A strategy for climbing a hill in a fog is to move upward.
A heuristic that estimates distance to the goal can be used to guide a hill-climbing search. A discrete depth-first search guided by such a heuristic is called greedy best-first search; it can be very efficient. For example, in route finding, hill climbing could be implemented by selecting the next city that is closest to the goal.
Unfortunately, hill-climbing sometimes gets into trouble on a local maximum:
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