Due to high gain and low production costs, Yagi-Uda antennas still find wide applications in wireless communication systems. The sensitivity of the gain due to variations of the element lengths and distances between the elements makes the design optimization quite challenging. In this paper, the multi-objective optimization of a six-element Yagi-Uda antenna applying an enhanced version of the firefly algorithm is proposed. The application of this optimization algorithm in the multi-objective sense allows the finding of local solutions, too. To minimize the computational time, an adaptive cost function is applied. The numerical analyses are performed by the partial element equivalent circuit method and the mutual impedance method.