Autism Spectrum Disorder (ASD) is a chronic neurodevelopmental condition characterized by repetitive behaviors and impairments in social and communication skills. Despite the clear manifestation of these symptoms, many individuals with ASD remain undiagnosed. This paper proposes a methodology for ASD detection using a three-dimensional walking video dataset, leveraging supervised machine learning classification algorithms combined with nature-inspired optimization algorithms for feature extraction. The approach employs supervised classifiers to identify ASD cases, while nature-inspired optimization techniques select the most relevant features, enhanced by the use of ranking coefficients to identify initial leading particles. This strategy significantly reduces computational time, thereby improving efficiency and accuracy. Experimental evaluation with various algorithmic combinations demonstrates an exceptional classification accuracy of 100% in the best case when using the Random Forest classifier coupled with the Gravitational Search Algorithm for feature selection. The methodology's application to additional datasets promises improved robustness and generalizability. With its high accuracy and reduced computational requirements, the proposed framework offers significant contributions to both medical and academic fields, providing a foundation for future advances in ASD diagnosis.