With the widespread adoption of phased array radars, mechanical scanning antennas continue to be widely utilized in mobile platform radar systems owing to their cost-effectiveness. However, the rotation time of mechanical scanning antennas poses a limitation on their detection efficiency, rendering the optimization of radar beam scheduling a crucial aspect in enhancing system performance. To tackle this challenge, a mathematical model for radar beam scheduling is established, and an efficient beam scheduling strategy is devised to optimize time resource allocation and augment task completion efficiency. Additionally, the paper delves into the optimization scheduling impacts of Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Genetic Algorithm (GA) on radar beam scheduling, and introduces an optimized radar beam scheduling approach grounded in Simulated Annealing Particle Swarm Optimization (SAPSO). Simulation outcomes demonstrate that this algorithm exhibits superior optimization scheduling performance, particularly under multitasking scenarios, outperforming traditional methods. This serves as a valuable reference for the optimization of radar beam scheduling in mobile platform radar applications.