Curved mesh generation starting from a P1 mesh relies on mesh deformation and mesh optimization techniques. Mesh optimization techniques consist in locally modifying the mesh in order to improve it with respect to a given quality criterion. This work presents the generalization of two mesh quality-based optimization operators to P2 meshes. The generalized operators consist in mesh smoothing and generalized swapping. With the use of these operators, P2 mesh generation starting from a P1 mesh is more robust and P2 connectivity-change moving mesh methods for large displacements are now possible.