In this paper, a system for LTE Cell Outage Compensation (COC) based on hybrid Genetic Algorithms (GA) and Artificial Neural Networks (ANN) has been proposed. COC aims to minimize the impact of cell outage which leads to decrease in operator revenue and/or the customer satisfaction. The proposed system adopts an optimization module to search for an optimal setting of a set of LTE operational parameters to achieve a targeted set of key performance indicators. The optimization process always leads to good enough solutions, but it also requires a huge number of trials. So, in the proposed system, a huge set of outage scenarios is collected along with their optimal argument settings that are acquired by the optimization module and they are used to train an artificial neural network (ANN) module, which acts as an expert that can optimally act on the different situations in real-time mode. Simulation environment is set to evaluate different LTE measures and Key Performance Indicators (KPIs) on different outage scenarios. Simulation results proved the capability and robustness of the proposed system to minimize the number of users experiencing outage. Simulation results also show that the proposed system achieves optimal parameter settings without violating the overall system performance and with minimal processing time, while introducing significant impact on the performance of LTE.