Chapter: Artificial Intelligence

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Uninformed Search Strategies

Uninformed search methods: • Breadth-first search • Uniform-cost search • Depth-first search • Depth-limited search • Iterative deepening search

UNINFORMED SEARCH STRATEGIES

 

                      Uninformed strategies use only the information available in the problem definition

 

–  Also known as blind searching

 

–  Uninformed search methods:

 

                                                                                          Breadth-first search

 

                                                                                          Uniform-cost search

 

                                                                                          Depth-first search

 

                                                                                          Depth-limited search

 

                                                                                          Iterative deepening search

 


BREADTH-

FIRSTSEARCH

Definition:

 

The root node is expanded first, and then all the nodes generated by the node are expanded.

 

                   Expand the shallowest unexpanded node

 

                   Place all new successors at the end of a FIFO queue

 

Implementation:



 

Properties of Breadth-First Search

 

                   Complete

 

–  Yes if b (max branching factor) is finite

 

                   Time

 

–  1 + b + b2 + … + bd + b(bd-1) = O(bd+1)

 

–  exponential in d

 

                   Space

 

–  O(bd+1)

 

–  Keeps every node in memory

 

– This is the big problem; an agent that generates nodes at 10 MB/sec will produce

860 MB in 24 hours

 

                   Optimal

 

–  Yes (if cost is 1 per step); not optimal in general

 

Lessons from Breadth First Search

 

The memory requirements are a bigger problem for breadth-first search than is execution time


                   Exponential-complexity search problems cannot be solved by uniformed methods for any but the smallest instances

 

Ex: Route finding problem

 

Given:


Task: Find the route from  S to G using BFS.

 

Step1:



Answer : The path in the 2nd depth level that is SBG (or ) SCG.

 

Time complexity



DEPTH-FIRST SEARCH OR BACK TRACKING SEARCHING

 

Definition:

 

Expand one node to the depth of the tree. If dead end occurs, backtracking is done to the next immediate previous node for the nodes to be expanded

 

                      Expand the deepest unexpanded node

 

                      Unexplored successors are placed on a stack until fully explored

 

                      Enqueue nodes on nodes in LIFO (last-in, first-out) order. That is, nodes used as a stack data structure to order nodes.

 

                      It has modest memory requirement.

 

                      It needs to store only a single path from the root to a leaf node, along with remaining unexpanded sibling nodes for each node on a path

 

                      Back track uses less memory.

 

Implementation:

 




 


 





 

Properties of Depth-First Search

 

                   Complete

 

–  No: fails in infinite-depth spaces, spaces with loops

 

                                                                 Modify to avoid repeated spaces along path

 

–  Yes: in finite spaces

 

                   Time

 

–  O(bm)

 

–  Not great if m is much larger than d

 

–  But if the solutions are dense, this may be faster than breadth-first search

 

                   Space

 

–  O(bm)…linear space

 

                   Optimal

 

–  No

 

                   When search hits a dead-end, can only back up one level at a time even if the “problem” occurs because of a bad operator choice near the top of the tree. Hence, only does “chronological backtracking”

 

Advantage:

 

                   If more than one solution exists or no of levels is high then dfs is best because exploration is done only a small portion of the white space.

 

Disadvantage:

 

                     No guaranteed to find solution.

 

Example:  Route finding problem

 

Given problem:


Task: Find a route between A to B

 

Step 1:




Answer: Path in 3rd level is SADG

 

DEPTH-LIMITED SEARCH

A cut off (Maximum level of the depth) is introduced in this search technique to overcome the disadvantage of Depth First Sea rch. The cut off value depends on the number o f states.DLS can be implemented as a simple modification to the general tree search algo rithm or the recursive DFS algorithm.DLS im poses a fixed depth limit on a dfs.

 

A variation of depth-first searc h that uses a depth limit

 

–  Alleviates the problem of unbounded trees

 

–  Search to a predet ermined depth l (“ell”)

 

–  Nodes at depth l h ave no successors

 

                      Same as depth-first search if l = ∞

 

                      Can terminate for failure and cutoff

 

                      Two kinds of failure

 

Standard failure: indicates no solution

 

Cut off: indicates no solution within the depth limit


 

Properties of Depth-Limited Search

 

                      Complete

 

–  Yes if l < d


 

                      Time

 

 

–  N(IDS)=(d)b+(d-1)b²+……………………..+(1)

 

 

                   Space

 

–  O(bl)

 

                   Optimal

 

–  No if l > d

 

Advantage:

 

                   Cut off level is introduced in DFS Technique.

 

Disadvantage:

 

                   No guarantee to find the optimal solution.

 

E.g.: Route finding problem

 

Given:


The number of states in the given map is five. So it is possible to get the goal state at the maximum depth of four. Therefore the cut off value is four.

 

Task: find a path from A to E.


 

Answer: Path = ABDE Depth=3

 

 

 

ITERATIVE DEEPENING SEARCH (OR) DEPTH-FIRST ITERATIVE DEEPENING (DFID):

 

Definition:

 

                      Iterative deepening depth-first search It is a strategy that steps the issue of choosing the best path depth limit by trying all possible depth limit

 

Uses depth-first search

 

Finds the best depth limit

 

Gradually increases the depth limit; 0, 1, 2, … until a goal is found

 

Iterative Lengthening Search:

 

The idea is to use increasing path-cost limit instead of increasing depth limits. The resulting algorithm called iterative lengthening search.

 

 

Implementation:



 

Properties of Iterative Deepening

Search:

 

                      Complete

 

–  Yes

 

                      Time : N(IDS)=(d)b+(d-1)b2+…………+(1)bd

 

–  O(bd)

 

                      Space

 

–  O(bd)

 

                      Optimal

 

–  Yes if step cost = 1

 

–  Can be modified to explore uniform cost tree

 

Advantages:

 

                      This method is preferred for large state space and when the depth of the search is not known.

 

                      Memory requirements are modest.

 

                      Like BFS it is complete

 

Disadvantages:

 

Many states are expanded multiple times.

 

Lessons from Iterative Deepening Search

 

                   If branching factor is b and solution is at depth d, then nodes at depth d are generated once, nodes at depth d-1 are generated twice, etc.

 

–  Hence bd + 2b(d-1) + ... + db <= bd / (1 - 1/b)2 = O(bd).

 

– If b=4, then worst case is 1.78 * 4d, i.e., 78% more nodes searched than exist at depth d (in the worst case).

 

                   Faster than BFS even though IDS generates repeated states

 

–  BFS generates nodes up to level d+1

 

–  IDS only generates nodes up to level d

 

                   In general, iterative deepening search is the preferred uninformed search method when there is a large search space and the depth of the solution is not known

 

Example: Route finding problem

 

Given:





 

Answer: Since it is a IDS tree the lowest depth limit (i.e.) A-F-G is selected as the solution path.

 

BI-DIRECTIONAL SEARCH

 

Definition:

 

It is a strategy that simultaneously searches both the directions (i.e) forward from the initial state and backward from the goal state and stops when the two searches meet in the Middle.

 

 

                      Alternate searching from the start state toward the goal and from the goal state toward the start.

 

                      Stop when the frontiers intersect.

 

                      Works well only when there are unique start and goal states.

 

                      Requires the ability to generate “predecessor” states.

 

                      Can (sometimes) lead to finding a solution more quickly.

 

Properties of Bidirectional Search:

 

1.                          Time Complexity: O(b d/2)

 

2.                            Space Complexity: O(b d/2)

 

3.                          Complete: Yes

 

4.                          Optimal: Yes

 

 

Advantages:

 

Reduce time complexity and space complexity

 

Disadvantages:

 

The space requirement is the most significant weakness of bi-directional search.If two searches do not meet at all, complexity arises in the search technique. In backward search calculating predecessor is difficult task. If more than one goal state exists then explicitly, multiple state searches are required.

 

COMPARING UNINFORMED SEARCH STRATEGIES

 

 

                   Completeness

 

–  Will a solution always be found if one exists?

 

                   Time

 

–  How long does it take to find the solution?

 

– Often represented as the number of nodes searched

 

                      Space

 

–  How much memory is needed to perform the search?

 

–  Often represented as the maximum number of nodes stored at once

 

                      Optimal

 

–  Will the optimal (least cost) solution be found?

 

                    Time and space complexity are measured in

 

–  b – maximum branching factor of the search tree

 

–  m – maximum depth of the state space

 

–  d – depth of the least cost solution


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