In this paper, we use particle swarm optimization (PSO) to design a randomly excited and randomly spaced linear array with either the lowest side lobe level (SLL) or the narrowest beamwidth. The positions and the excitation amplitudes of the array elements are considered as variables to be controlled. The beam pattern is optimized by controlling the two variables simultaneously and randomly. The best beam patterns are obtained using PSO in the fitness function where performance is improved by the random assignment of weight coefficients to each angular sector of the beam Pattern. The weight coefficients and angles are obtained through several trial runs. Also, an extra term, ${eta}{ast}BW$, is added to the fitness function to account for the beamwidth as well as the SLL. Is produces the best result for the beam pattern with either the lowest SLL or the narrowest beamwidth. In the former case, the SLL and beamwidth are about -43dB and $32.2^{circ}$, respectively, with only 10 elements. In the latter case, the SLL and beamwidth are about -26dB and $24.2^{circ}$, respectively.