This seems like it would be a fun competition, for those who don’t have way too much work to do already ... !! http://azspcs.com/Contest/Nearness …
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I agree it would be more interesting to make it a speed game, though. As it stands, someone with free college supercomputer credits might just run 1000 CPU-days of brute force for the win.
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I am not even convinced yet that the problem space has local minima. If I did pairwise swaps as long as each of them decreases the score, would I get stuck in a suboptimal solution?
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My thinking is scramble the board and then do greedy pairwise swaps until you stop getting gains. Repeat for a few days and submit the best result. I thiiink you'll get stuck in local minima, but I'm not 100% sure.
End of conversation
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