27 Jan 2005
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,
h(n) ≤ c(n,a,n') + h(n')
nIf h is consistent, we have
f(n') = g(n') + h(n')
= g(n) + c(n,a,n') + h(n')
≥ g(n) + h(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
