We return to the geometry optimization problem of Lennard-Jones clusters to analyze the performance dependence of 'cut and splice' genetic algorithms (GAs) on the employed population size. We generally find that admixing twinning mutation moves leads to an improved robustness of the algorithm efficiency with respect to this a priori unknown technical parameter. The resulting very stable performance of the corresponding mutation + mating GA implementation over a wide range of population sizes is an important feature when addressing unknown systems with computationally involved first-principles based GA sampling. (C) 2009 Elsevier B.V. All rights reserved.