  The design of isophoric phased arrays composed of two-sized square-shaped
tiles that fully cover rectangular apertures is dealt with. The number and the
positions of the tiles within the array aperture are optimized to fit desired
specifications on the power pattern features. Toward this end, starting from
the derivation of theoretical conditions for the complete tileability of the
aperture, an ad hoc coding of the admissible arrangements, which implies a
drastic reduction of the cardinality of the solution space, and their compact
representation with a graph are exploited to profitably apply an effective
optimizer based on an integer-coded genetic algorithm. A set of representative
numerical examples, concerned with state-of-the-art benchmark problems, is
reported and discussed to give some insights on the effectiveness of both the
proposed tiled architectures and the synthesis strategy.
