Magnetic light and matter interactions are generally too weak to be detected, studied, and applied technologically. However, if one can increase the magnetic power density of light by several orders of magnitude, the coupling between magnetic light and matter could become of the same order of magnitude as the coupling with its electric counterpart. For that purpose, photonic nanoantennas, in particular dielectric, are proposed to engineer strong local magnetic field and therefore increase the probability of magnetic interactions. Unfortunately, dielectric designs suffer from physical limitations that confine the magnetic hot spot in the core of the material itself, preventing experimental and technological implementations. Here, it is demonstrated that evolutionary algorithms can overcome such limitations by designing new dielectric photonic nanoantennas, able to increase and extract the optical magnetic field from high refractive index materials. It is also demonstrated that the magnetic power density in an evolutionary optimized dielectric nanostructure can be increased by a factor 5 compared to state-of-the-art dielectric nanoantennas and that the fine details of the nanostructure are not critical in reaching these aforementioned features, as long as the general shape of the motif is maintained. This advocates for the feasibility of nanofabricating the optimized antennas experimentally and their subsequent application.