Add basic first version of random kahypar+

[CSNWEB]

Based on https://github.com/ti2-group/hybrid_contraction_tree_optimizer/

Unfortunately I just realized that the RandomOptimizer does not optimize the costmod and temperature. Not sure how I missed that while going over the code. Without that the results are much worse though. I think ideally these parameters should be randomly chosen within the optimize function for each trial. For now I just hacked it over the optimize functions, which will probably lose some performance in the accelerated rust case.

[pep8speaks]

Hello @CSNWEB! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

There are currently no PEP 8 issues detected in this Pull Request. Cheers! 🍻

Comment last updated at 2024-05-05 00:03:57 UTC

[jcmgray]

Thanks for this! Yes random sampling of costmod and temperature can be very easily added to the python and rust version, though actual optimization / tuning of the distribution they sample from a bit harder. Do you have any assessment of how good the performance is with uniform sampling?

[CSNWEB]

The basic version I added in this PR (temperature exponential, costumed uniform), which comes from your original hyperoptimizer if I remember correctly, was very effective in my tests. It nearly always performed better in terms of best path found after x seconds than optuna or nevergrad. It definitely seems to be sufficient to find reasonably good greedy paths.

[CSNWEB]

I reduced the code size quite a bit by removing all the contract tree related stuff and merging the paths directly while removing the duplicated tree traversal. Apart from the hacked in costmod and temperature tuning I am happy with the code now.

[jcmgray]

Great, could you maybe add a basic test? e.g. just to the matrix in test_optimizers.py.

I'll take a look and add the costmod and temperature sampling soon.

[jcmgray]

OK I've added costmod and temperature sampling now, which yes does increase the path quality quite nicely without much drawback. It's in cotengra main now and v0.1.3 of cotengrust (https://github.com/jcmgray/cotengrust/releases/tag/v0.1.3) has it enabled also.

[CSNWEB]

Awesome, thanks. I will try to add some tests towards the end of the week.