Mobile Edge Computing (MEC) and fog computing are the key technologies in fifth generation (5 G) networks. In an MEC system, the data of terminal devices can be processed at the edge nodes also known as fog nodes, which can reduce the data transmission from the terminal devices to the cloud, thus reducing the latency and pressure of network traffic. Due to the huge amount of users’ data, a large number of edge nodes need to be deployed. Therefore, we study how to optimally deploy the edge devices on 5G-based small cells (SC) networks based on many-objective evolutionary algorithm (MaOEA). Our goal is to optimize the deployment of edge devices to maximize service quality and reliability, while minimizing cost and energy consumption. This is an NP-hard problem with many objectives. To solve this problem, we propose an improved optimization algorithm named grouping-based many-objective evolutionary algorithm (GMEA). We also compare the performance of GMEA with the state-of-the-art algorithms, and the experimental results demonstrate that GMEA performs better than the other methods in both visualization results and hypervolume (HV) indicators.