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The standard Lagrangian relaxation (SLR) method is an efficient method for solving the routing and wavelength assignment (RWA) problems in optical networks. However, previous work did not deal with multiple connection requests with identical source and destination pairs, which are frequently encountered in practice and can cause serious issues when using SLR. More specifically, in solving the dual subproblems after the wavelength capacity constraints are relaxed, the shortest path algorithms such as Dijkstra's typically assign the same route to such connection requests, which possibly leads to a poor RWA solution. In this paper, we introduce a new method, i.e., the successive subproblem solving (SSS) method and one of its implementations, within the Lagrangian relaxation framework. The essence of SSS is to introduce coupled penalty terms and use the surrogate subgradients for search direction at the high level. The homogenous subproblems at the low level are then solved sequentially to avoid the nondecomposable difficulty. Theoretical analysis is performed to provide convergence proof. Numerical results are presented to show that the new method is effective and efficient.