Background,Motivation and Objective During the last decade,the increasing interest in 3D ultrasound imaging pushed the development of 2D-matrix arrays.In particular,state-of-the-art methods for 2D sparse array footprint optimization use simulated annealing(SA) to reduce the number of elements and to find their best position,intensity and size [Trucco,99] [Cheng,10] [Diarra,13].The typical cost function to be minimized measures the fidelity of the beam simulated from the current footprint solution to a template beam pattern(TBP).