We present an implementation of a genetic algorithm in the structural design of cemented triplets according to a prespecified set of Gaussian characteristics and primary aberration targets. The approach is directed toward obtaining a suite of promising solutions allowing some floating of the primary aberration targets. This method obviates the need for any heuristic preselection of glasses for the three elements of the triplet. Searches for optimal solutions are conducted in the total configuration space of the degrees of freedom, consisting of continuous variables like shape factor and power distributions, and discrete variables like available glass types. The role of genetic diversity in the evolving population on convergence of the optimization runs has been investigated, and, accordingly suitable modifications are incorporated in the basic genetic algorithm to eliminate undue stagnation and premature convergence problems. Some illustrative examples are given.