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A novel approach to the synthesis of linear arrays is presented in this letter. It is based on the Schelkunoff method and an efficient interpolation scheme which provides a clever reduction of the optimization variables, maintaining, at the same time, a sufficiently large degree of freedom. The optimization procedure is, therefore, employed into a Genetic Algorithm (GA) which reveals very efficient and with a strongly improved convergence rate. Some examples of linear arrays exhibiting very narrow beamwidth and low side lobe level (SLL) are reported to show the effectiveness of the procedure.