2) Fundacao CPqD, Rodovia Campinas -Mogi-Mirim (SP-340) -km 118,5 -Campinas -SP, Brazil, CEP 13086-902.Abstract -In this paper a genetic algorithm is used as a tool for topology searching and splitter placement in Passive Optical Networks. In order to apply such approach, a graph representation scheme, associated to a street map , is proposed. The formulation has been applied to minimize the amount of optical cabling, num ber of splitters and power budget, based on standards for the ITV-T GPON parameters. II. PASSIVE N ETWORK TOPOLOGI ES A telecom network may be represented by a graph, G = (V, E), where V = {VI, V2,..., v n } represents a collection of nodes, and E = {e., e2,... ,.e m }a collection of transmission media. Fig. I shows a network and its equivalent graph, for example, G = ({VI , V2,"" v6}{et, e2,"" eg}) [5]. 4F ig. I -Example of a network and its equivalent graph.The network physical topology corresponds to the way the nodes are interconnected. The way the information is conveyed through the network corresponds to the logical topology. As illustrated in Fig. I, node 1 works as a distributer node and the whole communication is performed directly between different nodes and node I. Therefore, the physical and logical topologies are different , as it may be inferred from Fig. 2, which shows the correspondent graphs. Fig. 2 -Representation of physica l and logical topologies corresponding to the same network.During the network planning , the topology choice is affect by the development strategy and the type of services to be offered. The bus topology (Fig. 3a) is the simplest one, with the sharing of the transmission media among all network elements . Although simple, it makes the communication process more difficult and imposes the use of a special protocol to avoid collisions of simultaneous signals, sent by different users. The bus topology is commonly used in Ethernet networks , associated to the CSMAlCD (Carrier Sense Multiple Access with Collision Detection) protocol. In the ring topology (Fig. 3b), each node is connected to two neighbor nodes so that a message circulates throughout the nodes. A ring may be uni-or bidirectional and is used in many cases, such as data (token ring), SDH (synchronous digital hierarchy) and RPR (Resilient Packet Ring) networks. 3
