A new technique for broadband shaped beam reflector antennas synthesis is presented. The surface of the shaped reflector is represented by a set of orthogonal Jacobi-Fourier expansion functions. To achieve a cosecant squared pattern in the elevation plane and a pencil beam in the azimuth plane, the expansion coefficients are optimized using invasive weed optimization and particle swarm optimization algorithms. High accuracy is achieved by combining optimization tools and analysis methods such as physical optics and integral equation. Besides, in the optimization procedures, a complex object function is used to achieve the desired performance over the entire 26-40 GHz operating bandwidth. The simulation results via FEKO and CST Microwave Studio software packages prove the validity and versatility of this technique for solving shaped reflector synthesis problems. There are several features that distinguish this technique from the previous methods. First of all is the wide bandwidth. The second is its ability to shape the radiation patterns in the elevation and azimuth planes simultaneously (two-dimensional synthesis). Moreover, compared with other techniques, the proposed method allows achieving extra desired features such as high directivity, low sidelobe levels, and small ripples in the shaped beam region.