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In cognitive radios (CRs), secondary users (SUs) transmit alongside primary users (PUs). In order to avoid interference SU perform spectrum sensing and adaptive transmission. Reliable detection in wide geographical regions needs to perform collaborative sensing. The state of the art for efficient cooperative sensing is linear statistics combination. Spatial-spectral joint detection also provides multiband cooperative sensing to access opportunistically several bands at a time. Convex maximization is able to solve only an approximation of the optimization within a restricted solution domain, due to its non-convex nature. In this paper, we demonstrate that convex constraints are counterproductive and we propose an alternative optimization technique based on genetic algorithms. The genetic programming performs direct search of the optimal solution one step before the reformulations needed previously. We demonstrate that, by operating directly on the objective and abstracting from the convexity, the collaborative multiband sensing is optimized consistently with the problem formulation.