We compare a sphere radii of 2, 3, 4, 5, and 6 Å. This is the only setting we change that affects the systems generated instead of the algorithm itself. From figure , we observe that our concerns about too small a sphere radii leading to an erroneous constriction of the PES are unfounded and that by decreasing the sphere radii close to that of the cuboctohedral Pt 13 structure (2.7 Å, c.f. figure ) we maximise ULES per iteration. This is likely due to the LO algorithms being able to resolve the compressed structure rather than the structure actually being that compressed. This is evidenced by looking at the maximum radii in the low energy structures in section S3.