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Over the past century, the fixed point theory has emerged as a very useful and efficient tool in the study of nonlinear problems. This study introduced a progressed genetic algorithm (GA) based on a particular mutation operator applying on a subdivided search space where integer label and relative coordinates are used. This algorithm eventually categorizes each fixed point as its solution in appropriate set. Extensive computational experiments are conducted to assess the performance of the proposed technique with a standard GA for solving some nonlinear numerical functions from the literature.