Magnetic light and matter interactions are generally considered 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 have been proposed, and in particular dielectric nanostructures, 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, we demonstrate 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. We also demonstrate 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 . In addition, we show 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. By designing all-dielectric magnetic antennas that feature local magnetic hot-spots outside of high refractive index materials, this work highlights the potential of evolutionary methods to fill the gap between electric and magnetic light-matter interactions, opening up new possibilities in many research fields.