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As a novel particles swarm optimization algorithm, r/KPSO takes the advantages of r-selection and K selection. Particles in high fitness (K-subswarm called in this paper) perform K-selection. K-subswarm only can produce few progenies but the progenies are nurtured delicately with much parent care. On the other hand, r-selection is performed for other particles in relatively low fitness (r-subswarm called). r-subswarm can produce a large number of progenies with little parent care and the progenies have to compete for survival according to fitness and only the best ones can survive. In r/KPSO, the particles performed r-selection mainly explore the search space as possible as they can to find more potential solutions in large speed, and those particles performed K-selection keep the current optimum solutions and exploit the space as they can to find more ideal solutions. To evaluate convergence speed quantitatively, a novel criterion named first converging generation (FCG) is introduced. Experiments were conducted on standard benchmark functions, and experimental results showed r/KPSO could converge in higher speed in terms of FCG and in higher precision than standard PSO (SPSO).