Multicast Routing with Quality of Service and Traffic Engineering Requirements in the Internet, Based On Genetic Algorithm Paulo Teixeira de Araújo, Gina Maira Barbosa de Oliveira Pós-Graduação em Engenharia Elétrica, Universidade Presbiteriana Mackenzie paulo.araujo@sudameris.com.br; gina@mackenzie.br The prevalent Internet service model is the best-effort, which does not permit users to obtain Quality of Service (QoS) because it does not have a differentiated treatment for data flows. The IETF (Internet Engineering Task Force) has proposed several solutions for QoS, among them, the Traffic Engineering (TE), which asks for Constraint-Based Routing. In the routing process, the combination of additive and/or multiplicative metrics is an NP-complete problem. Thus, the Constraint-Based Routing is viewed as an intractable implementation problem. In order to deal with the high computational power required by the QoS routing, the use of a Genetic Algorithm (GA) as a method to obtain the appropriate routes has been presented in various works [1, 2]. The GA discussed in this work was adapted from the model presented in [2] that uses bandwidth, delay and cost as metrics to evaluate the routes. Two innovations were incorporated in the GA in order to attend TE requirements: inclusion of the metric number of steps (or hops) in the route evaluation, and a mechanism to avoid the generation of repeated individuals producing several optimal and sub-optimal routes. These two modifications are important for TE because they enable fast re-routing, load balancing and an improvement in the general performance of the network, by reducing hops steps. In order to test the proposed genetic algorithm, two examples of network topology were used: Net0 (15 nodes, 5 destination nodes and delay constraint of 25 ms) and Net1 (18 nodes, 5 destination nodes and delay constraint of 9 ms); they were extracted from [2] and [1], respectively. The best route obtained in [2] for Net0 with delay constraint = 25 ms has delay = 24 ms and cost = 80 in 9 steps. The best route obtained in [1] for Net1 (delay constraint = 9 ms) has delay = 8 ms and cost = 114 in 10 steps. The tests for each network were composed by 4 experiments: 2 different population sizes (15 and 30) and 2 different numbers of generations (20 and 50); 20 GA runs formed each experiment. The best route found for Net0 is the optimal solution and has cost = 69, delay = 24 ms and 10 hops. This result is better than the one published in [2]. This result was relatively easy to obtain: the worst of the 4 experiments converged to the global optimum in 70% of the runs, that is, 14 GA runs reached the optimal route. The GA also found the optimal solution for Net1: a multicast route that has cost = 92, delay = 8 ms and 9 hops. This solution is also better than the one presented in the original work [1]. For this topology, the convergence to the global optimum was worse than to Net0: in the best experiment, only 30% of the GA runs converged to its. The results indicate that the GA discussed in this work converges to the global optimal solution, while the implementations discussed in [1] and [2] did not reach it. Besides, even in the runs that the GA did not converge to the global optimum, sub-optimal solutions that attend to the constraint delay were obtained with a small increment in the cost. In relation to the mechanism that avoids the generation of repeated individuals, an analysis of the final population diversity has been done. This mechanism provokes extra mutations when a route already presents in the population is generated. In the new algorithm, diversity in the range between 79% and 89% has been observed, while in other experiments, where the extra mutations are inhibitted, diversity collapses down to values between 0% and 11%. This means that, with the extra mutations, the GA does indeed obtain a high number of alternative routes, which can be used as backup routes. In relation to the inclusion of the number of steps metric, it has been observed that even when the GA does not converge to the route that represents the global optimum, the best rules obtained maintain a number of steps close to the optimum, with a little increment of the cost. Another important point is that it was observed that the GA performance is sensitive to the network topology and to cost and delay distributions. New experiments are being carried out in order to obtain a new GA environment that can yield good convergence for both tested networks but at smaller execution times. References [1] Ravikumar, C. P; Bajpai, R.. "Source-based delay- bounded multicasting in multimedia networks". Computer Communications. 1998. Vol. 21, pp. 126-132. [2] Zhengying, W.; Bingxin, S.; Erdun, Z.. "Bandwidth- delay-constraint least-cost multicast routing based on heuristic genectic algorithm". Computer Communications. 2001. Vol. 24. pp. 685-692. Proceedings of the VII Brazilian Symposium on Neural Networks (SBRN’02) 0-7695-1709-9/02 $17.00 © 2002 IEEE