Optical wavelength-division multiplexed (WDM) networks often include optical cross-connects with multigranularity switching capability, such as switching on a single lambda, a waveband, or an entire fiber basis. In addition, it has been shown that routing and wavelength assignment (RWA) in an arbitrary mesh WDM network is an NP-complete problem. In this paper, we propose an efficient approximation approach, called Lagrangean relaxation with heuristics (LRH), aimed to resolve RWA in multigranularity WDM networks particularly with lambda and fiber switches. The task is first formulated as a combinatorial optimization problem in which the bottleneck link utilization is to be minimized. The LRH approach performs constraint relaxation and derives a lower-bound solution index according to a set of Lagrangean multipliers generated through subgradient-based iterations. In parallel, using the generated Lagrangean multipliers, the LRH approach employs a new heuristic algorithm to arrive at a near-optimal upper-bound solution. With lower and upper bounds, we conduct a performance study on LRH with respect to accuracy and convergence speed under different parameter settings. We further draw comparisons between LRH and an existing practical approach via experiments over randomly generated and several well-known large sized networks. Numerical results demonstrate that LRH outperforms the existing approach in both accuracy and computational time complexity, particularly for larger sized networks.

For WDM networks with multi-granularity switching, optical tunnel allocation (OTA) deals with the real-time establishment of optical tunnels between optical nodes through various optical multi-granularity switching devices. OTA is in principle a dynamic routing and wavelength assignment (RWA) problem with multi-granularity switching devices taken into account. In this paper, we propose a novel approximation approach, called Lagrangean relaxation with heuristics (LRH), aimed to resolve RWA considering both fiber and lambda switches. Such RWA is first formulated as a combinatorial optimization problem in which the bottleneck link utilization is to be minimized. To tackle the problem, the LRH approach performs constraint relaxation and derives a lower-bound solution index according to a set of Lagrangean multipliers generated through subgradient-based iterations. In parallel, using the generated Lagrangean multipliers, the LRH approach employs a new heuristic algorithm to arrive at a near-optimal upper-bound solution. Through numerical results and comparisons, we delineate that the LRH approach achieves a near-optimal solution, which is profoundly tight to its lower bound, at the expense of low computational time complexity.