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Efficient identification of people and objects, segmentation of regions of interest and extraction of relevant data in images, texts, audios and videos are evolving considerably in these past years, which deep learning methods, combined with recent improvements in computational resources, contributed greatly for this achievement. Although its outstanding potential, development of efficient architectures and modules requires expert knowledge and amount of resource time available. In this paper, we propose an evolutionary-based neural architecture search approach for efficient discovery of convolutional models in a dynamic search space, within only 24 GPU hours. With its efficient search environment and phenotype representation, Gene Expression Programming is adapted for network's cell generation. Despite having limited GPU resource time and broad search space, our proposal achieved similar state-of-the-art to manually-designed convolutional networks and also NAS-generated ones, even beating similar constrained evolutionary-based NAS works. The best cells in different runs achieved stable results, with a mean error of 2.82% in CIFAR-10 dataset (which the best model achieved an error of 2.67%) and 18.83% for CIFAR-100 (best model with 18.16%). For ImageNet in the mobile setting, our best model achieved top-1 and top-5 errors of 29.51% and 10.37%, respectively. Although evolutionary-based NAS works were reported to require a considerable amount of GPU time for architecture search, our approach obtained promising results in little time, encouraging further experiments in evolutionary-based NAS, for search and network representation improvements.