Artificial neural networks (ANNs) are actively utilized by researchers due to their extensive capability during the training process of the networks. The intricate training stages of many ANNs provide a powerful mechanism in solving various optimization or classification tasks. The integration of an ANN with a robust training algorithm is the supreme model to outperform the existing framework. Therefore, this work presented the inclusion of three satisfiability Boolean logic in the Hopfield neural network (HNN) with a sturdy evolutionary algorithm inspired by the Imperialist Competitive Algorithm (ICA). In general, ICA stands out from other metaheuristics as it is inspired by the policy of extending the power and rule of a government/country beyond its own borders. Existing models that incorporate standalone HNN are projected as non-versatile frameworks as it fundamentally employs random search in its training stage. The main purpose of this work was to conduct a comprehensive comparison of the proposed model by using two real data sets with an elementary HNN with exhaustive search (ES) versus a HNN with a standard evolutionary algorithm, namely- the genetic algorithm (GA). The performance evaluation of the proposed model was analyzed by computing plausible errors, such as root mean square error (RMSE), mean absolute error (MAE), global minima ratio (R_m), computational time (CT) and accuracy (Q). The computational simulations were carried out by operating the different numbers of neurons in order to validate the efficiency of the proposed model in the training stage. Based on the simulations, the proposed model was found to execute the best performance in terms of attaining small errors and efficient computational time compared to other existing models.