The genetic algorithm (GA) is a popular random search and optimization method inspired by the concepts of crossover, random mutation, and natural selection from evolutionary biology. The real-valued genetic algorithm (RGA) is an improved version of the genetic algorithm designed for direct operation on real-valued variables. In this work, a modified version of a genetic algorithm is introduced, which is called a modified genetic algorithm with micro-movement (MGAM). It implements a particle swarm optimization(PSO)-inspired micro-movement phase that helps to improve the convergence rate, while employing the e'cient GA mechanism for maintaining population diversity. In order to test the capability of the MGAM, we firrst implement it on five generally used test functions. Then we test the MGAM on two typical nonlinear dynamical systems. The performance of the MGAM is compared to a basic RGA on all these applications. Finally, we implement the MGAM on the most important application, which is the plasma physics-based model of the solar wind-driven magnetosphere-ionosphere system (WINDMI). In order to use this model for real-time prediction of geomagnetic activity, the model parameters require up-dating every 6-8 hours. We use the MGAM to train the parameters of the model in order to achieve the lowest mean square error (MSE) against the measured auroral electrojet (AL) and Dst indices. The performance of the MGAM is compared to the RGA on historical geomagnetic storm datasets. While the MGAM performs substantially better than the RGA when evaluating standard test functions, the improvement is about 6-12 percent when used on the 20D nonlinear dynamical WINDMI model.