The Hill Climbing Search has three limitations:
Local Maxima: It is a state which is better than all of its neighbours but is not better than some other states which are farther away. It is a state where we have climbed to the top of the hill and missed the mountain.
Plateau: A plateau is the flat area of the search space in which all the neighbour states of the current state contain the same value, because of this algorithm does not find any best direction to move. A hill-climbing search might be lost in the plateau area.
Ridge: A ridge is a special form of the local maximum. It has an area which is higher than its surrounding areas, but itself has a slope, and cannot be reached in a single move.