated for a variant of PSO called Standard PSO2011 (SPSO2011). We experimentally define boundaries for the parameters of this algorithm in such a way that if the parameters are selected in these boundaries, the particles are stable, i.e. particles converge to a point in the search space. Also, we show that, unlike earlier versions of PSO, these boundaries are dependent on the number of dimensions of the problem. Moreover, we show that the algorithm is not locally convergent in general case. Finally, we provide a proof and experimental evidence that the algorithm is rotation invariant.