Some remarks on the deterministic particle swarm optimization algorithm

In this paper, we give a simple proof for the convergence of the deterministic particle swarm optimization algorithm under the weak chaotic assumption and remark that the weak chaotic assumption does not relax the stagnation assumption in essence. Under the spectral radius assumption, we propose a convergence criterion for the deterministic particle swarm optimization algorithm in terms of the personal best and neighborhood best position of the particle that incorporates the stagnation assumption or the weak chaotic assumption as a special case.