Abstract We consider active shape morphing to optimize the flight performance of flapping wings. To this end, we combine a three-dimensional version of the unsteady vortex lattice method (UVLM) with a deterministic global optimization algorithm to identify the optimal kinematics that maximize the propulsive efficiency under lift and thrust constraints. The UVLM applies only to incompressible, inviscid flows where the separation lines are known a priori. Two types of morphing parameterization are investigated here—trigonometric and spline-based. The results show that the spline-based morphing, which requires specification of more design variables, yields a significant improvement in terms of propulsive efficiency. Furthermore, we remark that the average value of the lift coefficient in the optimized kinematics remained equal to the value in the baseline case (without morphing). This indicates that morphing is most efficiently used to generate thrust and not to increase lift beyond the basic value obtained by flapping only. Besides, our study gives comparable optimal efficiencies to those obtained from previous studies based on gradient-based optimization, but completely different design points (especially for the spline-based morphing), which would indicate that the design space associated with the flapping kinematics is very complex.