The relative positions of the antennas of a direction finder are critical regarding the efficiency and the robustness of the indications of the apparatus. The state of the art in direction finder optimization is limited with classical methods to the case of direction finders with 3 antennas, with naive trial-and-error methods for more complex cases. The use of Genetic Algorithms brings a tremendous increase to that domain, allowing the optimization of direction finders with up to 10 antennas in a reasonable computing time. Moreover, as GAs provide multiple optimal solutions on multi-modal problems, a thorough numerical investigation of all possible optima provides a new insight in the underlying optimization problem, finally leading to the derivation of a formula for the optimal direction finders.