Supports are an important ingredient of the building process of structures by additive manufacturing technologies. They are used to reinforce overhanging regions of the desired structure and/or to facilitate the mitigation of residual thermal stresses due to the extreme heat flux produced by the source term (laser beam). Very often, supports are, on purpose, weakly connected to the built structure for easing their removal. In this work, we consider an imperfect interface model for which the interaction between supports and the built structure is not ideal, meaning that the displacement is discontinuous at the interface while the normal stress is continuous and proportional to the jump of the displacement. The optimization process is based on the level set method, body-fitted meshes and the notion of shape derivative using the adjoint method. We provide 2-d and 3-d numerical examples, as well as a comparison with the usual perfect interface model. Completely different designs of supports are obtained with perfect or imperfect interfaces.