We consider a general form of the swarm intelligence as a function optimization tool. This form is derived from a basis of mathematical swarming differential equation model, where several parameters are included in the model. These parameters are corresponding to a repulsion effect, an attractive effect and a gradient direction. We mainly consider a repulsion effect and unknown gradient estimation in this study. The nature of the proposed model by some typical numerical simulation results is described. Then, the numerous simulation results show that the behaviors of the swarm will change significantly, for example, aggregation and clustering by parameter setting. We are able to see basic behaviors of the swarm intelligence by the introduced model, the model could give us the insight to understand search behavior of swarm intelligence.
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