Artificial Intelligence: n-Queens Problem

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Questions and Answers

What issue arises in hill-climbing that can hinder finding a global maximum?

Global maxima

Random search

Local maxima (correct)

Infinite loops

What does random-restart hill climbing do to overcome local maxima?

It implements heuristic evaluations only.

It repeatedly starts the search from different initial points. (correct)

It uses deterministic paths to find solutions.

It relies solely on the first successful run.

What does simulated annealing allow that differentiates it from traditional hill climbing?

Allows some 'bad' moves to escape local maxima. (correct)

Requires fixed step sizes.

Only allows transitions to better states.

Only works in continuous spaces.

How does local beam search enhance the hill-climbing process?

By keeping multiple states and choosing the best successors. Signup and view all the answers

In the context of random-restart hill climbing, what is the expected number of restarts related to?

Probability of success for each trial. Signup and view all the answers

What is a potential downside of using local beam search?

All states may converge to the same local maximum. Signup and view all the answers

Which method incorporates the concept of gradually decreasing the frequency of 'bad' moves?

Simulated annealing Signup and view all the answers

What best describes K parallel hill-climbing?

It runs multiple independent searches simultaneously. Signup and view all the answers

What is the main objective in solving the n-queens problem?

To ensure no two queens threaten each other. Signup and view all the answers

Which technique is used to solve problems where the path to the goal state is irrelevant?

Iterative improvement algorithms Signup and view all the answers

What does the cost function 'h' represent in hill-climbing for the n-queens problem?

The number of pairs of queens that are attacking each other. Signup and view all the answers

What is the strategy used in hill-climbing to improve the current state?

Move a queen to reduce the number of conflicts. Signup and view all the answers

In the context of hill-climbing, how is one best conceptualized?

As climbing in dense fog with no memory of the past. Signup and view all the answers

What is a key characteristic of the local search space in solving the n-queens problem?

Only adjacent positions can be moved to. Signup and view all the answers

Which of the following best describes the goal of hill-climbing?

To locate the highest point in the search space. Signup and view all the answers

Which of the following could be considered a problem when using hill-climbing?

It can get stuck in local maxima. Signup and view all the answers

What does moving a queen to adjacent positions help achieve in the n-queens problem?

To optimize the current arrangement by reducing conflicts. Signup and view all the answers

Study Notes

n-Queens Problem

Objective: Place 𝑛 queens on an 𝑛 × 𝑛 chessboard without conflicts in rows, columns, or diagonals.

Iterative Improvement Algorithms

Applied when the path to the solution is irrelevant; only the end state matters.
Focuses on maintaining a single "current" state and improving it.

Hill-Climbing Strategy

Strategy involves moving a queen to minimize conflicts with other queens.
Cost function: ℎ measures the number of attacking pairs of queens.

Local Search Space

For solving the n-queens problem, queens can be moved to adjacent board positions.
Alternative local search techniques can be utilized to explore different configurations.

Hill-Climbing Challenges

Finding a global maximum in problem context likened to climbing Everest in dense fog.
Challenges include local maxima, shoulders, and plateaus in the search space.

Solutions for Hill-Climbing Problems

Random sideways moves can help escape from local shoulders, though it may lead to flat maxima.
Random-restart hill climbing technique can overcome local maxima, ensuring a more thorough search.

Random-Restart Hill Climbing

A method to maximize success probability across multiple trials.
Expected number of restarts hinges on the probability of success in individual trials.

Global Minimum and Hill-Declining

The goal shifts to finding a global minimum, although the technique is still referred to as hill-climbing.

Simulated Annealing

Technique allows for temporary "bad" moves to escape local maxima, with a controlled decrease in move frequency and magnitude over time.

Parallel Hill-Climbing

Concept involves executing 𝑘 independent hill-climbing searches to improve overall results.

Local Beam Search

Strategy keeps track of 𝑘 states and selects the top 𝑘 successors from all.
Unlike parallel searches, this method recruits successful searches to explore better states.
Potential drawback: multiple states may converge on the same local peak, limiting diversity in exploration.

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Description

This quiz explores the n-queens problem, a classic algorithmic challenge involving the placement of queens on a chessboard. Participants will learn about iterative improvement algorithms and how they can be applied to various problems where the goal state is the ultimate focus. Test your knowledge and problem-solving skills in complex environments within artificial intelligence.