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Puzzling

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  • $\begingroup$ How long did the solver take for this one? $\endgroup$ Commented Feb 22, 2025 at 5:49
  • $\begingroup$ @justhalf Not sure how long it would have taken to solve directly. I got impatient and wanted to see some progress, so I changed from a feasibility problem to an optimization problem by adding a binary slack variable $s_{ij}$ to \eqref{1}, relaxing \eqref{2} from $=$ to $\le$, and minimizing the infeasibility $\sum s_{ij}$. This got down to objective value $4$ (one small T missing) but then stalled. To finish things off, I performed a local search by fixing the variables for two of the ten types at a time, and solving over the rest. Took a few hours (maybe longer than solving directly). $\endgroup$ Commented Feb 22, 2025 at 14:08
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    $\begingroup$ ah, interesting. Thanks for sharing the details and some tricks, Rob. $\endgroup$ Commented Feb 22, 2025 at 14:10
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    $\begingroup$ For comparison, my 'slightly sharpened sledgehammer' approach which is simple backtracking with a beam search aided by scoring heuristic took 248.5 hours $\endgroup$ Commented Feb 23, 2025 at 2:01
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    $\begingroup$ @RobPratt it's taken me rather longer, but I finally solved it too. $\endgroup$ Commented Mar 5, 2025 at 12:47