This paper presents a proposal for a minimun energy feedforward control technique for flexible structures to suppress residual vibrations in point-to-point(PTP) motion. In the proposed method, the trajectory profile of the PTP motion is generated through a cycloidal function whose input is the output of a polynomial function. To achieve the suppression of the residual vibration as well as the operating energy of this PTP motion,the coefficients are tuned by metaheuristic algorithms. In the numerical simulations, we investigated the PTP motions of a single-link flexible manipulator and a robotic arm attached to a flexible link.The simulation results were compared with those of previous studies, revealing the effectiveness of the proposed method.