A Lagrangean relaxation and subgradient framework for the routing and wavelength assignment problem in WDM networks

Unlike traditional heuristics, we provide in this paper an optimization framework for the routing and wavelength assignment (RWA) problems with the objective of minimizing the rejection penalty of the connection demands in an all-optical wavelength-division-multiplexing (WDM) network. Our new link-based formulation takes the fairness issue and the limited wavelength conversion into consideration. The framework employs a decomposition approach to decide on the rejection/selection of the route and wavelength assignment for a semilightpath, by appropriately relaxing some of the constraints in the Lagrangean relaxation (LR) method. At the higher level, we update Lagrange multipliers iteratively with the subgradient method. At the lower level, we propose the modified minimum cost semilightpath (MMCSLP) algorithm to solve all the subproblems. A heuristic algorithm is also proposed to generate a feasible RWA scheme based on the solution to the dual problem. When compared with some latest methodology in the literature, we demonstrate that our framework can achieve better performance in terms of the computation time and the number of connection demands rejected. The much shorter computation time is due to the polynomial time complexity of our framework. In addition to achieving a very good (near-optimal) solution, the influence from the change of the number of converters is studied. Finally, we demonstrate that our framework produces fairer routing decisions by adjusting some design parameters in our framework.