this is not done yet. If you are interested, refer to the links instead. (and don’t expect what I will randomly write here to exceed these professional materials!)
https://en.wikipedia.org/wiki/P_versus_NP_problem
https://en.wikipedia.org/wiki/Local_search_(optimization)
The search method is common in AI industry and any decision-making / solution-finding programs.
Complete search algorithms enumerate every possibility and grant a final answer, but it is mostly slow and less heuristic.
Incomplete algorithms walk in the wilds and make progress with best efforts.
https://en.wikipedia.org/wiki/Gradient_descent
https://en.wikipedia.org/wiki/Machine_learning
Read along about advanced SAT problem solving techniques.