This paper uses a Genetic Algorithm (GA) to reduce total tardiness in an identical parallel machine scheduling problem. The proposed GA is a crossover-free (vegetative reproduction) GA but used for four types of mutations (Two Genes Exchange mutation, Number of Jobs mutation, Flip Ends mutation, and Flip Middle mutation) to make the required balance between the exploration and exploitation functions of the crossover and mutation operators. The results showed that use of these strategies positively affects the accuracy and robustness of the proposed GA in minimizing the total tardiness. The results of the proposed GA are compared to the mathematical model in terms of the time required to tackle the proposed problem. The findings illustrate the ability of the propounded GA to acquire the results in a short time compared to the mathematical model. On the other hand, increasing the number of machines degraded the performance of the proposed GA.