The sociological concept of family has been introduced in the particle swarm optimization (PSO) and the family PSO (FPSO) has been proposed, in which the particle swarm consisted of different families, each family consisted of different members, and there were different constraint relationships between familymembers. To further study the sensitivity of FPSO to the control parameters, this paper proposed a specialmodel of FPSO and analyzed the convergence of FPSO theoretically. This model offered a new view to research the particle trajectory and divided the position sequence of particle into the even and odd subsequences. Bymathematical analysis, the condition of two subsequences convergence was obtained and the related convergent theories and corollaries were proved. Simulations for benchmark functions showed that the convergence behavior of model and experimental results provided a valuable guideline for selecting control parameters.
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