Artificial Intelligence Chapter 4

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Questions and Answers

What type of search algorithm uses problem-specific knowledge to guide the search process towards the goal more effectively?

Informed search algorithm

What is the purpose of the heuristic function h(n) in informed search algorithms?

To estimate the optimal cost to the goal from node n

What is the evaluation function used in A* search?

f(n) = g(n)+h(n)

Why is the quality of the heuristic function important in informed search algorithms?

Because it affects the search efficiency Signup and view all the answers

What is the main difference between tree search and graph search?

Tree search does not keep track of visited states, while graph search does Signup and view all the answers

What type of search implementation orders nodes in the frontier by h(n)?

Greedy Best-First search Signup and view all the answers

Who are involved in determining heuristic values in informed search algorithms?

Domain experts, algorithm designers, data scientists, and software engineers Signup and view all the answers

What is the role of g(n) in informed search algorithms?

To represent the known path cost so far to node n Signup and view all the answers

What is the time complexity of greedy best-first search?

O(bm) Signup and view all the answers

Is the graph version of greedy best-first search complete in finite spaces?

Yes Signup and view all the answers

What is the space complexity of greedy best-first search?

O(bm) Signup and view all the answers

Is greedy best-first search optimal?

No Signup and view all the answers

What is the condition for a heuristic to be consistent?

c(n,a,n') + h(n') ≥ h(n) Signup and view all the answers

What is the importance of a good heuristic in greedy best-first search?

A good heuristic can give dramatic improvement Signup and view all the answers

What is the problem with the tree version of greedy best-first search?

It can get stuck in loops Signup and view all the answers

What is the non-decreasing property of a consistent heuristic?

f(n) is non-decreasing along any path Signup and view all the answers

What is the main purpose of keeping track of visited states in a search algorithm?

To avoid revisiting and to handle cycles. Signup and view all the answers

What type of search is suitable for problems with complex graphs, including cycles and shared states?

Greedy best-first search. Signup and view all the answers

What is a potential issue with tree-search algorithms?

They may become stuck in a loop. Signup and view all the answers

What is the cost of the path found in the example of tree-search?

None. Signup and view all the answers

What is the priority of the node [S,A,B,C] in the UCS example?

<ol start="6"> <li></li> </ol> Signup and view all the answers

What is the purpose of the VISITED set in the UCS example?

To keep track of visited states and avoid revisiting. Signup and view all the answers

What is the main difference between the UCS and Greedy Search examples?

The priority calculation. Signup and view all the answers

What is the estimate used in Greedy Search, and what is its limitation?

An estimate of the distance to the goal state, which is not the true state space distance. Signup and view all the answers

What is the priority of the node [S,B,C] in the Greedy Search example?

<ol start="2"> <li></li> </ol> Signup and view all the answers

What is the key advantage of Greedy Search over UCS?

It is more efficient and can be faster. Signup and view all the answers

What is the relationship between consistency and admissibility of a heuristic function?

A consistent heuristic is also admissible. Signup and view all the answers

What is the implication of using a consistent heuristic function in A* search with graph search?

The A* search is optimal. Signup and view all the answers

What is the purpose of the admissibility condition in heuristic search algorithms?

To ensure the search algorithm finds the optimal solution. Signup and view all the answers

What is the difference between g(n) and h(n) in the evaluation function f(n) of A* search?

g(n) is the cost so far to reach n, and h(n) is the estimated cost from n to the goal. Signup and view all the answers

How does the A* algorithm differ from UCS (Uniform-Cost Search)?

The priority queue sort function is f(n) = g(n) + h(n) in A*, but not in UCS. Signup and view all the answers

What is the significance of the triangle inequality in the context of heuristic search?

It implies that a consistent heuristic is also admissible. Signup and view all the answers

Study Notes

Informed Search Algorithm

Informed search algorithms use problem-specific knowledge (heuristics) to guide the search process towards the goal more effectively.
Heuristic values are determined through a collaborative effort involving domain experts, algorithm designers, data scientists, and software engineers.
A heuristic function h(n) is used for each node, which estimates the optimal cost to reach the goal from node n.

Evaluation Function

The evaluation function f(n) provides an estimate of the total cost to reach the goal through node n.
f(n) is calculated as g(n) + h(n), where g(n) is the known path cost so far to node n and h(n) is the estimated cost to reach the goal from node n.

"Best First" Search Implementation

"Best First" search implementation orders nodes in the frontier by an evaluation function.
Two types of "Best First" search implementation:
- Greedy Best-First: orders by h(n).
- A* search: orders by f(n).

Search Efficiency

Search efficiency depends heavily on heuristic quality.
A better heuristic leads to a faster search.

Tree Search vs Graph Search

Tree search treats the search space as a tree structure, where each state is represented by a unique node, and nodes do not share children.
Graph search treats the search space as a graph, where nodes can have multiple parents and can be revisited.
Graph search is suitable for search problems with complex graphs, including cycles and shared states.

Greedy Best-First Search

Greedy best-first search can get stuck in a loop with tree-search.
Greedy best-first search is not optimal.

Properties of Greedy Best-First Search

Completeness:
- Tree version can get stuck in loops.
- Graph version is complete in finite spaces, but not in infinite spaces.
Time complexity: O(bm).
Space complexity: O(bm).
Optimality: No.

Consistency of Heuristics

A heuristic h(n) is consistent if, for every node n and every successor n' of n, the estimated cost of reaching the goal from n is no greater than the step cost of getting to n' plus the estimated cost of reaching the goal from n'.
Consistency implies admissibility.
If h(n) is consistent, A* using Graph-Search is optimal.

Key Concepts in Informed (Heuristic) Search

Heuristic Function (h(n)): an estimate of the cost to reach the goal from a given state.
Admissibility: a heuristic that never overestimates the true cost to reach the goal.
Consistency (Monotonicity): a heuristic that ensures the estimated cost of reaching the goal from a node is no greater than the cost of getting to a successor node plus the estimated cost of reaching the goal from the successor node.

A* Search: Summary

Idea: avoid expanding paths that are already expensive.
Optimal if heuristic is admissible (tree search) or consistent (graph search).
Always terminates with a solution path.
Evaluation function f(n) = g(n) + h(n).

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Description

Informed search algorithms are used in artificial intelligence to find solutions to problems more efficiently than uninformed search algorithms. These algorithms use problem-specific knowledge to guide the search process towards the goal.