Autism Spectrum Disorder (ASD) is a neurodevelopmental condition characterized by challenges in communication, social interactions, and repetitive behaviors. The heterogeneity of symptoms across individuals complicates diagnosis. Neuroimaging techniques, particularly resting-state functional MRI (rs-fMRI), have shown potential for identifying neural signatures of ASD, though challenges such as high dimensionality, noise, and small sample sizes hinder their clinical application. This study proposes a novel approach for ASD detection utilizing deep learning and advanced feature selection techniques. A hybrid model combining Stacked Sparse Denoising Autoencoder (SSDAE) and Multi-Layer Perceptron (MLP) is employed to extract relevant features from rs-fMRI data in the ABIDE I dataset, which was preprocessed using the CPAC pipeline. Feature selection is enhanced through an optimized Hiking Optimization Algorithm (HOA) that integrates Dynamic Opposites Learning (DOL) and Double Attractors to improve convergence toward the optimal subset of features. The proposed model is evaluated using multiple ASD datasets. The performance metrics include an average accuracy of 0.735, sensitivity of 0.765, and specificity of 0.752, surpassing the results of existing state-of-the-art methods.