Anomaly detection tools and methods present a key capability in modern cyberphysical and failure prediction systems. Despite the fast-paced development in deep learning architectures for anomaly detection, model optimization for a given dataset is a cumbersome and time-consuming process. Neuroevolution could be an effective and efficient solution to this problem, as a fully automated search method for learning optimal neural networks, supporting both gradient and nongradient fine-tuning. However, existing methods mostly focus on optimizing model architectures without taking into account feature subspaces and model weights. In this work, we propose anomaly detection neuroevolution (AD-NEv)-a scalable multilevel optimized neuroevolution framework for multivariate time-series anomaly detection. The method represents a novel approach to synergically: 1) optimize feature subspaces for an ensemble model based on the bagging technique; 2) optimize the model architecture of single anomaly detection models; and 3) perform nongradient fine-tuning of network weights. An extensive experimental evaluation on widely adopted multivariate anomaly detection benchmark datasets shows that the models extracted by AD-NEv outperform well-known deep learning architectures for anomaly detection. Moreover, results show that AD-NEv can perform the whole process efficiently, presenting high scalability when multiple graphics processing units (GPUs) are available.