Recently, various approaches using manually designed convolutional neural networks (CNNs) and U-shaped (encoder-decoder) models have yielded encouraging results in the automatic segmentation of medical images. Nevertheless, the manual construction of these models is laborious, requires a high level of expertise, is time-consuming, error-prone and can result in the loss of crucial details. To improve segmentation performance, these models often incorporate numerous parameters, which can lead to problems such as overfitting, vanishing and exploding gradient and increased computational complexity. In this study, we implement a genetic algorithm (GA) specifically designed for a U-Net architecture to segment images of skin lesions, using two datasets ISIC-SMALL1 and ISIC-SMALL2 constructed from ISIC-2017 dataset. The main objective is to optimize internal block topologies within the U-Net, in order to identify a high-performance deep neural network with a minimum of parameters. Compared to the U-Net baseline, our proposed methodology demonstrates favorable outcomes in terms of both the number of trainable parameters and Intersection over Union (IoU). For the ISIC-SMALL1 dataset, the leading model surpasses U-Net with a reduced parameter count (0.352001M) and an elevated IoU score (0.826052 vs. 0.736352). Similarly, the second-best model outperforms U-Net with fewer parameters (0.258781M vs. 31.043586M) and a higher IoU score (0.821956 vs. 0.736352). In the ISIC-SMALL2 dataset, both top models outshine U-Net in IoU (0.753122 and 0.722079 vs. 0.725363, respectively) while maintaining lower parameter counts.