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Considering a multicast scenario, we want to minimize the resources used for network coding while achieving the desired throughput. We demonstrate a standard genetic algorithm (GA) approach to the solution of this NP-hard problem. Features of standard GA are shown through simulations, based on which we propose our improved GA approach. By enlarging initial population, adopting dynamic mutation and crossover rate and improving the evaluation of fitness value, our improved GA's performance is priory to the standard GA, which is testified through simulations on networks randomly generated.