Electroencephalogram (EEG) is one of the most common methods used for seizure detection as it records the electrical activity of the brain. Symmetry and asymmetry of EEG signals can be used as indicators of epileptic seizures. Normally, EEG signals are symmetrical in nature, with similar patterns on both sides of the brain. However, during a seizure, there may be a sudden increase in the electrical activity in one hemisphere of the brain, causing asymmetry in the EEG signal. In patients with epilepsy, interictal EEG may show asymmetric spikes or sharp waves, indicating the presence of epileptic activity. Therefore, the detection of symmetry/asymmetry in EEG signals can be used as a useful tool in the diagnosis and management of epilepsy. However, it should be noted that EEG findings should always be interpreted in conjunction with the patient's clinical history and other diagnostic tests. In this paper, we propose an EEG-based improved automatic seizure detection system using a Deep neural network (DNN) and Binary dragonfly algorithm (BDFA). The DNN model learns the characteristics of the EEG signals through nine different statistical and Hjorth parameters extracted from various levels of decomposed signals obtained by using the Stationary Wavelet Transform. Next, the extracted features were reduced using the BDFA which helps to train DNN faster and improve its performance. The results show that the extracted features help to differentiate the normal, interictal, and ictal signals effectively with 100% accuracy, sensitivity, specificity, and F1 score with a 13% selected feature subset when compared to the existing approaches.