Convolutional neural networks (CNNs) are the backbones of deep learning paradigms for numerous vision tasks. Early advancements in CNN architectures are primarily driven by human expertise and elaborate design. Recently, neural architecture search (NAS) was proposed with the aim of automating the network design process and generating task-dependent architectures. This paper introduces NSGA-Net -- an evolutionary search algorithm that explores a space of potential neural network architectures in three steps, namely, a population initialization step that is based on prior-knowledge from hand-crafted architectures, an exploration step comprising crossover and mutation of architectures, and finally an exploitation step that utilizes the hidden useful knowledge stored in the entire history of evaluated neural architectures in the form of a Bayesian Network. The integration of these components allows an efficient design of architectures that are competitive and in many cases outperform both manually and automatically designed architectures on CIFAR-10 classification task. The flexibility provided from simultaneously obtaining multiple architecture choices for different compute requirements further differentiates our approach from other methods in the literature.