N-Queens can be solved (find a single valid solution) in polynomial time [1]. That being said, Local Search is a powerful technique that can solve a lot of problems such as employee scheduling, vehicle routing, or maintenance scheduling. You might want to take a look at Timefold [2], which is a local search solver that can be configured to use simulated annealing, tabu search, late acceptance and other local search algorithms. Note: I work for Timefold.
[1] https://stackoverflow.com/a/13109557
[2] https://solver.timefold.ai/