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This study aims to investigate the feasibility and potential of sparse random arrays driven by the particle swarm optimization (PSO) algorithm to generate multiple-focus patterns and a large scanning range without grating lobes, which extends the scanning range of focused ultrasound in the treatment of brain tumors, opening the blood-brain barrier, and neuromodulation. Operating at 1.1 MHz, a random spherical array with 200 square elements (sparseness 58%) and a sparse random array with 660 square elements (sparseness 41%) driven by PSO are employed to simulate different focus patterns. With the same radius of curvature and diameter of transducer and element size, the scanning range of the off-axis single focus of a random 200-element array is two times that of an ordinary array using symmetric arrangement. The focal volume of multiple-focus patterns of the random array is 18 times that of the single focus. The single focus of the sparse random array with 660 elements could steer up to ±23 mm in the radial direction, without grating lobes. The maximum distance between two foci in a multiple-focus "S"-shaped deflection is approximately 25 mm. Simulation results illustrate the capability of a focused beam steered in 3-D space. Multiple-focus patterns could significantly increase the focal volume and shorten the treatment time for large target volumes. Simulation results show the feasibility and potential of the method combining PSO with a sparse random array to generate flexible focus patterns that can adapt to different needs in different tissue treatments.