A novel methodology for designing thinned arrays with controlled pattern features is presented. The optimization of the binary weighting coefficients of the array elements is carried out through a multi-step procedure. In a first stage, a Genetic Algorithm (GA) is used to determine the binary sequence whose autocorrelation function is closest to a target one. Then, the thinned array is constructed from one of its cyclic sequences which optimizes a given figure of merit. A preliminary numerical example is illustrated in order to show the potentialities of the proposed approach.