Sonet Network Design Problems

Y. Deville and C. Solnon (Eds): Sixth International Workshop on Local Search Techniques in Constraint Satisfaction (LSCS’09). EPTCS 5, 2009, pp. 81–95, doi:10.4204/EPTCS.5.7 c⃝M. Pelleau & P. Van Hentenryck & C. Truchet Sonet Network Design Problems Marie Pelleau†,‡ Pascal Van Hentenryck‡ Charlotte Truchet† marie.pelleau@univ-nantes.fr pvh@cs.brown.edu Charlotte.Truchet@univ-nantes.fr † Universit´e de Nantes ‡ Brown University D´epartement informatique Computer Science 2 rue de la Houssini`ere 115 Waterman Street 44322 Nantes cedex 3 Providence, RI 02912 France USA This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Net- work Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP). These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in COMET allow us to compare our method to previous ones and show that we obtain better results. 1 Introduction This paper presents a new algorithm and an objective function to solve two real-world combinatorial optimization problems from the field of network design. These two problems, the Synchronous Optical Network Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP), have been shown N P-hard and have already been solved by combinatorial optimization techniques. This work extends the seminal ideas introduced by R. Aringhieri and M. Dell’Amico in 2005 in [2]. This paper is organized as follows. In the sequel of this section we introduce the two problems we have worked on, and the local search techniques which have been used to solve them. We will also introduce the models in a constrained optimization format for the two problems. We then present the previous works on SRAP and IDP in section 2. Section 3 describes the key ingredients necessary to implement the local search algorithms. Finally, the results are shown in Section 4. 1.1 Optical networks topologies During the last few years the number of internet based application users has exponentially increased, and so has the demand for bandwidth. To enable fast transmission of large quantities of data, the fiber optic technology in telecommunication is the current solution. The Synchronous Optical NETwork (SONET) in North America and Synchronous Digital Hierarchy (SDH) in Europe and Japan are the standard designs for fiber optics networks. They have a ring-based topology, in other words, they are a collection of rings. arXiv:0910.1255v1 [cs.AI] 7 Oct 2009 82 Sonet Network Design Problems Rings Each customer is connected to one or more rings, and can send, receive and relay messages using an add-drop-multiplexer (ADM). There are two bidirectional links connecting each customer to his neighboring customers on the ring. In a bidirectional ring the traffic between two nodes can be sent clockwise or counterclockwise. This topology allows an enhanced survivability of the network, specifically if a failure occurs on a link, the traffic originally transmitted on this link will be sent on the surviving part of the ring. The volume traffic on any ring is limited by the link capacity, called B. The cost of this kind of network is defined by the cost of the different components used in it. There are different ways to represent a network. In this paper, we consider two network topologies described by R. Aringhieri and M. Dell’Amico in 2005 in [2]. In both topologies the goal is to minimize the cost of the network while guaranteeing that the customers’ demands, in term of bandwidth, are satisfied. The model associated to these topologies are based on graphs. Given an undirected graph G = (V,E), V = {1,...,n}, the set of nodes represent the customers and E, the set of edges, stand for the customers’ traffic demands. A communication between two customers u and v corresponds to the weighted edge (u,v) in the graph, where the weight duv is the fixed traffic demand. Note that duv = dvu, and that duu = 0. 1.1.1 First topology (SRAP) In the first topology, each customer is connected to exactly one ring. All of these local rings are con- nected with a device called digital cross connector (DXC) to a special ring, called the federal ring. The traffic between two rings is transmitted over this special ring. Like the other rings, the federal ring is limited by the capacity B. Because DXCs are so much more expensive than ADMs we want to have the smallest possible number of them. As there is a one-to-one relationship between the ring and the DXC, minimizing the number of rings is equivalent to minimizing the number of DXCs. The problem associated to this topology is called SONET Ring Assignment Problem (SRAP) with capacity constraint. Figure 1 shows

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