In this paper, we proposed a novel numerical algorithm for nth-order cascaded Raman fiber lasers (CRFLs) with the
combination of genetic algorithm (GA) and shooting method. Although shooting method possesses fast speed in solving
nonlinear two-point boundary-value ordinary differential equations, calculating process may diverge if it is directly
applied in the coupled equations of CRFLs when arbitrarily guessed initial values are out of the domain of convergence.
To overcome the problem, genetic algorithm which has rather strong searching ability in global space is firstly employed
to search for the initial value in convergent domain for each Stokes power; and then, the task of finding the more
accurate initial values is finished by shooting method instead of GA whose searching ability is weak in local region. As
an example, a sixth-order Ge-doped CRFL has been simulated by the novel algorithm. Calculated results show that the
new method can effectively and quickly solve the coupled equations of the CRFL without the problem of divergence.