Artificial-Intelligence
April 14, 2024Artificial-intelligence
April 14, 2024Artificial-Intelligence
| Question 43 |
Consider following sentences regarding A*, an informed search strategy in Artificial Intelligence (AI).
- (a) A* expands all nodes with f(n)<C*.
(b) A* expands no nodes with f(n)/C*.
(c) Pruning is integral to A*.
Here, C* is the cost of the optimal solution path.
Which of the following is correct with respect to the above statements ?
| Both statement (a) and statement (b) are true. | |
| Both statement (a) and statement (c) are true. | |
| Both statement (b) and statement (c) are true. | |
| All the statements (a), (b) and (c) are true.
|
Question 43 Explanation:
A* search:
→ A* combines the value of the heuristic function h(n)and the cost to reach the node ‘n’, g(n).
→ Evaluation function f(n) = g(n) + h(n) thus estimates the cost of the cheapest solution through ‘n’.
→ A* tries the node with the lowest f(n) value first.
→ This leads to both complete and optimal search algorithm, provided that h(n) satisfies certain conditions.
Optimality of A*:
→ A* expands all nodes ‘n’ for which f(n)<c*, and="" some="" of="" those="" for="" which="" f(n)="C*"
→ However, all nodes n for which f(n) > C* get pruned.
→ It is clear that A* search is complete.
→ A* search is also optimally efficient for any given heuristic function, because any algorithm that does not expand all nodes with f(n)<c* runs="" the="" risk="" of="" missing="" optimal="" solution.
→ Despite being complete, optimal, and optimally efficient, A* search also has its weaknesses.
→ The number of nodes for which f(n)< C* for most problems is exponential in the length of the solution.
Reference:
http://www.cs.tut.fi/~elomaa/teach/AI-2011-3.pdf
→ A* combines the value of the heuristic function h(n)and the cost to reach the node ‘n’, g(n).
→ Evaluation function f(n) = g(n) + h(n) thus estimates the cost of the cheapest solution through ‘n’.
→ A* tries the node with the lowest f(n) value first.
→ This leads to both complete and optimal search algorithm, provided that h(n) satisfies certain conditions.
Optimality of A*:
→ A* expands all nodes ‘n’ for which f(n)<c*, and="" some="" of="" those="" for="" which="" f(n)="C*"
→ However, all nodes n for which f(n) > C* get pruned.
→ It is clear that A* search is complete.
→ A* search is also optimally efficient for any given heuristic function, because any algorithm that does not expand all nodes with f(n)<c* runs="" the="" risk="" of="" missing="" optimal="" solution.
→ Despite being complete, optimal, and optimally efficient, A* search also has its weaknesses.
→ The number of nodes for which f(n)< C* for most problems is exponential in the length of the solution.
Reference:
http://www.cs.tut.fi/~elomaa/teach/AI-2011-3.pdf
Correct Answer: B
Question 43 Explanation:
A* search:
→ A* combines the value of the heuristic function h(n)and the cost to reach the node ‘n’, g(n).
→ Evaluation function f(n) = g(n) + h(n) thus estimates the cost of the cheapest solution through ‘n’.
→ A* tries the node with the lowest f(n) value first.
→ This leads to both complete and optimal search algorithm, provided that h(n) satisfies certain conditions.
Optimality of A*:
→ A* expands all nodes ‘n’ for which f(n)<c*, and="" some="" of="" those="" for="" which="" f(n)="C*"
→ However, all nodes n for which f(n) > C* get pruned.
→ It is clear that A* search is complete.
→ A* search is also optimally efficient for any given heuristic function, because any algorithm that does not expand all nodes with f(n)<c* runs="" the="" risk="" of="" missing="" optimal="" solution.
→ Despite being complete, optimal, and optimally efficient, A* search also has its weaknesses.
→ The number of nodes for which f(n)< C* for most problems is exponential in the length of the solution.
Reference:
http://www.cs.tut.fi/~elomaa/teach/AI-2011-3.pdf
→ A* combines the value of the heuristic function h(n)and the cost to reach the node ‘n’, g(n).
→ Evaluation function f(n) = g(n) + h(n) thus estimates the cost of the cheapest solution through ‘n’.
→ A* tries the node with the lowest f(n) value first.
→ This leads to both complete and optimal search algorithm, provided that h(n) satisfies certain conditions.
Optimality of A*:
→ A* expands all nodes ‘n’ for which f(n)<c*, and="" some="" of="" those="" for="" which="" f(n)="C*"
→ However, all nodes n for which f(n) > C* get pruned.
→ It is clear that A* search is complete.
→ A* search is also optimally efficient for any given heuristic function, because any algorithm that does not expand all nodes with f(n)<c* runs="" the="" risk="" of="" missing="" optimal="" solution.
→ Despite being complete, optimal, and optimally efficient, A* search also has its weaknesses.
→ The number of nodes for which f(n)< C* for most problems is exponential in the length of the solution.
Reference:
http://www.cs.tut.fi/~elomaa/teach/AI-2011-3.pdf
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