AI & Machine Learning ITCS-3153

Complete Algorithm

An algorithm that can search through the entire state space. It is guaranteed to find a solution if one exists.

What is the definition of optimality for local search algorithms?

An algorithm that is optimal will always find max or min state.

How are successor nodes generated?

Applying actions to states

What data structure should be used to push on and pop off nodes from the open list in BFS? in DFS?

BFS - FIFO queue DFS - LIFO queue, stack

What is difference between BFS and uniform-cost search?

BFS expands nodes based on depth, UCS expands nodes with the smallest path cost

Why does the heuristic function influence the time complexity of the A* algorithm?

Because it affects which nodes get expanded. A good heuristic will estimate the cost well and will lower the E term in O(b^(Ed)) (note: the E is a Greek letter)

What is the value of f(n)?

Combined path and heuristic cost.

What is the value of h(n)?

Heuristic Cost

What condition leads BFS and Uniform-cost search behaving the same?

If all step costs are equal

In simulated annealing, how does the algorithm determine if it moves to the next node?

If the next node is better, then move next else, only move to the next node based on a probability that decreases as time goes on.

What scenario leads to depth-limited search being incomplete?

If the solution has greater depth than the depth limit

Why does depth-first search have a smaller space complexity than breadth-first search?

It only needs to store the current path instead of entire search tree as BFS does.

Closed List

List of nodes already expanded

Open List

List of nodes to expand

What is the difference between local search and the previous searching algorithms covered (classical search algorithms)?

Local search only stores the current state instead of entire search tree.

What heuristic could be used for finding a route for a taxi driver.

Manhattan Distance, or Euclidean Distance.

Are greedy search algorithms (tree search version) complete?

No, Because the are subject to local minima and may get stuck in an infinite loop near local minima.

What heuristic could be used making a move in Tic-Tac-Toe?

Number of connected tiles left to win or Number of opponent tiles adjacent to a tile.

What heuristic could be used for the Missionary-Cannibal problem?

Number of people on the initial bank or Number of Missionaries on the initial bank.

What is the space complexity of A* given an admissible heuristic?

O(b^(Ed)) (note: the E is a Greek letter)

What is the time complexity of A* given admissible heuristics?

O(b^(Ed)) (note: the E is a Greek letter)

What is the value of g(n)?

Path cost

How can the size of a state space be reduced?

Use a different state representation of set of actions

In each iteration, a reproduction operation is performed. How are the individuals for that chosen?

Weighted sampling from the population based on the fitness function.

When does a genetic algorithm terminate?

When it finds a good enough solution based on fitness or after a specified amount of time has passed.

What is the difference between a cost function and an objective function?

When using cost function smaller is better, when using objective larger is better.

What is the difference between A* and Greedy search algorithms?

A* expands nodes based on both the path cost and heuristic cost, but greedy search only considers heuristic cost.

What are two advantages of local search over the classical searching algorithms?

1. Reduced space complexity 2. Local search can find good solutions in infinite state space

List steps of formulating a problem:

1. State Representation 2. Initial state 3. Actions 4.Transition Model 5. Goal state 6. Path cost

What is a successor node?

A Child node, A node generated by applying an action to a state.

Leaf node

A node with no children/successors

What is a solution for an uninformed search algorithm?

A path from the initial state (or node) to the goal state.

Optimal path

A path with the lowest possible path cost

What is a path in the state space?

A sequence of states connected by actions.

Why may a hill climbing algorithm give a different goal for different initial states?

Different initial states may be closer to different extrema points.

Why is random-restart considered complete?

Each restart has a probability to reach the global maximum. If enough restarts occur, the probability of finding the global maximum approaches 1.

Describe a strategy/algorithm for making hill climbing complete.

Random Restart - If local extrema found move to random point. Simulated Annealing: Allow downhill moves based on prob.

What is a strategy for finding admissible heuristics?

Relax a constraint for a problem and design a heuristic for the relaxed problem.

What is the main drawback of A* algorithm?

Space complexity

What is the rule for node expansion using greedy search? Which node will it always expand first?

The node with the lowest heuristic cost h(n).

How is the optimal solution for a problem defined?

The path with the lowest path cost.

What is the population

The set of Individuals

What component(s) determine the state space of a problem?

The state representation, initial state, actions, and transition model. State Space - All possible states reachable from the initial state.

Why are informed search algorithms considered faster than uninformed search algorithms?

They expand fewer nodes than uninformed search algorithms.

Why are local extrema a problem for hill climbing algorithms?

They get stuck because all neighbors will be worse than the local extrema. After getting stuck, it will not be able to find the global extrema.

Why are local search algorithms suitable for optimization problems?

They search based on an objective function, and are only concerned with finding extrema values( instead of finding a path through a space).

What is the purpose of problem formulation?

To enable an agent to systematically find a solution by searching through the state space.

What is the purpose of a fitness function?

To evaluate the states

How are touring problems different from routing problems?

Touring problems must visits all nodes, they need the state representation to include information about all nodes thus the space is much larger.

Describe how a state is represented when using a GA to solve the 8-queens problem in the textbook.

string of n integers between [1, n] n = # of rows. Each element is the row that a queen is on for the column (index of the element)

For the n-queens problem what is the advantage of a complete-state formulation?

the state space is much smaller.