Cognitive Radio Networks (CRN) were introduced as a means to more efficiently reuse the licensed radio frequency spectrum. One of their salient features is the ability of unlicensed nodes to dynamically adapt their radio parameters according to their needs. This paper investigates the resource allocation problem in CRN by jointly considering power control and bandwidth for a set of secondary users (SU) transmitting simultaneously with a set of licensed users (PU), which transmissions must remain unaltered. The proposed allocation scheme is based on a Genetic Algorithm (GA) where the chromosome's genes represent the reconfigurable interface radio parameters, by defining genetic operations the GA is empowered to find a set of radio parameters that maximize the overall network capacity and under the physical interference model enforced to the transmissions of both PU’s and SU’s. The numerical results illustrate the prominent effect of adjusting jointly multiple radio parameters on the network capacity.