This paper offers a comparative study of different Covariance Matrix Adaptation Evolution Strategy (CMA-ES) techniques, evaluating their performance in autonomous parking navigation and maneuvering scenarios. The two-stage trajectory optimization framework is employed, where the global path is first generated using the A-star algorithm, followed by local optimization using various CMA-ES-based algorithms. The study evaluates the performance of these algorithms under four parking mission cases, classified as either simple or difficult, with a planning horizon of four waypoints. The results indicate that while CMA-ES algorithms are effective, certain variants trade off performance for computational efficiency. The findings suggest that hybrid or ensemble versions of CMA-ES might offer improved solutions for optimization-based autonomous parking tasks. The analysis provides insights into the suitability of different CMA-ES variants, which can inform choices for specific autonomous driving applications.