We theoretically analyze the generation of broadened and multi-peak terahertz (THz) radiation in aperiodically poled lithium niobate (APPLN), whose sequence of opposite domains is optimized by simulated annealing (SA) algorithm. The full-width at half maximum (FWHM) of the broadened THz radiation in our simulation is 0.26 THz. Both of the central wavelength and FWHM can be easily tuned by choosing proper objective functions. THz radiation with wider and flatter FWHM can be achieved by increasing the length of the lithium niobate crystal. The two-peak THz generation is also provided as an example of multi-peak with the central wavelengths at 1.68 and 1.80 THz, respectively.