Convergence criteria for the particle swarm optimization in a full iterative process

Although the theoretical aspects of the particle swarm optimization (PSO) seem to be forsaken, the few previous modeling studies -even with some assumptions- enlarged our knowledge of the PSO process. Here, we suggest a new model of PSO where all the N particles of the swarm and their components are considered. The iterative process is formulated by a 3N×3N block triangular matrix and its spectral radius is evaluated and displayed. Besides, the convergence related parametrization criteria are derived. Compared to previous results, a more restrictive acceleration coefficients criterion is found. Simulations are then carried out on CEC 2017 benchmark functions using eight PSO variants and show better results when considering the more restrictive criterion.