In this work a heuristic optimization algorithm known as the Fruit fly Optimization Algorithm is applied to antenna design problems. The original formulation of the algorithm is presented and it is adapted to array factor and horn antenna optimization problems. Specifically, it is applied to the array factor synthesis of uniformly-fed, non-equispaced arrays and to the profile optimization of multimode horn antennas. Several numerical examples are presented and the obtained results are compared with those provided by a deterministic optimization based on a simplex method and another well-known heuristic approach, the Genetic Algorithm.