To test the performance of the algorithm described in Methods 6.3, four benchmark sequences were scored and compared with our results. A comparison of the performance of the different benchmarks is given in Table , which includes a) a sample of randomly generated sequences, b) ordering by atomic number (Z), c) Pettifor's scale , d) Glawe et al.'s GA optimised scale , e) Glawe et al.'s modified Pettifor scale and f) Allahyari and Oganov's Universal Sequence of Elements (USE) . Cost L was calculated using the similarity matrices S for 1980, 2016 and 2021, and results of our optimisations for each year are provided in Table , row g. These years were selected based on the publication years of the sequences by Pettifor , Glawe et al. and Allahyari and Oganov .