We present the experimental demonstration of a technique for the nonlinear generation of tailored broadband optical spectra. Our technique relies on the capability to precisely shape short optical pulses at the input of a highly nonlinear fibre. The precise pulse shape that needs to be fed to the nonlinear fibre is calculated from the spectral shape we wish to generate through inverse propagation calculations. A programmable optical filter is then used to transform the pulses of a short-pulse laser to the calculated waveform. An automated evolutionary algorithm is employed to monitor and optimise the filter characteristics. As an application example, we present the generation of a 10 GHz ultra-flat (less than 1 dB power fluctuations), broadband (> 30 nm) optical spectrum, starting from a 2 ps mode-locked laser.