An unsupervised Physics-Informed Neural Network (PINN) for solving optimal control problems with the direct method to design and optimize transfer trajectories is proposed. The network adheres analytically to boundary conditions and includes the objective fitness as regularization in its loss function. A test scenario of a planar Earth-Mars low-thrust optimalfuel transfer and rendezvous is chosen. Comprehensive examination of training strategies reveals that convergence is highly dependent on the initialization of the network and that correctly balancing loss terms is essential for navigating the intricate loss landscape. This balance is achieved by carefully selecting the loss weights and implementing a refined learning rate schedule. Comparative analysis to hodographic shaping solutions demonstrates that the PINN effectively identifies near-optimal solutions across a wide range of initial and final constraints for the Earth-Mars transfer problem, with a maximum improvement of 4.5 km s−1 and median improvement of 0.55 km s−1. The PINN shows promise as a preliminary design tool for trajectory optimization in challenging dynamical conditions.