Optical focusing through scattering media plays a significant role in various fields, such as medicine, communications, and detection. Over recent years, population optimization algorithms have been successfully applied to these fields with remarkable results. However, the current algorithms have limitations, such as offspring inheriting bad genes from their parent, parameter-tuning, and complex operation mechanisms. To address these challenges, we propose the mutate greedy algorithm (MGA), which innovatively combines greedy strategy with real-time feedback of mutation rate. MGA can achieve fast convergence speed and high enhancement by balancing the contradiction between greedy strategy and population diversity. There is only one parameter, i.e., population size, to adjust in the MGA. The MGA structure is simple and can save many computational resources. Our research is expected to advance wavefront shaping from laboratory to practical applications.