21 Jan 2004
CS 3243 - Heuristics
23
Consistent heuristics
nA heuristic is consistent if for every node n, every successor n' of n generated by any action a,
 
n
n h(n) ≤ c(n,a,n') + h(n')
n
nIf h is consistent, we have
nf(n') = g(n') + h(n')
n      = g(n) + c(n,a,n') + h(n')
n      ≥ g(n) + h(n)
n      = f(n)
ni.e., f(n) is non-decreasing along any path.
nTheorem: If h(n) is consistent, A* using GRAPH-SEARCH is optimal