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This letter focuses on the problem of network capacity assignment to accommodate the introduction of additional multicast services in existing unicast networks. The problem is firstly formalized by defining a cost function to evaluate the goodness of a given capacity allocation configuration. Then, a novel approach based on the genetic algorithms is provided to find the near-optimal solution. Experimental results are compared with those of a heuristic algorithm that provides a lower bound for the optimization problem, showing that the proposed method allows for a strong reduction of the processing time.