Traditional heuristic algorithms are time consuming in searching the pump configuration to obtain a wide-band flat-gain fiber Raman amplifier (FRA). In this paper, two methods are proposed to deal with this problem. One is called combined generic algorithm (CGA). By using the quadratic programming algorithm instead of generic algorithm (GA) to solve the pump integral, the search space dimension is reduced by half, and obviously, this method will converge faster. Based on a linear time-invariant (LTI) system model, another method is also presented under the assumption that the effective area of fiber is weakly dependent on stokes wave. Then, the amplifier gain can be viewed as the output of a special LTI system, which characterizes the normalized Raman gain profile as its unit impulse response and the pump power integral impulse sequence in frequency domain as its input. By using the nonnegative constraint least-square error (LSE) and clustering technique, we will solve this problem quickly. Numerical simulations shows that the total computation time will be halved at the cost of a slight deterioration in gain flatness.
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