For the single-screw extrusion process of solid propellant, the geometric optimization of the homogenization section faces a core problem: the high coupling between pressure establishment, material transport and energy consumption, and it is difficult to achieve a balance between different performance indicators by traditional empirical methods. Therefore, a numerical optimization framework combining CFD simulation and genetic algorithm is constructed to systematically explore the optimal screw geometric configuration. Propellant slurries are regarded as non-Newtonian fluids and are described by the Arrhenius temperature-dependent Bird-Carreau model, on which the flow field, pressure field and temperature field are solved. The key geometric parameters such as outlet core diameter, pitch, front and rear wedge angle, and thread width are selected as the optimization variables, and the ratio of pump power to shaft power is used as the objective function of energy efficiency to measure the degree of mechanical energy conversion into effective pressure work, and thermal safety constraints are introduced to control the upper limit of propellant temperature. The optimization results show that compared with the initial configuration, the volume flow rate is increased by 123% and the energy efficiency is only slightly reduced under the premise of maintaining a stable pressure drop. The flow field analysis shows that the optimized structure enhances the resistance-led conveying capacity and effectively inhibits the backflow phenomenon. Further analysis shows that the design with a larger pitch and narrower thread can reduce energy consumption while increasing the output, but its pressure accumulation ability is significantly weakened, revealing the inherent trade-off between screw geometry and pressure generation, conveying efficiency and energy consumption. The resulting optimized configuration achieves a good balance between multiple properties, which provides a theoretical reference for the continuous extrusion process of high-performance solid propellants.