Additive Manufacturing (AM) through a Laser Powder Bed Fusion (LPBF) process consists in building objects layer by layer, by deposing energy in metallic powder with a laser along a chosen path. Despite huge advantages, such as the freedom in the design, this manufacturing process causes defects in the resulting object. Choosing the laser path is of high significance, since it is tightly related to both the manufacturing speed and the temperature distribution in each layer. The design of the laser path is often based on optimizing parameters of existing patterns and combining them. A different approach is proposed here. Without presupposing any specific pattern, our method is based on shape optimization theory and a descent algorithm is drafted to adapt the path to the manufacturing requirements.