In particle swarm optimization (PSO), (x_{\text{min}}) and (x_{\text{max}}) typically define the boundaries of the search space for the particles. (x_{\text{min}}) represents the lower limit and (x_{\text{max}}) the upper limit of the parameters being optimized. These values ensure that the particles remain within defined constraints during the optimization process, preventing them from exploring infeasible regions of the solution space. The specific values of (x_{\text{min}}) and (x_{\text{max}}) depend on the particular problem being addressed.
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