Time Modulated Array offers a simple way to synthesize radiation patterns with low sidelobe levels, in timeaverage, using an optimized strategy of switching ON and OFF the elements of the array. In this work we show that the complexity of the optimization strategy can be reduced by first shrinking the search space to a subset, or database, of useful solutions over which the optimization will be launched. This reduction is obtained by applying the constraints in a progressive and hierarchical order. In this way, this problem of exponential growth is reduced to a polynomial growth, with respect to the size of the antenna array. We present the case of designing the time modulated array for radar applications where constant directivity and ability of intereference rejection is needed.