Parkinson's disease (PD) is the second most prevalent long-term progressive neurodegenerative disease after Alzheimer's. Individuals with PD experience tremors, rigidity, difficulty maintaining balance, and coordination of motion. Typically, the symptoms manifest gradually and worsen over time. As the condition progresses, individuals may experience difficulty in both movement and verbal communication. In order to employ the most effective treatment, gait analysis is regarded as one of the most important approaches to identifying and evaluating the presence of PD. Therefore, selecting the most optimal gait features for the purpose of detecting PD is a challenging endeavor. In today's computing environment, several strategies are required to solve various challenges. Metaheuristic algorithms represent a category of methodologies that possess the ability to offer pragmatic resolutions to such challenges in various fields. In this study, we present a robust hybrid Harris Hawks and Arithmetic optimization algorithm (Hybrid HH-AO Algorithm) with a Random Forest (RF) classifier to choose the optimal gait features and classify normal and abnormal individuals. The proposed approach has been evaluated on the benchmark INIT Gait database. The proposed approach achieves a better accuracy of 98.12%, sensitivity of 99.26%, specificity of 92.00%, precision of 98.53%, and F1-score of 98.89% using an RF classifier on the Gradient Gait Energy Image (GGEI) template. The experimental results show that our proposed method can accurately distinguish PD patients' gait patterns from healthy people with a high classification rate.