This paper presents an automated method for solving the initial structure of compact, high-zoom-ratio mid-wave infrared (MWIR) zoom lenses. Using differential analysis, the focal length variation process of zoom lenses under paraxial conditions is investigated, and a model for the focal power distribution and relative motion of three movable lens groups is established. The particle swarm optimization (PSO) algorithm is introduced into the zooming process analysis, and a program is developed in MATLAB to solve for the initial structure. This algorithm integrates physical constraints from lens analysis and evaluates candidate solutions based on key design parameters, such as total lens length, zoom ratio, Petzval field curvature, and focal length at tele end. The results demonstrate that the proposed method can efficiently and accurately determine the initial structure of compact MWIR zoom lenses. Using this method, a mid-wave infrared zoom lens with a zoom ratio of 50×, a total length of less than 530 mm, and the ratio of focal length to total length approximately 2:1 was successfully designed. The design validates the effectiveness and practicality of this method in solving the initial structure of zoom lenses that meet complex design requirements.