Uninformed Search (2) Lecture 5 Introduction to Artificial - - PDF document

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Uninformed Search (2)

Lecture 5 Introduction to Artificial Intelligence

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Introduction to Artificial Intelligence Hadi Moradi moradi@usc.edu

Review: BFS

Completeness: Completeness:

Yes,

Time complexity:

O(b d),

Space complexity:

O(b d),

Optimality:

S A D

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Optimality:

Yes b – max branching

factor

d – depth of the

least-cost solution

m – max depth

B D A E E C E E B B F D F B F C E A C G G G G F C

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Review: Uniform Cost

Completeness:

S

Yes,

Time complexity:

O(b d),

Space complexity:

O(b d),

Optimality:

S A D B D A E E E B B F 3 4 4 5 5 5 2 5 4

3 4 7 8 9 6 10 10 11 11

C E 4 5

11 11 12 12 13 13 13 13

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3

Optimality:

Yes

B F C E A C G G G F C 3 D F G

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Review: DFS

Completeness:

Yes

Completeness:

Yes,

Time complexity: O(b m), Space complexity:O(bm), Optimality:

No

b – max branching factor d – depth of the least-cost

solution

B S S A

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solution

m – max depth

C E D F G

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Depth First Search

Problem: Not remembering the previous Problem: Not remembering the previous

states

Time complexity

Solution:

Combine the depth first search and breath first

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p search

Depth-limited search

It i d th fi t h ith d th li it It is a depth-first search with depth limit

I mplementation:

Nodes at depth l have no successors.

Complete: Optimal:

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p

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Iterative deepening search

Function Iterative-deepening-Search(problem) returns a solution, or failure p g (p ) , for depth = 0 to ∞ do result Depth-Limited-Search(problem, depth) if result succeeds then return result end return failure

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Combines the best of breadth-first and depth-first search strategies.

• Completeness:
• Time complexity:
• Space complexity:
• Optimality:

Romania with step costs in km

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5

9 10

6

11 12

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13 14

8

15 16

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Iterative deepening complexity

Iterative deepening search may seem wasteful Iterative deepening search may seem wasteful

because so many states are expanded multiple times.

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Bidirectional search

Both search forward from initial state

Both search forward from initial state,

and backwards from goal.

Stop when the two searches meet in

the middle.

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Goal Goal Start Start

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Bidirectional search

1 QUEUE1 < 1 QUEUE1 < path only containing the root; path only containing the root;

• 1. QUEUE1 <
• 1. QUEUE1 < --
• - path only containing the root;

path only containing the root; QUEUE2 < QUEUE2 < --

• - path only containing the goal;

path only containing the goal; 2.

• 2. WHILE

WHILE both QUEUEs are not empty both QUEUEs are not empty AND AND QUEUE1 and QUEUE2 do NOT share a state QUEUE1 and QUEUE2 do NOT share a state DO DO remove their first paths; remove their first paths; create their new paths (to all children); create their new paths (to all children);

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p ( ); p ( ); reject their new paths with loops; reject their new paths with loops; add their new paths to back; add their new paths to back; 3.

• 3. IF

IF QUEUE1 and QUEUE2 share a state QUEUE1 and QUEUE2 share a state THEN THEN success; success; ELSE ELSE failure; failure;

Bidirectional search

• Completeness:
• Completeness:
• Time complexity:
• Space complexity:
• Optimality:

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Bidirectional search

Bidirectional search merits

Bidirectional search merits

Big difference for problems with branching

factor b in both directions

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Bidirectional search

Bidirectional search issues

Predecessors of a node need to be generated What to do if there is no explicit list of goal

states?

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What is the best search strategy for the two

searches?

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Comparing uninformed search strategies

Criterion Breadth Uniform DepthFirst DepthLim Iterative Bidirectional Time b^ d b^ d b^ m b^ l b^ d b^ (d/2) Space b^ d b^ d bm bl bd b^ (d/2) Optimal? Yes Yes No No Yes Yes

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Complete? Yes Yes No Yes if l≥d Yes Yes

b – max branching factor of the search tree d – depth of the least-cost solution m – max depth of the state-space (may be infinity) l – depth cutoff

Summary

Problem formulation usually requires

Problem formulation usually requires

abstracting away real-world details to define a state space that can be explored using computer algorithms.

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Once problem is formulated in abstract

form, complexity analysis helps us picking out best algorithm to solve problem.

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Summary

Variety of uninformed search strategies;

Variety of uninformed search strategies;

difference lies in method used to pick node that will be further expanded.

Iterative deepening search only uses

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Iterative deepening search only uses

linear space and not much more time than other uniformed search strategies.