Consistent and Admissible Heuristics

Question

Any consistent heuristic is also admissible. But when is a heuristic admissible but not consistent (monotone)?

Please provide an example in which this is the case.

Answer 1

It best to think of a consistent heuristic as an admissible heuristic which obeys the triangle inequality:

Cost(a -> c) <= Cost(a -> b) + Cost(b -> c)

for any three nodes a, b and c in the search space, with the understanding that the cost is computed using the actual cost between adjacent nodes and using the heuristic otherwise.