The new expected fifth generation (5G) communication systems will serve users with data rates of several Gbps and will allow running new applications in mobile devices. In order to do so, several design challenges have to be met. One of these is the antenna design and fabrication for the 5G mobile devices, especially in the millimeter wave frequencies. In this paper, we address the above issue by designing two different antennas for 3.7 and 26 GHz. We apply a design procedure based on a new proposed evolutionary algorithm, the Grey Wolf Optimizer-Jaya (GWO-Jaya), which combines features from both GWO and Jaya. We evaluate the new algorithm on a set of widely exploited benchmark functions. We design both antennas using the new proposed algorithm. Moreover, we evaluate their performance characteristics through fabrication and measurements. Both antennas are circularly polarized at an acceptable bandwidth and also exhibit wide-band behavior. In both cases, simulation and measurement results are in good agreement.