3 ms·

Ooh nice! That's the first one I've seen below 376.0 I've gotten close, but not cracked it yet. I was wondering if anyone would break the 376.0 barrier!

zimpenfish 8y ago
I'm wondering if vertical symmetry might be involved (and a way of optimising future efforts) - plotting the journeys of the top three on this post definitely seems to imply that. https://rjp.is/calendars/topthree.png https://rjp.is/calendars/topthree.png Compare and contrast the original set from @jgc's article: https://rjp.is/calendars/originals.png https://rjp.is/calendars/originals.png
- jgrahamc 8y ago
  The symmetry thing makes sense, but now I wonder if there's are really "interesting" or not. Does the symmetry spoil the fun of searching or not?
- zero_iq 8y ago
  Thanks for keeping track. Quite fascinating how algorithms employing so much randomization can arrive at such structure and symmetry. Finally got a < 376.0 from my own code using simulated annealing method... 375.998672775885 [[13 20 7 18 5 10] [ 9 15 2 23 12 16] [ 4 22 24 1 3 21] [17 11 6 19 14 8]] ...only to realise it's the same as yours, but with the rows reversed! Rather surprised, but I now wonder if there is only a small number of very-low-scoring solutions. So perhaps this is less of a coincidence than it first appears. I'm now using a much more aggressive temperature drop-off to find decent candidates early, followed by a tempering phase to search for nearby solutions, and a final cool-off to refine the final answer. I'm still using only random pair swaps in Python, so probably wasting a lot of cycles, but I'm still quite surprised how quickly it converges to some pretty decent scores. Beyond that I'm just going to try lots of random starting layouts. I'm interested to see if my method can find any of the other posted solutions or (fingers crossed!) any new ones, but I may need to crunch through a lot more candidates... I will have to translate from Python into something faster to up my game!
  - zimpenfish 8y ago
    Not entirely scientific but starting from the trivial 1-24 board, I did 100M random swaps (in Go, keeping all of them, takes about 4 minutes) and counted how many scores were in each bucket of 10 (ie 370-379.99, 380-389.99, etc.) Having done this a few times and never got anything in 37, I'm thinking the number of solutions below 380 must be relatively small, yeah. 37 0 38 2377 39 1103812 40 16535778 41 39376324 42 29525491 43 10609914 44 2394340 45 395239 46 51463 47 4880 48 363 49 19 50 0
jffry 8y ago
375.923809971073 :-) https://gist.github.com/jffry/fab43b5b65499c3f513fea701597806b https://gist.github.com/jffry/fab43b5b65499c3f513fea70159780...
- zimpenfish 8y ago
  Added to https://rjp.is/calendars/topthree.png https://rjp.is/calendars/topthree.png (which is now four but nvm) to show the exceptional symmetry. I'm thinking we might be right on the lower limit here - doesn't seem much room for more symmetricalising.

zimpenfish 8y ago

I'm wondering if vertical symmetry might be involved (and a way of optimising future efforts) - plotting the journeys of the top three on this post definitely seems to imply that. https://rjp.is/calendars/topthree.png https://rjp.is/calendars/topthree.png Compare and contrast the original set from @jgc's article: https://rjp.is/calendars/originals.png https://rjp.is/calendars/originals.png

jgrahamc 8y ago
The symmetry thing makes sense, but now I wonder if there's are really "interesting" or not. Does the symmetry spoil the fun of searching or not?
zero_iq 8y ago
Thanks for keeping track. Quite fascinating how algorithms employing so much randomization can arrive at such structure and symmetry. Finally got a < 376.0 from my own code using simulated annealing method... 375.998672775885 [[13 20 7 18 5 10] [ 9 15 2 23 12 16] [ 4 22 24 1 3 21] [17 11 6 19 14 8]] ...only to realise it's the same as yours, but with the rows reversed! Rather surprised, but I now wonder if there is only a small number of very-low-scoring solutions. So perhaps this is less of a coincidence than it first appears. I'm now using a much more aggressive temperature drop-off to find decent candidates early, followed by a tempering phase to search for nearby solutions, and a final cool-off to refine the final answer. I'm still using only random pair swaps in Python, so probably wasting a lot of cycles, but I'm still quite surprised how quickly it converges to some pretty decent scores. Beyond that I'm just going to try lots of random starting layouts. I'm interested to see if my method can find any of the other posted solutions or (fingers crossed!) any new ones, but I may need to crunch through a lot more candidates... I will have to translate from Python into something faster to up my game!
- zimpenfish 8y ago
  Not entirely scientific but starting from the trivial 1-24 board, I did 100M random swaps (in Go, keeping all of them, takes about 4 minutes) and counted how many scores were in each bucket of 10 (ie 370-379.99, 380-389.99, etc.) Having done this a few times and never got anything in 37, I'm thinking the number of solutions below 380 must be relatively small, yeah. 37 0 38 2377 39 1103812 40 16535778 41 39376324 42 29525491 43 10609914 44 2394340 45 395239 46 51463 47 4880 48 363 49 19 50 0

jffry 8y ago

375.923809971073 :-) https://gist.github.com/jffry/fab43b5b65499c3f513fea701597806b https://gist.github.com/jffry/fab43b5b65499c3f513fea70159780...

zimpenfish 8y ago
Added to https://rjp.is/calendars/topthree.png https://rjp.is/calendars/topthree.png (which is now four but nvm) to show the exceptional symmetry. I'm thinking we might be right on the lower limit here - doesn't seem much room for more symmetricalising.