In the past few years, cybersecurity is becoming very important due to the rise in internet users. The internet attacks such as Denial of service (DoS) and Distributed Denial of Service (DDoS) attacks severely harm a website or server and make them unavailable to other users. Network Monitoring and control systems have found it challenging to identify the many classes of DoS and DDoS attacks since each operates uniquely. Hence a powerful technique is required for attack detection. Traditional machine learning techniques are inefficient in handling extensive network data and cannot extract high-level features for attack detection. Therefore, an effective deep learning-based intrusion detection system is developed in this paper for DoS and DDoS attack classification. This model includes various phases and starts with the Deep Convolutional Generative Adversarial Networks (DCGAN) based technique to address the class imbalance issue in the dataset. Then a deep learning algorithm based on ResNet-50 extracts the critical features for each class in the dataset. After that, an optimized AlexNet-based classifier is implemented for detecting the attacks separately, and the essential parameters of the classifier are optimized using the Atom search optimization algorithm. The proposed approach was evaluated on benchmark datasets, CCIDS2019 and UNSW-NB15, using key classification metrics and achieved 99.37% accuracy for the UNSW-NB15 dataset and 99.33% for the CICIDS2019 dataset. The investigational results demonstrate that the suggested approach performs superior to other competitive techniques in identifying DoS and DDoS attacks.