Gas cyclic pressure pulsing is an effective IOR method specifically for naturally fractured reservoirs. Due to the computational cost of simulating a large number of scenarios, it is an arduous task to determine the optimum operational conditions for the process. In this study, a practical screening and optimization workflow is utilized to determine the most optimum operating conditions for cyclic pressure pulsing applications with N2 and CO2 in a fully-depleted reservoir. Two huff'n' puff design schemes with variable and constant injection volumes are implemented in a compositional, dual-porosity reservoir simulation model. A set of representative design scenarios is created and run using this model. Then, the collected performance indicators are fed into the neural network for training and two neural network-based proxies are developed: 1) A forward proxy to predict the corresponding performance indicators once given the design scenarios, 2) An inverse proxy to predict the corresponding design scenarios once given a set of desired performance characteristics. Finally, the genetic algorithm is used to search for the best design scenario that would maximize the efficiency of the process for a given time of operation. To evaluate the objective function, the forward proxy is used for computational efficiency. The methodology is tested with a single-well reservoir model of the Big Andy Field which is a depleted, naturally fractured reservoir in Eastern Kentucky with stripper-well production. Predictive capability and accuracy of developed networks are checked by comparing simulation outputs with network outputs. It is observed that networks are able to accurately predict the performance indicators including the peak rate, time to reach the peak rate, cycle flow rates, incremental oil production, and gas-oil-ratio. The proposed methodology is practical and computationally efficient in structuring more effective decisions towards the optimum design of the process.