The contribution discusses a framework for optimizing porous structures in a multi-scale framework using a combination of FFT-based interpolations and isogeometric analysis to model associated governing equations of the gradient-based optimization scheme efficiently. Inspired by biological structures such as wood and bone, the scheme aims to equip porous cells with anisotropic properties to optimally transfer loads through a structure for various load cases. The framework is embedded into a novel scheme that, at the macro-scale, models the minimal compliance problem using a phase-field model that discretizes C1-continuous flux-vectors. Due to the inherent variational-based structure that minimizes an incremental energetic potential, several benefits ensue, such as an easier algorithmic implementation, an easier incorporation of boundary conditions, and a more favorable representation of the corresponding linear system that allows for more efficient solvers. It is further discussed how FFT-schemes for gradient-based optimization principles can be enhanced by novel preconditioning strategies that drastically improve the computational effort of the highly demanding multi-scale framework. In this context it is shown that corresponding update equations can be perturbed to allow for much faster iterative solvers by improving the condition number of the system matrices of the schemes.