A genetic algorithm technique is introduced for the purpose of optimizing a broadband Peano-Gosper fractile array to eliminate grating lobes during scanning. It has been shown that when the element spacing of a Peano-Gosper fractile array is increased to one wavelength, no grating lobes occur in the entire visible region for broadside operation. However, when the minimum element spacing is one wavelength or greater and the main beam is scanned away from broadside, grating lobes occur in the far-filed radiation pattern of the array. It will be shown that a genetic algorithm technique can be used to perturb the element locations in an optimal way on the interior of the Peano-Gosper fractile array to eliminate the grating lobes and provide acceptable sidelobe levels during scanning. The genetically optimized stage 1 Peano-Gosper fractile array with perturbed element locations can be used to create higher order stages through an efficient iterative procedure while, at each stage, the array maintains its broadband characteristics within a specified scan volume.