Many partial differential equation (PDE)-based engineering and scientific applications have multiple requirements for the finite element mesh discretizing the geometric domain. For example, such requirements may include having non-inverted mesh elements, elements that are well-shaped, elements with uniform element size, and/or elements which yield small PDE interpolation error. Despite there being multiple mesh requirements for various PDE applications, most traditional mesh optimization algorithms optimize only a single objective function and hence imp rove only one aspect of the mesh. There are several existing multi objective mesh optimization methods, however most of the existing methods are not flexible and/or not easy to use in practice. In this talk, we will present a mesh optimization framework for mesh quality improvement and mesh untangling, which is flexible and easy to implement in practice. We will extend the idea of mesh optimization framework for mesh deformation problems.