Optimizing trajectory execution time is critical for enhancing the operational efficiency of redundant robotic arms in industrial and collaborative applications. This paper proposes an improved genetic algorithm for optimizing trajectory planning in hybrid redundant robotic arms. Focusing on reducing trajectory execution time, the algorithm enhances the search strategy and fitness function to efficiently resolve complex kinematic constraints. Validated through simulations on a hybrid redundant manipulator model, the optimized trajectories achieve a significant 22.13% reduction in execution time-reducing the baseline duration to 10.31 s. The results demonstrate the effectiveness of the improved genetic algorithm in accelerating task completion while maintaining smooth joint torque profiles. This approach enables high-performance operations in time-sensitive applications, advancing the utility of redundant manipulators in dynamic environments.