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For the discretization of particles in particle swarm optimization (PSO), we have proposed the family PSO (FPSO) previously. To further study the internal structure of FPSO, this paper defined two kinds of relationships between particles: equal relationship (ER) and generational relationship (GR). FPSO of equal relationship (ER-FPSO) and FPSO of generational relationship (GR-FPSO) were proposed. Simulations for seven benchmark functions demonstrated that the advantage and the effectiveness of ER-FPSO and GR-FPSO. In the experiments, the performances of ER-FPSO and GR-FPSO were also compared. Results indicate GR-FPSO has stronger judgment ability and intelligence. This conceptualization has a great of academic and realistic meaning.