Rotationally resolved electronic spectroscopy yields a wealth of information on molecular structures in different electronic states. Unfortunately, for large molecules the spectra get rapidly very congested owing to close-lying vibronic bands, other isotopomers with similar zero-point energy shifts, or large-amplitude internal motions. A straightforward assignment of single rovibronic lines and, therefore, line position assigned fits are impossible. An alternative approach is unassigned fits of the spectra using genetic algorithms (GAs) with special cost functions for evaluation of the quality of the fit. This paper decribes the improvements we established on the GA method discussed before (J.A. Hageman, R. Wehrens, R. de Gelder, W.L. Meerts, and L.M.C. Buydens. J. Chem. Phys. 113, 7955 (2000)). In particular, we succeeded in obtaining a dramatic reduction in computing time that made it possible to apply the GA process in a large number of cases. A completely automated fit of a rotationally resolved laser-induced fluorescence spectrum without any prior knowledge of the molecular parameters can now be performed in less than 1 h. We demonstrate the power of the method on a number of typical examples such as very dense rovibronic spectra of van der Waals clusters and overlapping spectra due to different isotopomers. The discussed results demonstrate the extreme power of the GA in automated fitting and assigning of complex spectra. It opens the road to the analysis of complex spectra of biomolecules and their building blocks. Key words: high-resolution spectroscopy, genetic algorithm, biomolecules, structure, van der Waals clusters.