The metalens, a significant branch of metasurfaces, holds substantial application potential. However, it often faces issues such as chromatic aberration and narrow bandwidth. This paper compares various optimization methods for the inertia weight (ω) and learning factors (C) of the particle swarm optimization (PSO) algorithm and integrates it with the genetic algorithm (GA). After the comparison, we selected the optimized algorithm that best fits our needs to design a broadband achromatic metalens operating in the wavelength range of 1–1.25 µm. The average efficiency reached 76%, providing a valuable reference for the development and application of achromatic metalenses.