Informed Methods

Algorithm A*

Use the same evaluation function as used by Algorithm A except add the constraint that for all nodes n in the search space, h(n) <= h*(n), where h*(n) = the true cost of the minimal cost path from n to a goal.

When the condition h(n) <= h*(n) holds, we say that h is admissible.
Using an admissible heuristic guarantees that a node on the optimal path can never look so bad that you bypass it forever
A* is complete whenever the branching factor is finite, and every operator has a fixed positive cost
A* is admissible
If h(n) = h*(n) for all n, then only the nodes on the optimal solution path will be expanded. So, no extra work will be performed.
If h(n) = 0 for all n, then this is an admissible heuristic and results in A* performing exactly as the Uniform-Cost Search does
If h1(n) < h2(n) <= h*(n) for all n that are not goal nodes, then h2 is a better heuristic than h1 in the sense that if A1* is a version of the A* algorithm which uses h1, and A2* is a version of the A* algorithm which uses h2, then every node expanded by A2* is also expanded by A1*. In other words, A1* expands at least as many nodes as A2*. We say that A2* is better informed than A1*.
The closer h is to h*, the fewer extra nodes that will be expanded