In this paper, we present a novel neuroevolutionary method to identify the architecture and hyperparameters of convolutional autoencoders. Remarkably, we used a hypervolume indicator in the context of neural architecture search for autoencoders, for the first time to our current knowledge. Results show that images were compressed by a factor of more than 10, while still retaining enough information to achieve image classification for the majority of the tasks. Thus, this new approach can be used to speed up the AutoML pipeline for image compression.