I’ve equipped the packing algorithm with simulated annealing schedule and used it to pack 8 octahedra in a unit cell. Here are some pictures from one run.
Left is the initial packing and right final packing.
27 unit cells of the above packings.
Initial density is 0.1667. The final density is 0.9178. Optimal lattice packing density is 0.9474 (a result by Minkowski) which is hypothesised to be general optimal packing.
I ran also the algorithm without the simulated annealing with same parameters and the final density was 0.8281. Now the question is if the simulated annealing schedule is an improvement or this was achieved just by chance.