Today, wireless technology has reached a point that has no choice other than using only one compact and multiband antenna to simultaneously answer all the demands of users at different frequencies. A fractal antenna is created by repeating a motif over two or more scale sizes, or “Iterations”. For this reason, fractal antennas are very compact, multiband or wideband and have useful applications in cellular telephone and microwave communications. In this paper, the authors will investigate the multiband characteristics of a fractal array based on a 4-element circular subarray generator and will optimize it for the maximum directivity using Particle Swarm Optimization (PSO) algorithm.