Particle convergence time in the PSO model with inertia weight

Particle Swarm Optimization (PSO) is a powerful heuristic optimization method being subject of continuous interest. Theoretical analysis of its properties concerns primarily the conditions necessary for guaranteeing its convergent behaviour. Particle behaviour depends on three groups of parameters: values of factors in a velocity update rule, initial localization and velocity and fitness landscape. The paper presents theoretical analysis of the particle convergence properties in the model with inertia weight respectively to different values of these parameters. A new measure for evaluation of a particle convergence time is proposed. For this measure an upper bound formula is derived and its four main types of characteristics are discussed. The way of the characteristics transformations respectively to changes of velocity equation parameters is presented as well.