A mechanism-free ornithopter, also referred to as a “solid-state” ornithopter, works based on utilizing piezocomposite actuators to achieve heaving and pitching motions for producing lift and thrust. A set of piezocomposite actuators are attached to a composite substrate, and as the piezocomposite devices are excited, a flapping motion is generated due to the induced strain. Previously, parametric studies were conducted on a rectangular wing model as well as a wing-like planform using the finite element method. In this article, a new parameterized model for the wing planform is introduced. This model makes it possible to analyze the response of a parametric wing to variations of critical shape parameters. A preliminary analysis is conducted based on the model to explore the effects of each parameter on flight performance metrics. Furthermore, an optimization framework is developed to search for the optimal set of parameters that achieve best performance. The framework utilizes a single objective genetic algorithm optimizer, and the response is predicted using a parameterized finite element model. The convergence of the genetic algorithm is checked using well-known test functions with similar input space and specifications as the wing models considered. Parameters of the genetic algorithm are tuned to achieve convergence to global optima. The framework is used to optimize the geometry of the wing planform for a variety of performance metrics.