Efficient broadband reflective Extreme Ultraviolet (EUV) multilayers require superior control and precision of layer thickness. A solely time-controlled deposition system can not meet the requirements of high accuracy. In this paper, we present a scheme for the design of broadband multilayers with discrete thicknesses based on an evolutionary algorithm. This method greatly improves the reflectivity curve compared to that of conventional multilayer mirrors without discrete thicknesses. To verify the superiority of the design, the broadband multilayers were deposited using a magnetron sputtering system. The EUV measurements reveal that the deposited aperiodic broad angular multilayers exhibits reflectivity values greater than 41% over an angle of incidence range of 0-17° for a fixed wavelength of 13.5 nm, the broad angular multilayers in four different stacks exhibits reflectivity values greater than 35% with a wide angular bandpass over an angle of incidence range of 0-18.5° for a fixed wavelength of 13.5 nm, and the broadband multilayer mirrors exhibits reflectivity values greater than 21% for wavelengths ranging between 12.9-14.9 nm for a fixed angle of incidence of 3°. This study demonstrates a great potential for the application of discrete design in the fabrication of EUV broadband multilayers with high accuracy.