ai lecture 5

8/6/2019 AI Lecture 5

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General problem solving

and search methods

Artificial Intelligence


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Contents

5.1 Problem Solving by Search

5.2 Search Strategies

5.3 Blind Search 5.4 8-Puzzle Game


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Problem: A problem can be considered to consist of a goal and a set of

actions that can be taken to lead to the goal.

Search:

Search is a method that can be used by computers to examine a

problem in order to find a goal.

At any given time we consider the state of the search to

represent where we have reached as a result of the actions we

have applied so far. A problem can be considered to be a search because in order to

solve the problem, we will search for a goal state.

Problem solving ! Searching for a goal state


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Data Driven or Goal driven search:

Forward Chaining

Backward Chaining

Appr oaches: Top-Down Search:

Starts from an initial state and uses actions to moveforward until a goal is reached. This is known as

forward chaining search. Bottom-Up Search:

Search starts at the goal and work back toward a startstate by seeing what moves could have led to the goalstate known as backward chaining search.


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Requirements of a good search strategy:1. It causes motion

Otherwise, it will never lead to a solution.

2. It is systematic

Otherwise, it may use more steps than

necessary.

3. It is efficient

Find a good, but not necessarily the best,

answer.


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There are two search strategies

Blind/uninformed search

Informed/Heuristic search Any path/Non-optimal search

Optimal Search


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A. Blind/uninformed search

The uninformed orblind search is

The search methodology having no additionalinformation about search states beyond that

provided in the problem definitions. In thissearch total search space is looked forsolution

Having no information about the numberof

steps from the current state to the goal.

Zer o information search


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B. Informed/Heuristic Search

More efficient than uninformed search Heuristic:

involving or serving as an aid to learning, discovery, orproblem-solving by experimental and especially trial-and-

error methods.(Merriam-Websters dictionary)

A Heuristic is an operationally-effective piece ofinformation on how to direct search in a problem

space. Heuristics are only approximately correct. Theirpurpose is to minimize search on average.

Heuristic technique improves the efficiencyof asearch process


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Best-First Search an algorithm in which a

node is selected for expansion based on an

evaluation function f(n)

Traditionally the node with the lowest evaluationfunction is selected

Not an accurate nameexpanding the best node first

would be a straight march to the goal.

Choose the node that appears tobe the best A* (A star) is the most widely known form of Best-First

search


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Example of Mouse and Cheese

For example Suppose that cheese is fresh and it smells

The mouse will use this smell as guide to guess theposition of the cheese

Will choose the best from the alternative choices. As smell gets stronger he mouse knows that the cheeseis closer

Hence the mouse is informed about the cheese and thusthe search is informed

You might think that informed search is the bestsolution to the problem

But its not true

Mouse found the cheese but not from the bestoptimal path.


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Any path/Non optimal search

In this search we are concerned with finding

any solution

As we find the solution we stop the search

There could have been a better path which

might take lesser time

Optimal path search We find the solution that are least costly


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5.3 Blind Search

Breadth-first search Expand all the nodes of

one level first.

Depth-first search

Expand one of the nodesat the deepest level.


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5.3 Blind Search

Tree Search

A tree search starts at the

root and explores nodes from

there, looking for a goal node

For some problems, any goalnode is acceptable (N orJ);

forother problems, you want

a minimum-depth goal node,

that is, a goal node nearestthe root (onlyJ)

L M N O P

G

Q

H JI K

FED

B C

A

Goal nodes


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Depth-first searching

A depth-first search (DFS)explores a path all the wayto a leafbeforebacktracking and exploringanother path

For example, aftersearching A, then B, thenD, the search backtracksand tries another path fromB

Node are explored in theorderA B D E H L M N IO P C F G J K Q

N will be found before J

L M N O P

G

Q

H JI K

FED

B C

A


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Depth First Search

1

7

8

6

5

2

3

4

SG

SI


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Breadth-First Search

1

12

111098765

432

SG


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Backwards Breadth-First

Search9

87654

32

1

SI

SG


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Bi-Directional

Breadth-First Search1

3 4

8 9 10 11 12

2

13

75 6

SG

SI


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Breadth-first searching

A breadth-first search(BFS) explores nodesnearest the root beforeexploring nodes further

away For example, aftersearching A, then B,then C, the searchproceeds with D, E, F, G

Node are explored inthe orderA B C D E F GH I J K L M N O P Q

J will be found before N

L M N O P

G

Q

H JI K

FED

B C

A


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Depth- vs. breadth-first searching

When a breadth-first search succeeds, it finds aminimum-depth (nearest the root) goal node

When a depth-first search succeeds, the found

goal node is not necessarily minimum depth

For a large tree, breadth-first search memory

requirements maybe excessive

For a large tree, a depth-first search may take

an excessively long time to find even a verynearby goal node


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Depth- vs. breadth-first searching

Breadth-first is complete and optimal, but

has high space complexity

Bad when branching factor is high

Depth-first is space efficient, but neither

complete noroptimal

Bad when search depth is infinite

How can we combine the advantages (and

avoid the disadvantages)of these two

search techniques?


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Depth-limited searching

Depth-first searches maybe performed with adepth limit:

limit = 0;found = false;while (not found) {

found = limitedDFS(root, limit, 0);limit = limit + 1;

}

This searches to depth 0 (root only), then if thatfails it searches to depth 1, then depth 2, etc.

If a goal node is found, it is a nearest node and thepath to it is on the stack


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5.4 8-Puzzle Game

An unsolved 8-Puzzle


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A Sample Search Tree


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A Sample

Search Tree


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2727

A Sample

SearchTree


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A Sample

Search Tree

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