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The scan volume of a thinned periodic linear phased array is proportional to the spacing between array elements. As the spacing between elements increases beyond a half wavelength, the scan range of the array will be significantly reduced due to the appearance of grating lobes. This paper investigates a method of creating thinned aperiodic linear phased arrays through the application of genetic algorithms that will suppress the grating lobes with increased steering angles. In addition, the genetic algorithm will place restrictions on the driving-point impedance of each element so that they are well behaved during scanning. A genetic algorithm approach is also introduced for the purpose of evolving an optimal set of matching networks. Finally, an efficient technique for evaluating the directivity of an aperiodic array of half-wave dipoles is developed for use in conjunction with genetic algorithms.