The document discusses the A* search algorithm, which is an informed search or heuristic search algorithm. A* combines the best aspects of uniform cost search and greedy best-first search. It is guaranteed to find the shortest path to the goal, if such a path exists. A* evaluates nodes by using both the path cost from the start node to the current node, plus an estimate of the cost to get from the current node to the goal node. It prioritizes expanding the most promising nodes first, those with the lowest combined cost. A* is optimal and admissible if the heuristic function never overestimates the actual cost to the goal.

1. “A* Search in Artificial
Intelligence”
By:
Sohaib Saleem
To:
Resp. Inam-ul-Haq
By Sohaib Chaudhery,UE Okara Campus! 1

2. Uniform Cost Search
 Uniform Cost is a blind search algorithm that is optimal according to any specified path
length function.
 Do not have additional info about states beyond problem def.
 Total search space is looked for solution
 No info is used to determine preference of one child over other.
 Example: 1. Breadth First Search(BFS), Depth First Search(DFS), Depth Limited
Search (DLS).
A
B
C
E
D HF
G
State Space without any extra information associated with each state
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3. Informed/Heuristic Search
 Some info about problem space(heuristic) is used to compute
preference among the children for exploration and expansion.
 Examples: 1. Best First Search, 2. Problem Decomposition, A*,
Mean end Analysis
 The assumption behind blind search is that we have no way of
telling whether a particular search direction is likely to lead us to
the goal or not
 The key idea behind informed or heuristic search algorithms is to
exploit a task specific measure of goodness to try to either reach
the goal more quickly or find a more desirable goal state.
 Heuristic: From the Greek for “find”, “discover”.By Sohaib Chaudhery,UE Okara Campus! 3

4. Informed/Heuristic Search(conti…)
 Heuristic function:
 It maps each state to a numerical value which depicts goodness of a node.
 H(n)=value
 Where ,
 H() is a heuristic function and ‘n’ is the current state.
 Ex: in travelling salesperson problem heuristic value associated with each
node(city) might reflect estimated distance of the current node from the goal
node.
 The heuristic we use here is called HSLD Straight line Distance heuristic.
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5. A* Search
 A* search is a combination of lowest-cost-first and best-first searches that
considers both path cost and heuristic information in its selection of which path
to expand.
 For each path on the frontier, A* uses an estimate of the total path cost from a
start node to a goal node constrained to start along that path.
 It uses cost(p), the cost of the path found, as well as the heuristic function h(p),
the estimated path cost from the end of p to the goal.
 For any path p on the frontier, define f(p)=cost(p)+h(p). This is an estimate of
the total path cost to follow path p then go to a goal node.
 If n is the node at the end of path p, this can be depicted as follows:
actual estimate
start ------------> n --------------------> goal
cost(p) h(p)
-------------------------------------------->
f(p)
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6. A * Search(conti…)
 It is best-known form of Best First search. It avoids expanding paths that are
already expensive, but expands most promising paths first.
 Idea: minimize the total estimated solution cost
 f(n) = g(n) + h(n),
where
 g(n) the cost (so far) to reach the node
 h(n) estimated cost to get from the node to the goal
 f(n) estimated total cost of path through n to goal. It is implemented using
priority queue by increasing f(n).
 Minimize the total path cost to reach the goal.
 A* is complete, optimal, and optimally efficient among all optimal search
algorithms.
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7. A * Search(conti…)
At S we observe that the best node is A with a value of 4 so we
move to 4.
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8. A * Search(conti…)
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9. A * Search(conti…)
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10. A * Search(conti…)
Now we move to D from S.
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11. A * Search(conti…)
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12. A * Search(conti…)
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13. A * Search(conti…)
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14. A * Search(conti…)
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15. A* Search Example: Romania tour
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16. A* Search Example: Romania tour
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17. A* Search Example: Romania tour
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18. A* Search Example: Romania tour
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19. A* Search Example: Romania tour
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20. A* Search Example: Romania tour
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21. Search Terminology
 Problem Space − It is the environment in which the search takes place. (A set of
states and set of operators to change those states)
 Problem Instance − It is Initial state + Goal state.
 Problem Space Graph − It represents problem state. States are shown by nodes and
operators are shown by edges.
 Depth of a problem − Length of a shortest path or shortest sequence of operators
from Initial State to goal state.
 Space Complexity − The maximum number of nodes that are stored in memory.
 Time Complexity − The maximum number of nodes that are created.
 Admissibility − A property of an algorithm to always find an optimal solution.
 Branching Factor − The average number of child nodes in the problem space graph.
 Depth − Length of the shortest path from initial state to goal state.
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22. Admissible heuristics
 A heuristic h(n) is admissible if for every
node n, h(n) ≤ h*(n), where h*(n) is the
true cost to reach the goal state from n
 e.g., Straight-Line Distance
 an admissible heuristic never overestimates the
cost to reach the goal, i.e., it is optimistic
 THEOREM: If h(n) is admissible, A* using
Tree-Search is optimal
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23. Optimality of A*
A* expands nodes in order of increasing f value
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24. Evaluation: A* search
□ Complete
■ Yes
□ Optimal
■ Yes
□ Space
■ Keeps all nodes in memory
□ Time
■ Exponential
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25. Thank-You
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