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Simulated annealing and similar techniques such as Tabu Search are good for problems that have large search spaces due to combinatorial explosion (https://en.wikipedia.org/wiki/Combinatorial_explosion) and can be expressed as a state and an associated cost/fitness function.

This is true provided your cost function is "continuous" w.r.t. distance. Roughly what this means is that if you make a small change - e.g. one edit in this example - then your cost function shouldn't change a lot.

If you don't have some form of continuity condition you are actually just doing random search.

I've assigned this before...

https://ezekiel.encs.vancouver.wsu.edu/~cs330/archive/archiv...

both problems have constraints and you solve the puzzle by finding the right configuration of data that meets the constraints.

They're both examples of an exact cover problem: https://en.wikipedia.org/wiki/Exact_cover