Investigating Drug-Target Interactions (DTI) is crucial for drug repositioning and discovery tasks. However, discovering DTIs through experimental approaches is time-consuming and requires substantial financial resources. To address these challenges, machine learning-based methodologies have been adopted to reduce costs and save time. Unfortunately, the effectiveness of these methods has been limited due to the binary classification approach and the lack of empirically validated negative samples. The availability of abundant DTI datasets and protein structure data has enabled the development of new approaches, such as redefining the DTI problem as a regression task. Given this context, we propose an innovative deep-learning approach to predict binding affinities between drugs and targets. Our model, named the Convolution Self-Attention Network with Attention-based Bidirectional Long Short-Term Memory Network (CSAN-BiLSTM-Att), integrates convolutional neural network (CNN) blocks with self-attention mechanisms to create an attention-based bidirectional long short-term memory (BiLSTM) model, followed by fully connected layers. Due to the model's complexity, proper hyperparameter tuning is essential. To optimize this, we employ the Differential Evolution (DE) technique to select the most suitable hyperparameters. Experimental results demonstrate that the DE-based CSAN-BiLSTM-Att model outperforms previous approaches. Specifically, the model achieved a concordance index of 0.898 and a mean square error of 0.228 on the DAVIS dataset, and a concordance value of 0.971 with a mean square error of 0.014 on the KIBA dataset.