Unit 2 Topic 4 Informed search strategies AO.ppt

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Informed Search Strategies
Ms. Richa Singh
CSE(AI)

CONTENTS
 Basic
 AND/OR graph search problem
 AO* Search Algorithm
 AO* Search Procedure
 Example
 AO* V/s A*
 Advantages and Disadvantages
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BASIC
 In an AND-OR graph AO* algorithm is an
efficient method to explore a solution path.
 AO* algorithm works mainly based on two
phases.
AND and OR
 AO* algorithm will not give the best solution
in such cases.
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AND/OR GRAPH SEARCH PROBLEM
 Problem definition:
Given: [G, s, T]
where
•G: implicitly specified AND/OR graph
•S: start node of the AND/OR graph
• T: set of terminal nodes
• h(n) heuristic function estimating the h(n) heuristic
function estimating the cost of solving the sub cost of
solving at n problem.
 To find: – A minimum cost solution tree A minimum
cost solution tree 5

ALGORITHM AO*
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Step 1 Initialize Set G* = {s}, f(s) = h(s)
If s T, label s as SOLVED T
∈
Step 2 Terminate If s is SOLVED, then Terminate
Step 3 Select: Select a non-terminal leaf node n from the
marked sub-tree
Step 4 Expand Make explicit the successors of n
For each new successor, m:
Set f(m) = h(m)
If m is terminal, label m SOLVED
Step 5 Cost Revision: Call cost-revise(n)
Step 6 Loop Go To Step 2

CONTI…
7
 OPEN:
It contains the nodes that has been traversed but yet
not been marked solvable or unsolvable.
 CLOSE:
It contains the nodes that have already been processed.

AO* SEARCH PROCEDURE
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1. Place the start node on open.
2. Using the search tree, compute the most
promising solution tree TP .
3. Select node n that is both on open and a part
of tp, remove n from open and place it no
closed.
4. If n is a goal node, label n as solved. If the
start node is solved, exit with success where tp
is the solution tree, remove all nodes from open
with a solved ancestor.

CONTI…
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5. If n is not solvable node, label n as
unsolvable.
If the start node is labeled as unsolvable, exit
with failure.
Remove all nodes from open, with unsolvable
ancestors.
6. Otherwise, expand node n generating all of
its successor compute the cost of for each newly
generated node and place all such nodes on
open.
7. Go back to step(2)

CONTI…
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 In figure (a) the top node A has been expanded producing
two area one leading to B and leading to C-D.
 The numbers at each node represent the value of f ' at that
node (cost of getting to the goal state from current state).
 For simplicity, it is assumed that every operation(i.e.
applying a rule) has unit cost, i.e., each are with single
successor will have a cost of 1 and each of its components.
 With the available information till now , it appears that C
is the most promising node to expand since its f ' = 3 , the
lowest but going through B would be better since to use C
we must also use D' and the cost would be 9(3+4+1+1).
 Through B it would be 6(5+1).

CONTI…
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 Thus the choice of the next node to expand depends not
only n a value but also on whether that node is part of the
current best path form the initial mode.
 Figure (b) makes this clearer. In figure the node G
appears to be the most promising node, with the least f '
value.
 But G is not on the current beat path, since to use G we
must use GH with a cost of 9 and again this demands that
arcs be used (with a cost of 27).
 The path from A through B, E-F is better with a total cost
of (17+1=18).

AO* V/S A*
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 The main difference between A* (A star) and AO (AO
star) algorithm is that A* algorithm is a OR graph
algorithm and AO* is a AND-OR graph algorithm.
 In OR graph algorithm it just find only one solution.
 In AND-OR graph algorithm it find more than one
solution by ANDing two or more brances.
 A* algorithm mostly used in practical application (traffic
navigation system, games etc) while AO* algorithm
rarely used in practical application (alpha beta pruning
for game tree)

ADVANTAGES & DISADVANTAGES:
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Advantages:
 It is an optimal algorithm.
 If traverse according to the ordering of nodes. It can
be used for both OR and AND graph.
Disadvantages:
 Sometimes for unsolvable nodes, it can’t find the
optimal path. Its complexity is than other
algorithms.

Unit 2 Topic 4 Informed search strategies AO.ppt

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