This research introduces a novel technique to EEG data classification by leveraging evolutionary computation to optimize both the selection of important EEG features and the architecture of Artificial Neural Networks (ANNs). An advanced algorithm has been employed to extract the most informative features from a set of 2550 statistical EEG features. This step ensures that only the most relevant data is used for subsequent model training, which can enhance performance and reduce computational complexity. The topology of a Multilayer Perceptron (MLP) is optimized using advanced computation to identify the best hyperparameters for the network before classification. This includes tuning the number of layers, neurons per layer, activation functions, and other hyperparameters critical for effective model performance. Long Short-Term Memory (LSTM) networks are also explored, given their suitability for sequential data like EEG signals. The study tests Adaptive Boosting (AdaBoost) on both MLP and LSTM models to enhance classification accuracy. AdaBoost is a machine learning ensemble technique that merges multiple weak classifiers to form a strong classifier, improving overall model performance. The study conducts experiment to study the performance of various classifiers in Attention State Classification. Adaptive Boosted LSTM Achieved 99.30% accuracy for attention state classification. The datasets were collected using a Muse EEG headband with four electrodes placed at TP9, AF7, AF8, and TP10 according to the international EEG placement standard. The study revealed that the use of Adaboost further enhances the model performance and can effectively optimize both feature selection and neural network architecture, leading to significant improvements in EEG data classification.