Using a genetic algorithm optimisation scheme similar to the one used in (Methods 6.3), we generated representative ensembles of optimal element sequences for each year between 1800 and 2021. Such sequences place similar elements in neighboring positions within the sequence. To test the performance of our optimisation we compared them with a series of standards, including ensembles of random sequences, order by atomic number, and other previously optimised sequences (SI 7.2). This also allows for assessing the performance of these sequences in our dataset, showing, for instance, that Pettifor's scale is still one of the best performing, even after 40 years of its publication. To quantify the resemblance among periodic systems, we devised a similarity measure based on the relative overlapping of element sequences (Methods 6.5).