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Questions and Answers
What is the primary criterion used by the hill climbing algorithm to determine the 'best' solution at each step?
What is the primary criterion used by the hill climbing algorithm to determine the 'best' solution at each step?
- The solution that has been visited the fewest times.
- The solution that yields the highest immediate improvement. (correct)
- The solution that is closest to the initial state.
- The solution that has the lowest cost.
Why might a hill climbing algorithm fail to find the global optimum in a search space?
Why might a hill climbing algorithm fail to find the global optimum in a search space?
- It gets stuck in local optima. (correct)
- It always finds the optimal solution if one exists.
- It uses randomness to avoid local optima.
- It explores the entire search space exhaustively.
In the context of the Blocks problem with Heuristic Function 1, what does a '+1' indicate when assessing a specific block's position?
In the context of the Blocks problem with Heuristic Function 1, what does a '+1' indicate when assessing a specific block's position?
- The block is irrelevant.
- The block is in the correct location. (correct)
- The block is obstructing another block.
- The block is in the wrong location.
What describes the plateau problem in the context of hill climbing algorithms?
What describes the plateau problem in the context of hill climbing algorithms?
When using Heuristic Function 2 for the Blocks problem, what factor is incorporated into the cost calculation that is not considered in Heuristic Function 1?
When using Heuristic Function 2 for the Blocks problem, what factor is incorporated into the cost calculation that is not considered in Heuristic Function 1?
What is a common solution to the problems of getting stuck in local maxima or plateaus when using a hill climbing algorithm?
What is a common solution to the problems of getting stuck in local maxima or plateaus when using a hill climbing algorithm?
In the context of the Blocks problem, if Heuristic Function 1 assigns a '-1' to a block, what does this indicate about the block's current position?
In the context of the Blocks problem, if Heuristic Function 1 assigns a '-1' to a block, what does this indicate about the block's current position?
What does the term 'ridge problem' refer to in the context of hill climbing algorithms?
What does the term 'ridge problem' refer to in the context of hill climbing algorithms?
When using Heuristic Function 2 in the Blocks problem, how does the 'm' in the formula $h_2 = Add + m$ (if block in correct location) affect the heuristic value?
When using Heuristic Function 2 in the Blocks problem, how does the 'm' in the formula $h_2 = Add + m$ (if block in correct location) affect the heuristic value?
Which characteristic of the hill climbing algorithm contributes most significantly to its potential incompleteness?
Which characteristic of the hill climbing algorithm contributes most significantly to its potential incompleteness?
What is the formula used to calculate the overall cost in the Blocks problem, which combines the heuristic values of individual block positions when using Heuristic Function 1?
What is the formula used to calculate the overall cost in the Blocks problem, which combines the heuristic values of individual block positions when using Heuristic Function 1?
In the context of the Blocks problem, how does moving a block from an incorrect to a correct location affect the cost calculated by Heuristic Function 2?
In the context of the Blocks problem, how does moving a block from an incorrect to a correct location affect the cost calculated by Heuristic Function 2?
Why is the space complexity of the standard hill climbing algorithm described as $O(b^m)$?
Why is the space complexity of the standard hill climbing algorithm described as $O(b^m)$?
What is a local maximum in the context of a hill climbing algorithm?
What is a local maximum in the context of a hill climbing algorithm?
How does the random-restart hill climbing approach attempt to overcome the limitations of standard hill climbing?
How does the random-restart hill climbing approach attempt to overcome the limitations of standard hill climbing?
What generally happens to the time complexity of a hill climbing algorithm when a "good heuristic" is used?
What generally happens to the time complexity of a hill climbing algorithm when a "good heuristic" is used?
In hill climbing, if a new solution is not better than the existing solution, what action does the algorithm typically take?
In hill climbing, if a new solution is not better than the existing solution, what action does the algorithm typically take?
In the Block problem cost functions, what is the cost of the optimal solution?
In the Block problem cost functions, what is the cost of the optimal solution?
Which of the following is a major problem that reduces the chances of success for hill climbing algorithms compared to other search algorithms?
Which of the following is a major problem that reduces the chances of success for hill climbing algorithms compared to other search algorithms?
Does the hill climbing algorithm guarantee optimality?
Does the hill climbing algorithm guarantee optimality?
Flashcards
Hill Climbing Algorithm
Hill Climbing Algorithm
Iteratively improves a solution until a better one cannot be found. If the new solution is better, it becomes the best solution; otherwise, the old solution is retained.
Local Maximum Problem
Local Maximum Problem
A problem in hill climbing where the algorithm reaches a peak lower than the highest possible peak.
Plateau Problem
Plateau Problem
A problem in hill climbing where all neighboring moves appear equally unpromising, making it difficult to find a better direction.
Ridge Problem
Ridge Problem
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Random-Restart Hill Climbing
Random-Restart Hill Climbing
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Heuristic Function
Heuristic Function
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Completeness of Hill Climbing
Completeness of Hill Climbing
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Time Complexity of Hill Climbing
Time Complexity of Hill Climbing
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Space Complexity of Hill Climbing
Space Complexity of Hill Climbing
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Optimality of Hill Climbing
Optimality of Hill Climbing
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Study Notes
Hill Climbing Algorithm
- Generates a possible solution.
- If the new solution is better than the old solution, returns the best solution.
- Otherwise, it takes the old solution
- Repeats the process.
Maximization Example
- Starting node is 0.
- Child nodes A (value 3) and B (value 10) are considered.
- Traverse A and B's child nodes to evaluate the better result
- The algorithm aims to maximize the value.
Optimum Solution
- The algorithm follows a path until it finds a local optimum.
- In one example, it goes from 0 to A (value 3) to C (value 50), reaching 53
- In another example, it goes from node 0 to node A to node C, resulting in the optimum solution.
Problems with Hill Climbing
- Local Maximum: The algorithm finds a peak, but it's lower than the highest peak in the space.
- Plateau: All local moves are equally unpromising; peaks seem far away.
- Ridge: Almost every move takes the search down.
- Solution: Random-restart hill climbing involves multiple hill-climbing searches from randomly selected start nodes when the current search gets stuck.
Blocks Problem using Heuristic Function 1
- Heuristic Function 1 aims to maximize value.
- Assigns cost (+1 if correct, -1 if incorrect)
- Considers the positions of blocks A, B, C, D, and E relative to the goal state.
- The cost function is the sum of these h1(n) values.
- Stacking configuration can lead to a local solution, not necessarily the goal
- Goal = 5
Blocks Problem using Heuristic Function 2
- Heuristic Function 2 also involves maximizing values considering the level (m) of the block.
- Formula adds 'm' if the block is in the correct location and subtracts 'm' if in the wrong location.
- The cost function is the sum of these h2(n) values.
- The goal desired cost = 11
- With Heuristic Function 2 is possible to get to the best solution
Hill Climbing Algorithm - Completeness, Time and Space Complexity
- Completeness: Not complete, can get stuck in a loop
- Complete if loops are avoided.
- Time Complexity: O(b^m)
- With a good heuristic, could provide better results
- Space Complexity: O(b^m)
- Keeps all nodes in memory
- Optimality: No
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