Exam 1

If there are two sets of admissible heuristic values, h1 & h2, for the same search problem, then the heuristic h3 = (h1+h2)/2 is...

both consistent and admissible

Admissibility of a heuristic for A∗ search implies consistency as well.

false

Depth first search will always expand at-least as many nodes as A∗ search with a consistent heuristic.

false

It is impossible to be rational in a partially observable environment.

false

Iterative deepening involves re-running breadth-first search repeatedly.

false

greedy best-first search (sort queue by h(n)) is both complete and optimal when the heuristic is admissible and the path cost never decreases.

false

Depth-first search is the same (i.e. explores the same nodes in the same order) as uniform-cost search with costs of 1

false!

most search effort is expended while examining the interior branch nodes of a search tree

false, most search effort is expended while examining lead node of the tree

Consider two different A* heuristics, h1(s) and h2(s), that are each admissible. Now, combine the two heuristics into a single heuristic, using some (not yet specified) function g. Give the choice for g that will result in A* expanding a minimal number of nodes while still guaranteeing admissibility. Your answer should be a heuristic function of the form g(h1(s),h2(s)).

max(h1(s), h2(s))

For what reasons would iterative deepening be preferred over breadth-first search

space complexity! This is because BOTH iterative deepening and BFS are complete, optimal (if the step cost =1), time complexity = O(b^d). BUT they have different time complexities. Iterative deepening has a time complexity of O(bd) OR O(d). While BFS has a time complexity of O(b^d). Thus iterative deepening has a preferable time complexity.

To implement depth first search, what data structure should used for the fringe

stack

A reflex agent can be rational.

true

A* search with a heuristic that is not completely admissible may still find the shortest path to the goal state

true

Greedy search can return optimal solutions.

true

Greedy search can take longer to terminate than uniform-cost search.

true

Uniform-cost graph search is guaranteed to return an optimal solution.

true

best-first search when the queue assorted by f(n) =g(n) + h(n) is both complete and optimal when the heuristic is admissible and the total cost estimate f(n) is monotonic increasing on any path

true, because the search described is A* and the heuristic described is both admissible and consistent

uniform-cost search (sort queue by g(n)) is both complete and optimal when the path cost never decreases

true, because uniform-cost search is A* search with h(n) = 0, which is admissible

Breadth-first search is complete whenever the branching factor is finite, even if zero step costs are allowed

true. because if there exists a goal it occurs at finite depth d and will be found in O(b^d) steps. "Complete" means "will find a goal when one exists"--and does NOT imply "optimal" which means "will find a lowest-cost goal when one exists" Thus, the step costs are irrelevant to "complete"

An admissible heuristic is a heuristic that never overestimates the remaining cost (or distance) to the goal

true. by definition of admissible.

h(n)=0 is an admissible heuristic for the 8-puzzle

true. h(n)=0 NEVER over-estimates the remaining optimal distance to a goal node

Gradient descent uses O(constant) space and can escape from local optima.

FALSE. The space is constant, but it generally moves toward, and gets stuck on, a local optima.

If h1(s) is a consistent heuristic, and h2(s) is an admissible heuristic, then the minimum of the two must be consistent.

False

The sum of several admissible heuristics is still an admissible heuristic

False

A* graph search is guaranteed to expand no more nodes than uniform-cost graph search.

True. The heuristic could help to guide the search and reduce the number of nodes expanded. In the extreme case where the heuristic function returns zero for every state, A* and UCS will expand the same number of nodes. In any case, A* with a consistent heuristic will never expand more nodes than UCS.

A* search with the heuristic h(n) = 0 is equivalent to the uniform-cost search (T/F)

True. This is because the uniform-cost search is a special case of A* search. A*: f(n) = g(n) + h(n) uniform-cost search: f(n) = g(n) Thus, for h(n)=0, uniform cost search will produce the same result as A* search

Depth-first search always expands at least as many nodes as A* search with an admissible heuristic.

false. Depth-first search may possibly, sometimes, BY GOOD LUCK, expand fewer nodes than A* search with an admissible heuristic, e.g. it is logically possible that sometimes, by luck, depth-first search may march directly to the goal with no back-tracking

Depth-first graph search is guaranteed to return an optimal solution.

false. depth first search has no guarantees of optimality

What is h(x) = to so that the heuristic that is always admissible, for any search problem?

h(x) = 0

For what reasons would A* be preferred over DFS?

A*, unlike DFS is complete no matter what and optimal. DFS is only complete when the space is finite and is not optimal

Iterative deepening is sometimes used as an alternative to breadth first search. Give one advantage of iterative deepening over BFS, and give one disadvantage of iterative deepening as compared with BFS.

Advantage: iterative deepening requires less memory. Disadvantage: iterative deepening repeats computations and therefore can require additional run time.

For what reasons would bidirectional search be preferred over BFS

Bidirectional has a time complexity and space complexity, has half of BFS's time complexity and space complexity. Bidirectional has a time complexity and space complexity of O(b^d/2). Meanwhile, BFS has a time comp and space comp of O(b^d).

Breadth-first graph search is guaranteed to return an optimal solution.

False. Breadth first search has no guarantees of optimality unless the actions all have the same cost, which is not the case here.

A* graph search is guaranteed to expand no more nodes than depth-first graph search.

False. Depth-first graph search could, for example, go directly to a sub-optimal solution.

Greedy graph search is guaranteed to return an optimal solution.

False. Greedy search makes no guarantees of optimality.

Local beam search with a beam size k is equivalent to a parallel local search with k random restarts.

False. Local beam search with a beam size k will use k best locations to explore further and then again keep the best k locations. Random restart will start from scratch from different locations

Assume that a rock can move on a chessboard any number of squares in a straight line, vertically or horizontally, but cannot jump over other pieces; then Manhattan distance is an admissible heuristic for the problem of moving the rook from squareA to squareB in the smallest number of moves.

False. The Manhattan distance may over-estimate the optimal remaining number of moves to the goal because a rook may cover several squares in a single moves. NOTE: If the path cost instead were the number of squares covered, then Manhattan distance would be admissible.

To implement A* search, what data structure should be used for the fringe?

Heap/priority queue

Simulated annealing uses O(constant) space and can escape from local optima.

TRUE. The space is constant and it accepts bad moves with probability exp(-delta(Value)).

Genetic algorithms use O(constant) space and can escape from local optima.

TRUE. The space is constant and it can accept bad moves by creating bad offspring.

A* search with a heuristic that is not completely admissible may still find the shortest Pashto the goal state (T/F)

True

Iterative deepening search is guaranteed to expand more nodes than BFS (on any graph whose root is not the goal) (T/F)

True

A* graph search is guaranteed to return an optimal solution.

True, since the heuristic is consistent in this case.

Iterative deepening search has linear space requirement (O(bd) where b is the branching factor and d is the depth of the shallowest solution) for both tree search and graph search.

True. IDS needs to store O(b) nodes for each level it explores. If the shallowest solution is at depth d then O(bd) is required.

Uniform Cost Search (UCS) is an optimal uninformed search technique both for tree search and for graph search (assume positive step costs and a finite branching factor)

True. Uniform cost search will give an optimal solution in both cases, albeit slower than A* with a good heuristic

Which of the following search algorithms returns the optimal path if the costs are all are a fixed cost C > 0? Mark all that apply. UCS DFS BFS Iterative Deepening

UCS, BFS, Iterative Deepening