Based on hybrid genetic algorithm (HGA), the signal bandwidth of the distributed multi-pump Raman amplifiers is optimized, and the corresponding noise figure is obtained. The results show that: (1) the optimal signal bandwidth Δ λ decreases with the increase of the span length L, e.g., Δ λ is 79.6 nm for L=50 km and 41.5 nm for L=100 km under our simulated conditions; (2) the relationship between Δ λ and L is approximately linear; (3) the equivalent noise figure can be negative and increases with the extension of L; (4) there are one or several global maximum signal bandwidth on the determinate conditions; (5) to realize the fixed Δ λ, several candidates can be obtained by means of HGA, as has important applications on the design of distributed multi-pump Raman amplifiers in practice.