This paper proposes a computational framework for automatically optimizing the shapes of patient-specific tissue engineered vascular grafts. We demonstrate a proof-of-concept design optimization for aortic coarctation repair. The computational framework consists of three main components including 1) a free-form deformation technique exploring graft geometries, 2) high-fidelity computational fluid dynamics simulations for collecting data on the effects of design parameters on objective function values like energy loss, and 3) employing machine learning methods (Gaussian Processes) to develop a surrogate model for predicting results of high-fidelity simulations. The globally optimal design parameters are then computed by multistart conjugate gradient optimization on the surrogate model. In the experiment, we investigate the correlation among the design parameters and the objective function values. Our results achieve a 30% reduction in blood flow energy loss compared to the original coarctation by optimizing the aortic geometry.