In the contemporary field of optimal trajectory planning for industrial robots, it is customary to construct trajectories through the manual predefinition of interpolation functions. Unfortunately, this method frequently overlooks the influence of the interpolation function itself on the optimization objectives, resulting in suboptimal outcomes. To remedy this limitation, an optimal trajectory planning method with coupled interpolation function selection is proposed, in which the total task time and the integral squared jerk are defined as optimization objectives. This method minimizes the optimization objectives while also factoring in the optimal interpolation function, and avoiding subjective interference. To address the aforementioned biobjective optimization problem better, an Improved MultiObjective Golden Eagle Optimizer is introduced. Population diversity and the ability to escape local optima are enhanced through the incorporation of Chaotic Mapping, Opposition‐Based Learning, Differential Evolution, and adaptive inertia weight strategy into the algorithm. The superiority of the algorithm is validated through a series of simulations on 17 benchmark functions. In the context of the robotic stirring operation within the automated block cast charging process, the proposed method is utilized to derive the time–jerk optimal trajectory. The results demonstrate the effectiveness of the proposed method.