This paper presents an energy-saving, open-loop control technique for a flexible manipulator with point-to-point motion. In the proposed method, the joint angle of the manipulator is expressed by an artificial neural network (ANN). For the ANN, we use a vector evaluated particle swarm optimization (VEPSO) algorithm as the learning algorithm. The maximum residual vibration amplitude and the operating energy are adopted as the multi-objective functions of the VEPSO algorithm. By operating the manipulator along the trajectory obtained by the proposed method, the residual vibrations can be suppressed; thus, saving energy. In other words, the proposed method is an open-loop control that does not require sensors to measure unwanted vibrations. The performance of the proposed control scheme is confirmed by numerical simulations. In addition, the effectiveness of the proposed approach is experimentally verified.