Nguyen et al. are studying how to fool deep neural networks, specifically trained on MNIST or ImageNet, using evolutionary algorithms. In the easier case the evolutionary algorithm used chooses a sample from the population (here, the images) and randomly mutates it. If the generated sample gets a higher fitness value than the current champion, the champion is replaced by the new sample. The fitness function is the highest score predicted by the deep neural network over all classes. The champion is the sample with the highest fitness function. Details can be found in the paper.
They that using these evolutionary algorithms, it is possible to produce irregular images with very high confidence scores for networks trained on the MNIST dataset, see Figure 1. They attribute this property to the small training set. Indeed, on the ImageNet it is harder for the evolutionary algorithm to produce irregular images with high confidence. Therefore, on ImageNet, by changing the way samples are randomly mutated, they try to produce regular images fooling the deep neural network. Again, the evolutionary algorithm can easily generate images fooling the network into high confidences.