27 Jan 2005
CS 3243 - Heuristics
22
Optimality of
A* (proof)
nSuppose some suboptimal goal G2 has
been generated and is in the fringe. Let n be an unexpanded node in the fringe such that
n is on a shortest path to an optimal goal G.
nf(G2) > f(G) from above
nh(n) ≤ h^*(n) since h is admissible
ng(n)
+ h(n) ≤ g(n) + h*(n)
nf(n)
≤ f(G)
Hence f(G2) > f(n), and A* will never select G2 for expansion
