What is the difference between monotonicity and the admissibility of a heuristic?

Question

I\'m reading over my AI textbook and I\'m curious about what the difference is between monotonicity and admissibility of heuristics (I know they aren\'t mutually exclusive).

Answer 1

Admissibility :

A search algorithm is admissible if it is guaranteed to find a minimal path to a solution whenever such a solution exists. Breadth first search is admissible, because it looks at every state at level n before considering any state at level n+1.

Monotonicity : This property asks if an algorithm is locally admissible---that is, it always underestimates the cost between any two states in the search space. Recall that A* does not require that g(n) = g*(n). A heuristic function, h is monotone if: 1.For all states ni and nj, where nj is a descendant of ni, h(ni) - h(nj) <= cost(ni,nj).

2.The heuristic evaluation of the goal state is 0: h(Goal) = 0.