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Usually multiple quality of service (QoS) guarantees are required in most of multicast applications. In this paper, it is formulated as a multiobjective constrained combinatorial optimization problem for a protocol to determine multicast routes satisfying different QoS requirements. We use a multiobjective model and routing approach based on genetic algorithm that optimizes multiple QoS parameters simultaneously. The corresponding results demonstrate that the proposed approach is capable of discovering a set of nondominated routes within a finite evolutionary generation. Its feasibility and performance has been verified.