In this paper, an optimization method aimed at designing aperiodic linear sparse arrays is proposed that is based on the stochastic optimization methodology called simulated annealing. Such a method optimizes the positions and the weight coefficients of each element of a linear array in order to obtain a beam pattern that meets given requirements. Moreover, while positions and weights are optimized, minimization of both the number of elements and the spatial aperture is carried out. In this way, a beam pattern without grating lobes and close to the desired one is produced using a small number of elements and a short aperture. The results obtained are impressive in terms of improvement of array characteristics and performance over those reported in the literature, while a great flexibility in defining the desired beam pattern is allowed. Finally, it is proved that the array configurations need a number of elements very close to the absolute minimum to achieve the desired beam pattern.