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Quality of service (QoS) intends to guarantee that the end-to-end communication is obtained with the appropriate service level for each application. Traffic engineering (TE) supplies forms of obtaining QoS in computer networks. TE proposals try to optimize the use of network resources and the performance of QoS traffic. Genetic algorithms (GA) for QoS route computation was already proposed. The GA model discussed here incorporates innovations based on TE requirements: a "hops count" metric and a mechanism to avoid duplicated candidate routes. Our GA was applied to multicast routes and converged to better solutions than the ones previously published.