text: This paper presents a new method and a constraint-based objective function to solve two problemsrelated to the design of optical telecommunication networks, namely the Synchronous Optical Net-work Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network DesignProblem (IDP). These network topology problems can be represented as a graph partitioning withcapacity constraints as shown in previous works. We present here a new objective function and anew local search algorithm to solve these problems. Experiments conducted in C
  @cite_5: This paper considers two problems that arise in the design of optical telecommunication networks when a ring-based topology is adopted, namely the SONET Ring Assignment Problem and the Intraring Synchronous Optical Network Design Problem. We show that these two network topology problems correspond to graph partitioning problems with capacity constraints: the first is a vertex partitioning problem, while the latter is an edge partitioning problem. We consider solution methods for both problems, based on metaheuristic algorithms. We first describe variable objective functions that depend on the transition from one solution to a neighboring one, then we apply several diversification and intensification techniques including Path Relinking, eXploring Tabu Search and Scatter Search. Finally we propose a diversification method based on the use of multiple neighborhoods. A set of extensive computational results is used to compare the behaviour of the proposed methods and objective functions.
summary: The two other methods described in @cite_5 are based on the idea that to save ADMs a good solution should have very dense rings. They are both greedy and rely on a clique algorithm. In graph theory, a clique in an undirected graph @math is a subset of the vertex set @math , such that for every two vertices in @math , there exists an edge connecting the two. Finding a clique is not that easy, a way to do it is to use an "Union-Find" strategie, two clique @math and @math such that each node in @math is adjacent to each node in @math then merge the two cliques (). The associated heuristic starts by considering each node to be a clique of size one, and to merge two cliques into a larger clique until there are no more possible merges.