Simulated annealing to find the correct permutation of 20 words
No, that's not simulated annealing.  It's not really even close.

Whether it will be a good enough approach will depend on your metric.  Since you haven't told us what the metric is, it's not really possible to say.  In the worst case, if your metric is sufficiently horrible, you might need to explore all $20!$ permutations.   In any case, usually the only reliable way to find out whether your approach is a good one is to implement and see what happens.  There are few theorems that gives useful provable results about how effective the approach will be; instead, you need to use empirical evaluation.