Neural Architecture Search (NAS) aims to automate the design process of Deep Neural Networks (DNN) without requiring profound domain knowledge. The Deep Genetic Algorithm (DeepGA) was proposed to find the architectures of Convolutional Neural Networks (CNNs) for image processing, and its applications have covered a variety of data domains. Nonetheless, one of the main impediments of NAS is its computational cost, which is produced by evaluating candidate architectures. This work proposes using two cost-reduction mechanisms applied to DeepGA: using memory to avoid repeated evaluations and reducing the number of epochs for training in a low-fidelity estimation scheme for evaluations. The results indicate that the execution time of the algorithm was extensively reduced without diminishing the accuracy performance of the resulting architecture. The previous derives in a more efficient NAS procedure.