ITCS-3153 Exam 1

For the following problems, give an example of a heuristic that could be used. c. Making a move in Tic-Tac-Toe

--# of connected tiles left to win --# of opponent tiles adjacent to a tile

For the following problems, give an example of a heuristic that could be used. b. Missionary-Cannibal problem

--# of people on the initial bank --# of missionaries on the initial bank

For the following problems, give an example of a heuristic that could be used. a. Finding a route for a taxi driver (e.g., GPS system)

--Manhattan distance --Euclidean distance

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 spaces

List and describe the steps of formulating a problem.

1. Define state representation 2. Define initial state 3. Define a set of actions 4. Define the transition model 5. Define a goal state or condition (or test) 6. Define path costs for each action

What is a successor node?

A child node. A node generated by applying an action to a state.

What is a solution for an uninformed search algorithm?

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

What is a path in the state space?

A sequence of states connected by actions.

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

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

Under what condition is the A* algorithm optimal?

A* is optimal if the heuristic function is admissible (never overestimates the true cost)

What is the definition of optimality for local search algorithms?

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

What is the output of a heuristic function for some node n?

An estimate cost from n to the goal

How are successor nodes generated?

Applying actions to states.

What is the difference between BFS and Uniform-cost Search?

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

What data structure should be used to push on and pop off nodes from the open list in Breadth-first Search? In Depth-first Search?

BFS--FIFO Queue DFS--LIFO Queue, Stack

Describe each value of a node: a. f(n)

Combined path and heuristic costs

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 hill climbing 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.

How is the time complexity of A* classified?

Exponential

Which of these does NOT influence the state space?

Goal

What is the rule for node expansion using Greedy Search? In other words, which node will it always expand?

Greedy Search always expands the node with the lowest heuristic cost h(n).

Describe each value of a node: c. h(n)

Heuristic cost

In genetic algorithms, what is the fitness function?

Heuristic function

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

If all steps cost 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 to "next". Else, only move to "next" based on a probability that decreases as time goes on.

What scenario leads to Depth-limited search being incomplete?

If the solution has depth greater than the depth limit.

What does it mean if a heuristic is admissible?

It never over-estimates the true cost to the goal

Why does Depth-first Search have a smaller space complexity than Breadth-first Search?

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

What is the main problem when using Hill Climbing based algorithms?

Local minima/maxima

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 the entire search tree

What node will A* expand?

Lowest f cost

What node will greedy search expand?

Lowest heuristic cost

What node will UCS expand?

Lowest path cost

Are greedy search algorithms (tree-search version) complete? Why or why not?

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

What node will DFS expand?

Node with largest depth

What is the solution for a classical search algorithm (A*, BFS, etc)?

Path

Describe each value of a node: b. g(n)

Path cost

What factors do not influence the time complexity of A*?

Path cost error

Describe a strategy/algorithm for making Hill Climbing complete?

Random-restart hill climbing: If a local extrema is found, then move to a random state and start over. Simulate Annealing: Allow downhill moves based on a probability.

What is a strategy for finding admissible heuristics?

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

What is the main drawback of the A* algorithm?

Space complexity

What is a solution for local search algorithms?

State

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

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

In genetic algorithms, how are stated represented?

String of numeric values

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(s) the state space of a problem?

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

For the n-queens problem, what is the advantage of a complete state formulation over an incremental formulation?

The state space is much smaller.

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 extreme. 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 being concerned with the 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 route-finding problems?

Touring problems must visit each node in a graph, whereas route-finding problems only need to visit the goal node. The state representation for touring problems needs to include information about all nodes. Thus, the state space for touring problems are larger than route-finding problems' state space.

In simulated annealing, how is the "next" node chosen?

Uniformly sampled

How can the size of a state space be reduced?

Use a different state representation or set of actions.

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

Weight sampling from the population based on the fitness function

In genetic algorithms, how are the "parents" chosen when doing a crossover operations?

Weighted sampling

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 objective function?

When using a cost function, smaller values are better. When using objective functions, larger values are better.

Define the following terms in context of search algorithms: a. Leaf node b. Open list c. Closed list d. Complete algorithm e. Optimal path

a: A node without children/successors b: List of nodes to expand. c: List of nodes already expanded d: An algorithm that can search through the entire state space. It is guaranteed to find a solution if one exists. e: A path with the lowest possible path cost.

What condition makes A* and UCS expand nodes exactly the same?

h(n) = constant function