The Wavefront Sensorless (WFSless) Adaptive Optics (AO) system is simple and easy to implement because it does not require a wavefront sensor and can be applied to some environments where conventional adaptive optics systems cannot work, such as multiphoton microscopy for biological imaging. The WFSless AO technology has not been adopted pervasively in the early days due to the lack of suitable control algorithms. With the emergence of new optimization algorithms recently, it has been widely studied and applied in related fields. Metaheuristic algorithms, e.g., Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution Algorithm (DEA) are commonly used as the control algorithms of WFSless AO systems. However, these algorithms have some problems, i.e., slow convergence speed, insufficient global search efficiency, and poor adaptability to different wavefront aberrations, which make them insufficient to be applied in practice.We propose to adapt the RUNge Kutta optimizer (RUN) to the system control algorithm in this paper. An adaptive optics system model based on the RUN optimization algorithm is established with a 61-element deformable mirror as a wavefront correction device. Wavefront aberrations with different turbulence levels are used as correction objects. The performance, speed, and local extreme values of the optical systems based on RUN, PSO, DEA, and GA algorithms are compared and analyzed.Results show that all four algorithms can obtain good convergence, and performance metrics of the RUN algorithm and GA are similar and obviously better than those of PSO and DEA after convergence is achieved. The Analysis of convergence speed shows that the speed decreases with the increase of turbulence level, but the RUN algorithm is significantly faster than other three algorithms. Compared with PSO, DEA, and GA, the convergence speed of the RUN algorithm is about 4.5, 3.3, and 3.5 times faster under D/r₀=5, about 3.9, 3.8, and 4.1 times faster under D/r₀=10; and about 3.8, 3.4, and 5.3 times faster under D/r₀=15, respectively. Additionally, compared with other algorithms, RUN has a lower probability of falling into local extrema which shows the RUN has better convergence stability and better robustness. Additionally, we also find that the control algorithm is insensitive to parameters and easier to implement.The RUN optimization algorithm has strong adaptability and fast convergence for aberrated wavefronts correction under different turbulence levels when it is used as a control algorithm of WFSless AO systems. The proposed control method outperforms other classical metaheuristic algorithms and has great application potential in microscopic imaging, spot shaping and other fields. Above research results can provide a theoretical basis for the practical application of wavefront correction systems based on the RUN optimization algorithm.