The design of sub-arrayed planar phased arrays characterized by an irregular organization of domino-shaped tiles is addressed. Starting from optimal tiling theorems drawn from mathematical theory, an enumerative approach able to retrieve the optimal clustering providing the maximum aperture coverage and the best radiation performance is proposed to deal with the synthesis of low/medium-size rectangular arrays. Based on the same optimal theorems and still exploiting the algorithmic procedures at the basis of the enumerative approach, an innovative schemata-based optimization method is introduced for designing large arrays, as well. A set of representative results, concerned with ideal as well as real radiating elements, is reported and discussed to highlight the features and the potentialities of the proposed analytically-based design framework.