With the growing demand for data connectivity, network service providers are faced with the task of reducing their capital and operational expenses while simultaneously improving network performance and addressing the increased demand. Although Network Function Virtualization (NFV) has been identified as a promising solution, several challenges must be addressed to ensure its feasibility. In this paper, we address the Virtual Network Function (VNF) migration problem by developing the VNF Neural Network for Instance Migration (VNNIM), a migration strategy for VNF instances. The performance of VNNIM is further improved through the optimization of the learning rate hyperparameter through particle swarm optimization. Results show that the VNNIM is very effective in predicting the post-migration server exhibiting a binary accuracy of 99.07% and a delay difference distribution that is centered around a mean of zero when compared to the optimization model. The greatest advantage of VNNIM, however, is its run-time efficiency highlighted through a run-time analysis.