In this paper, we study an algorithm of route optimization using the first-derivative length (FDL) path in a hybrid-switching network with movable-boundary for heterogeneous traffics, and investigate the interactions among four different classes of traffics in a time division multiplexing (TDM) network. This algorithm has some desirable properties compared with the gradient projection method or the flow deviation method. That is, it requires no initial specification of traffic flow, and the convexity of the objective function is not required. The numerical results show that the solution is close to the optimal solution and this method yields a substantial improvement in convergence time over the gradient projection method.