Based on the standard coupled equations describing fiber Raman amplifiers (FRAs),a generalized automatic algorithm with the help of Genetic algorithm and global convergent Broyden method is proposed for the design of broadband backward pumped FRAs. The main advantages of this algorithm are higher efficient,easier convergent and wider suitable. The numerical calculation illustrates that the gain flatness for 10 THz gain bandwidth is well within ±0.6 dB for three kinds of FRAs: discrete amplifiers with different gain values, single-fiber and dispersion-managed distributed amplifiers with different structures. These results how the flexibility of the proposed design algorithm. The comparison of OSNR between linked amplification units of SMF+DCF and DMF shows the potential application merit of DM-FRA.