Abstract
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.
© 2007 IEEE
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