Modelling, algorithms, and analysis of survivable VP planning in ATM networks

In this paper, we consider the working VP and backup VP routing problems jointly and employ the integer programming based approach to maximize the system resource utilization and the network survivability. The VP planning problem is formulated as a nonlinear combinatorial optimization problem. The objective function is to minimize the resource usage while maximizing the network survivability. By proper transformation of the objective function and applying the cutting plane method, the original formulation is transformed into an integer linear program formulation which is suitable for applying Lagrangian relaxation techniques. After Lagrangian relaxation, the problem is further decomposed into several tractable subproblems. Unlike others' work, the candidate path set does not need to be prepared in advance and the best paths are generated while solving subproblems in our approach. Heuristic algorithms based on the solving procedure of the Lagrangian relaxation are developed. By assessing the gap between the heuristic upper bounds and the Lagrangian lower bounds, we find that our algorithm can efficiently provide a near optimal solution for the survivable VP layout design in ATM networks.