This paper investigates cost optimization and ANFIS computing for a double-orbit retrial queue with customer feedback and balking. The arriving customers in the system are divided into two classes: type-1 orbit and type-2 orbit. These two classes are made for different types of customers and also include real-life situations, such as customer feedback and balking. It is assumed that type-1 orbit’s customers pay high than type-2 orbit’s customers. In this manner, type-1 customers get more facilities than type-2 customers. The model’s governing equations are solved using the probability-generating function method then various performance indices are also derived using queue size distributions. The study first introduces the double-orbit retrial queue model with customer feedback and balking. Then, it presents an ANFIS-based approach to the system’s performance measures. The ANFIS model is trained using a dataset of historical data. The trained ANFIS model is then used to predict the system performance measures. We also analyze the effects of the arrival rate, retrial rate, and service rate of both classes (type-1 and type-2) on the expected number of customers in the system, expected waiting time in the system, idle server, and busy server probability. The cost function for the double-orbit queue is framed and minimized using the particle swarm optimization (PSO) algorithm.