The input layer, hidden layer, and output layer are three models of neural processors that comprise feedforward neural networks. In this paper, an enhanced tunicate swarm algorithm based on a differential sequencing alteration operator (ETSA) with symmetric cooperative swarms is presented to train feedforward neural networks. The objective is to accomplish minimum classification errors and the most appropriate neural network layout by regulating the layers’ connection weights and neurons’ deviation thresholds according to the transmission error between the anticipated input and the authentic output. The TSA mimics jet motorization and swarm scavenging to mitigate directional collisions and to maintain the greatest solution that is customized and regional. However, the TSA exhibits the disadvantages of low computational accuracy, a slow convergence speed, and easy search stagnation. The differential sequencing alteration operator has adaptable localized extraction and search screening to broaden the identification scope, enrich population creativity, expedite computation productivity, and avoid search stagnation. The ETSA integrates exploration and exploitation to mitigate search stagnation, which has sufficient stability and flexibility to acquire the finest solution. The ETSA was distinguished from the ETTAO, EPSA, SABO, SAO, EWWPA, YDSE, and TSA by monitoring seventeen alternative datasets. The experimental results confirm that the ETSA maintains profound sustainability and durability to avoid exaggerated convergence, locate the acceptable transmission error, and equalize extraction and prospection to yield a faster convergence speed, superior calculation accuracy, and greater categorization accuracy.