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A low-dimensional plasma physics based on the nonlinear dynamical model of the magnetosphere-ionosphere system called WINDMI is used as the basis for a real-time space weather prediction system. The input into the model is a driving voltage derived from solar wind parameters and the interplanetary magnetic field measured by the Advanced Composition Explorer satellite. The output is a field-aligned current proportional to the westward auroral electrojet AL index and the energy stored in the Earth's ring current which is proportional to the Dst index. In order to use the model for the real-time prediction of geomagnetic activity, the model parameters are required to update periodically. We developed a modified genetic algorithm (GA) with micromovement (MGAM) to train the parameters of the model in order to achieve the lowest mse against the measured AL and Dst indexes. The MGAM implements a particle-swarm-optimization-inspired movement phase that helps to improve the convergence rate while employing the efficient GA mechanism for maintaining the population diversity. The performance of the MGAM is compared to a basic real-valued GA (RGA) on five standard test functions and historical geomagnetic storm data sets. While the MGAM performs substantially better than the RGA when evaluating the standard test functions, the improvement is about 6%-12% when used on the 20-D nonlinear dynamical WINDMI model.