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This paper discusses the multicast routing problem with multiple QoS constraints in networks with uncertain parameters, and describes a network model that is suitable to research such QoS multicast routing problem. The paper mainly presents GAQMR, a multicast routing policy for Internet, mobile network or other high-performance networks, that is based on the genetic algorithm, and can provide QoS-sensitive paths in a scalable and flexible way, in the networks environment with uncertain parameters. The GAQMR can also optimize the network resources such as bandwidth and delay, and can converge to the optimal or near-optimal solution within few iterations, even for the networks environment with uncertain parameters. The incremental rate of computational cost can close to polynomial and is less than exponential rate. The performance measures of the GAQMR are evaluated using simulations. The results shows that GAQMR provides an available approach to QoS Multicast routing for uncertainty in network parameters.