This computational study analyzes the physical parameters regarding 'clusters' of spherical aluminum nanoparticles (NPs), and their role in the enhancement of light absorption and current generation in silicon thin-film solar cells (TFSCs). Plasmonic metal NPs have been known to enhance light-trapping abilities of semiconductor substrates through localized surface plasmon resonance (LSPR). The performance can be further improved by coupling NPs within clusters having different shapes or configurations to confine light within the absorbing layer. The NP clusters take on a circular arrangement, where all NPs are equidistant from the center of the cluster. The finite-difference time-domain (FDTD) method is used to calculate the initial value for short-circuit current density (JSC) from different TFSCs. Due to the large number of possible configurations for the clusters, the Particle Swarm Optimization (PSO) algorithm was deployed to search for the best possible combination of parameters to maximize JSC. The other electrical parameters were recalculated by accounting for different doping concentrations and recombination of electron-hole pairs in the silicon absorbing layer. The highest value obtained for JSC was 13.9 mA/cm2 for a 10 NP cluster with sphere radius of 48nm and cluster radius of 191nm which showed 38.8% efficiency enhancement compared to bare Si TFSC.