A genetic algorithm (GA)-based procedure for finding the global minimum of medium-sized SixHy clusters at the ab initio level is presented. Semiempirical calculations are used to prescreen the relative energies of the many locally optimized SixHy structures generated by the GA. The AM1 semiempirical method used in our original global optimization strategy produces cluster energies appreciably different from the ab initio ranking. To improve the AM1 energy ranking we recently explored using for each specific SixHy stoichiometry two coupled GAs: (1) a parametrization GA (PGA) for finding better semiempirical GAM1 parameters for Si and (2) a cluster global optimization GA (CGA) that uses the GAM1 parameters in the cluster energy prescreening. The two GAs method is a more reliable approach for global optimization of different SixHy stoichiometries because the GAM1 parameters adjust to whether the Si atoms are partially or completely passivated by H atoms. Unfortunately, even for medium-sized SixHy clusters we find the two GAs method is too computationally demanding. In this paper we examine under what conditions the GAM1 parameters obtained for a specific small SixHy stoichiometry could be successfully transferred to larger clusters so that only the CGA global search need be performed. We choose Si7H14 as the starting stoichiometry since it can adopt various possible structures which model a Si-7 Core completely passivated by H atoms. We find the resulting GAM1 parameters obtained from the Si7H14 training set produce relative cluster energies matching well with the ab initio energy rankings for larger SixHy clusters which also have complete H atom passivation. Whereas for the low H-passivated SixHy clusters, the GAM1 energy rankings are no better than the previous AM1 results. We use Si7H14 GAM1 parameters to repeat our search for the Si10H16 and Si14H20 global minima. Unlike the AMI method, now both GAM1 and MP2 ab initio calculations give the lowest energy for the cluster with a completely passivated diamond-like Si core structure. The Si7H14 GAM1 parameters not only improve our confidence that we are finding the true global minima but also reinforce our earlier conclusion that Si10H16 and Si14H20 are at their preferred level of H passivation. We illustrate the range of applicability of the Si7H14 GAM1 parameters by determining the global minima for Si10H14 and Si14H18 stoichiometries. The global minima for these two later clusters demonstrate why global optimization methods are useful since their structures cannot be easily obtained by local optimization calculations initiated by simply removing two H atoms from the Si10H16 and Si14H20 global minima.