The correct answer is: Local Beam search.
Local Beam search is a heuristic search algorithm that keeps track of $k$ states rather than just one. It is a greedy algorithm that always expands the state with the highest estimated value. However, unlike hill climbing, it does not immediately discard states that are not the best. Instead, it keeps track of the $k$ best states and expands them in the next iteration. This allows Local Beam search to escape local optima and find better solutions.
Hill Climbing search is a simple heuristic search algorithm that always expands the state with the highest estimated value. It is a greedy algorithm, which means that it does not consider any other options once it has found a state with a higher estimated value. This can lead to the algorithm getting stuck in local optima.
Stochastic hill climbing search is a variant of hill climbing search that adds a random element to the search process. This can help the algorithm to escape local optima and find better solutions.
Random restart hill climbing search is another variant of hill climbing search.
In this algorithm, the search process is restarted multiple times from different starting points. This can help the algorithm to find better solutions by exploring different parts of the search space.Local Beam search is a more sophisticated algorithm than hill climbing search. It is able to escape local optima and find better solutions. However, it is also more computationally expensive.