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Multicasting routing is an effective way to communicate among multiple hosts in computer networks. Usually multiple quality of service (QoS) guarantees are required in most of multicast applications. Several researchers have investigated genetic algorithms-based models for multicast route computation with QoS requirements. The evolutionary models proposed here use multi-objective approaches in a Pareto sense to solve this problem and to deal with the inheriting multiple metrics involved in QoS proposal. Basically, we construct three QoS-constrained multicasting routing algorithms; the first one was based on NSGA, the second one was based on NSGA-II and the third is an adaptation of NSGA-II incorporating the concept of epsiv-dominance. These algorithms were applied to find multicast routes over two network topologies. Three different pairs of objectives were evaluated; the first objective used in each pair is related to the total cost of a multicast route and the second metric is related to delay. The first evaluated delay metric computes the total delay involved in the tree solution; the second one computes the mean delay accumulated from the source to each destination node; the third one is the maximum delay accumulated from the source to a destination node. Our results indicated that the NSGA-II environment incorporating the concept of epsiv-dominance - named epsiv-NSGA-II multicasting routing-returned the best performance.