Thin-wall structures demonstrated huge potential in design development for path-planning-based applications, particularly for layer-based direct deposition Additive Manufacturing (AM). Yet, printability assessment in this context and its computational integration for design optimization remain challenging problems. To address this gap, we propose a Shape Optimization Method based on surface energies that modifies an existing surface-based geometry, defined within prescribed closed boundary curves, to enhance the printability of the given design while preserving the fixed boundaries. The key output is a surface-based design with improved fabrication feasibility with layer-based direct deposition AM. As an implicit output, the isolines that describe the printing paths for fabrication are derived. By using a scalar field and exploiting surface parametrization, we introduce a surface energy functional that helps in modelling the distribution of the isolines defining the non-continuous printing-path to realize in production. Printability is related to the uniformity of the isolines distribution throughout the surface. A fabrication metric is therefore introduced based on those concepts of printability and surface energy to measure the feasibility of the current design and a Shape Optimization problem is presented. The sensitivity analysis of such an objective function is central to a method, and it is computed with automatic differentiation followed by a diffusion-based post-processing for regularization. This is then used to simultaneously optimize in a nested loop, both for the parametric field and the shape. The method is demonstrated on different geometries and further validated with additional industrial examples.