The present era is facing lot of Security, Privacy, and Integrity issues because of tremendous development in communication technology, data storage devices, and computing advancements leading to unavoidable losses. As a result of the aforementioned technological revolutions day by day, many of the organizations or institutions started migrating to cloud environment. Because of this, security issues have increased coupled with the advent of new ways of penetration into networks. Unauthorized users and many professionals with malicious intent started exploiting the legitimate users through cyber-crimes. So, there is a need to implement a proper Intrusion Detection System with optimization procedures. This paper proposes a hybrid Intrusion Detection approach with a combination of Constraints Optimized Stacked Autoencoder (COSAE) for dimension reduction and grid search based SVM-RBF classifier (GSVM-RBF). The COSAE+GSVM-RBF model enhanced the performance using a two-fold. i) The SAE is optimized through regularization techniques with the adoption of weight and dropout constraints, ii) To enhance the performance of the SVM classifier with RBF for tuning the hyperparameters using grid search. Various experiments are conducted to validate this model with four activation functions Scaled Exponential Linear Unit (SELU), Rectified Linear Unit, softplus, and Exponential Linear Unit (ELU) for dimension reduction using COSAE. The improvements carried out in this paper result in exploding gradients and vanishing gradients avoids overfitting in large datasets, intrusion detection rate, gain in computational time, and 100% F-Measure in classifying minor class labels. The proposed approach is validated on the CICIDS2017 dataset. Further, a comparative analysis of the proposed approach with state-of-the-art approaches has been conducted. Based on the experimental results it is observed that the proposed approach outperforms the prevailing approaches.