We have carried out potential energy minimization calculations on benzene, naphthalene, and anthracene clusters using model potential energy functions. The primary purpose was to examine several techniques which use concepts from the field of genetic algorithms (GA). In particular, we compared the "traditional GA" in which the variables of the problem are coded into binary and genetic operations performed on these, and recent methods which use real-valued variables. Our primary technique, the "space-fixed modified GA" (SFMGA), also uses a conjugate gradient descent on the geometries generated by the GA. Our results show the convergence to the global minimum is greatly improved by the use of the descent minimization. In fact, it appears unlikely that the traditional GA's are useful for any but the very simplest clusters. We have also compared the SFMGA with simulated annealing (SA) and Wales and Doye's recent basin-hopping (BH) technique. We find our method to be superior to SA, and comparable to BH.