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The paper deals with the channel assignment problem in a hexagonal cellular network with two-band buffering, where channel interference does not extend beyond two cells. Here, for cellular networks with homogeneous demands, we find some lower bounds on the minimum bandwidth required for various relative values of s0, s1, and s2, the minimum frequency separations to avoid interference for calls in the same cell, or in cells at distances of one and two, respectively. We then present an algorithm for solving the channel assignment problem in its general form using the elitist model of genetic algorithm (EGA). We next apply this technique to the special case of hexagonal cellular networks with two-band buffering. For homogeneous demands, we apply EGA for assigning channels to a small subset of nodes and then extend it for the entire cellular network, which ensures faster convergence. Moreover, we show that our approach is also applicable to cases of nonhomogeneous demands. Application of our proposed methodology to well-known benchmark problems generates optimal results within a reasonable computing time.