Convolutional neural networks for visual recognition require large amounts of training samples and usually benefit from data augmentation. This paper proposes PatchMix, a data augmentation method that creates new samples by composing patches from pairs of images in a grid-like pattern. These new samples ground truth labels are set as proportional to the number of patches from each image. We then add a set of additional losses at the patch-level to regularize and to encourage good representations at both the patch and image levels. A ResNet-50 model trained on ImageNet using PatchMix exhibits superior transfer learning capabilities across a wide array of benchmarks. Although PatchMix can rely on random pairings and random grid-like patterns for mixing, we explore evolutionary search as a guiding strategy to discover optimal grid-like patterns and image pairing jointly. For this purpose, we conceive a fitness function that bypasses the need to re-train a model to evaluate each choice. In this way, PatchMix outperforms a base model on CIFAR-10 (+1.91), CIFAR-100 (+5.31), Tiny Imagenet (+3.52), and ImageNet (+1.16) by significant margins, also outperforming previous state-of-the-art pairwise augmentation strategies.