lect topic3 search sem1 0910[1]

8/9/2019 Lect Topic3 Search Sem1 0910[1]

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CSC 3301CSC 3301 -- Principles Of Artificial IntelligencePrinciples Of Artificial Intelligence

STRUCTURE and STRATEGIES for STATE SEARCHSTRUCTURE and STRATEGIES for STATE SEARCHSPACESPACE

Assoc. Prof. Dr. Normaziah Abdul Aziz

Semester 1 2009/2010

Note: Some parts of the lecture slides are referred to notes of Prof. Michael Pazzani, University of Irvine, California.


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The Relation of Problem SolvingThe Relation of Problem Solving

And SearchAnd Search


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Search is a method that can be used by the computer toexamine a problem space in order to find a goal.

Many problems in AI are represented as search spaces.

A search space is a representation of the set of the possible

choices in a given problem. One or more of the choices leads tothe solution to the problem.

Problem Solving as Search (1)

Example

Find the word adab from an Arabic-English

dictionary that has 500 pages.

The page that is being searched for is called a goal,

and it can be identified by seeing whether the word

we are searching for is on the page or not.


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The aim of most search procedures is to identify one or more

goals and identify one or more paths to those goals.

Often the shortest path or path with least cost is selected as

the best solution path.


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A search space is a representation of the set of the possiblechoices in a given problem. One or more of the choices leads

to the solution to the problem.

State spaces - A search space that consists of a set of states,

connected by paths that represent actions.

Many search problems can be represented by a state space,

where the aim is to start with the world in one state and end

with the world in another more desirable state.


Initial state or start state the situation where we begin.

Goal state the final situation that we want it to be.

Illegal state the situation where we have to avoid. This is also

referred to as constraint.


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Search Trees

We can represent search space in the form of a tree. This tree

is referred to as search tree. node represents a situation or a state. Several types of

nodes: a root node, leaf node, goal node, parent node, child node

path connects one node to another node

branch the path between the parent node and child node(s). A

tree can have deep orshallow branching and high number of

branching in terms ofbreadth.

Note: Goalnode(s) can be from anyof the

leafnodes that has the value/contentof the

problems goal

A

B

D E

C

FG

IH

parent nodes

leaf nodes

root node


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Problem Solving Example 2


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Searching ApproachSearching Approach


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Data-driven search search process starts from aninitial state and uses actions that are allowed to move

forward until a goal is reached. Also known as forward

chaining.

Goal-driven search search process begins from

the goal and work back towards a start state, by

seeing what moves could have led to the goal state.This is also known as backward chaining.

Searching Approaches the broad perspective


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ExampleA system that analyses astronomical data and thus makes

deduction about the nature of stars and planets. Here, there is a lot

of data but it would not necessarily be given any direct goals. It is

expected to analyse the data and determine conclusions of its own.

In this case, data-driven search is appropriate.

Other examples: weather forecast, _________________

Data-driven is most useful when the initial data are provided,

and it is unclear what the goal is.

Searching Approaches (cont.)

Goal-driven is most useful in situations where the goal can be

clearly specified.

ExampleA situation in medical diagnosis where the goal (i.e. the condition to

be diagnosed) is known, but the data (i.e. the causes of the sickness

condition) need to be discovered.

Other examples: finding right path in a maze, ______________


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Generate and Test

generates each nodes in the search space and test it to find out

if it is a goal node. If it is, the search has succeed and need not

carry on. Else, the process moves on to the next node.

the simplest brute-force search (also known as exhaustive

search).

no additional knowledge besides knowing how to traverse he

search tree, and how to identify leaf nodes and goal nodes.

Techniques of Searching (1)

3 properties for successful Generate & Test searching process:

complete must generate all possible solution to avoid missing

a suitable node

non-redundant should not generate the same solution twice

well informed should only propose suitable solutions & should

not examine possible solution that do not match the search

space.

A

B

D E

C

FG

IH


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Depth-First Search

the search process follows each path to its greatest depthbefore moving on to the next path.

if we start from the left side of a search tree and work

towards the right, depth-first search goes all the way down

the left-most path in the tree until the leaf node is reached. If

this is a goal state, the search stops & success is reported.

if the leaf node is not the goal state, search backtracks up

to the next highest node that has unexplored path.

A

B

D E

C

J

H

1

8

2

5

6

3

G

I

7

4

910 13

12

11

14

F

KL

15

If node I is the goal node, hence node J, K

& L need not be examined.

ExamplesLocating files on a disk and web search

engines.Other examples: ______________



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Breadth-First Search

the search process starts by examining all nodes one

level (also known as ply) down from the root node.

if the goal state is reached, success is reported. Else,

search continues by expanding paths from all nodes in

the current level down to the next level.

search continues until a goal node is met and

success is reported. Failure is reported when all nodes

have been examined but no goal node has been found.A

B

DE

C

J

H

1

11

3

10G

I7

4

2

65

F

KL

89



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Comparison between Depth-First and

Breadth-First Search

Situation Depth first performance Breadth first performance

Some path are extremely

long or even infinite

All path are of similar

length

All path are of similar

length & all path lead to a

goal state

High branching factor

Bad Well

WellWell

WellTime & memory

wasted

PoorDepends on otherfactors

A

B

D E

C

FG

IH

Depth-first search is usually simpler to implement than breadth-first search.

Depth-first search requires less memory usage because it needs to store only theinformation the current path it is exploring.

Breadth-first search needs more memory to store information of all paths that reach

the current depth.



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Depth-First Search with Iterative Deepening

Depth-First Search Iterative Deepening (DFID) is also calledIterative Deepening Search (IDS) is an exhaustive search

technique that combines both dept-first with breadth-first search.

DFID technique involves repeatedly carrying out depth-first

search on the tree until a depth bound that is set.

The depth bound forces a failure on a search space once it gets

below a certain level. This causes a breadth-like sweep of the

search space at that particular depth level.

This technique is suitable when it is known that a solution lies

within a certain depth or when time constraints. such as thoseoccur in an extremely large search space.

ExamplesIn playing chess, we can limit the number of states that

are to be considered; then a depth-first search with a

depth bound can be applied.



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Properties of Search Approaches

Several important properties that search methods should have in

order to be most useful. How efficient the method is, are based on time

and space required.

Complexity. The time complexity is a related to the length of time that

the method takes to to find a goal state. The space complexity is related

to the amount of memory that the method needs to use.

Big-O notation is used to describe the complexity of a method. As

example, breadth-first search has a time complexity ofO(b ), where

b is the branching factorof the tree and d is the depth of the goal

node in the tree.

Depth-first is efficient in space but not efficient in terms of time.

Complexity must be balanced against the adequacy of the solution

generated by the method. Ex. A very fast search methodmaynot

find the best solution, and a search method that examines all

possible solution will guarantee to find the best solution though it is

verytime-consuming.

d


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Completeness. A search method is considered complete if it is

guaranteed to find a goal state if one exists.

Breadth-first search is complete but depth-first search is not

complete because it may explore a path of infinite length and

never find a goal node that exist on another path.

this is a desirable property because the objective of running asearch is to find the solution (goal state)).


Optimality. A search method is optimal if it is guaranteed to find

the best solution that exists. It will find the path to a goal state that

involves taking the least number of steps.

The method may not be efficient it may take longer time for

an optimal search to identify the optimal solution but once it

has found, it is guaranteed to be the best one.

Breadth-first search is an optimal method.


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Irrevocablility. A search method that do not use backtracking &

therefore examine just a path not more than once.

A

B

D E

C

J

H

1

8

2

5

6

3

G

I

7

4

9

1013

12

11

14

F

KL

15


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Some Calculations

For a tree of depth d and with a branching factor of b, the total

number of nodes is:1 root node

b nodes in the first layer

b nodes in the second layer

b nodes in the n layer

Therefore, the total number of nodes is

1 + b + b + b+ + b

which is a geometric progression equal to

2

2

n th

d3

1 - bd+1

1 - b

ExampleA tree with depth of2 with a branching factor of2, has

1 8

1 2= 7 nodes

Using depth-first or breadth-first search, the total number

of nodes to be examined is7

.

Calculating the number of nodes that need to be examined:

A

B

D E

C

F G

IH


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Some Calculations

Using DFID, nodes need to be examined more than once, resultingto the following progression: number of nodes is:

(d + 1) + b (d) + b (d 1) + b (d 2)+ + b

Hence, DFID has a time complexityofO(b ). It has the memory

efficiencyof depth-first search because itonlyeverneeds to storeinformation about the currentpath.

Hence, its space complexityis O(bd).

2

n

d3

Example

A tree with depth of4 with a branching factor of10. Using

DFID, it has the following number of nodes to be examined

(4+1) +10(4) +100(3) +1000(2) +10,000

= 12,345 nodes

Calculating the number of nodes that need to be examined:

d


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Using Heuristics for SearchUsing Heuristics for Search


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Heuristic a commonsense rule (or set of rules) intended to

increase the success probability of solving some problems

In the context of state space search, heuristic are rules for

choosing those branches in a state space that are most likely to lead

to an acceptable problem solution.

The heuristic used in search is one that provides an estimate of

the distance from any given node to a goal node. This estimate

assist us to get better results than our pure/random guesswork.

Heuristic Search

Example

A problem may not have an exact solution because of inherentambiguities in the problem statement or available data. Medical

diagnosis is an example. A given set of symptoms may have

several possible causes; doctors use heuristics to choose the most

likely diagnosis and formulate a plan of treatment.


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Informed and Uninformed Search Methods

Search method is informed if it uses additional informationabout nodes that have not yet been explored to decide which nodes

to examine next.

If the search method is not informed, it is referred to as

uninformed orblind search method.

Search method that uses heuristics are informed.

Best-first search is an example ofinformed search, whereas

breadth-first and depth-first are uninformed or blind.

A heuristic, h is said to be more informed than another heuristicj,if h(node) < = j(node) for all nodes in the search space.

The more informed a search method is , the more efficiently it will

search.


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Hill Climbing

Hill climbing is an informed search method. It uses informationabout the search space to search in a reasonably efficient manner.

Hill climbing strategies expand the current state of search and

evaluate its children nodes. The best child is selected for further

expansion; neither its sibling or parent are retained.

In examining a search tree, hill climbing will move to the first

successor node that is better than the current node.


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Best-First Search

Best-first search - employs a heuristic in a similar manner to hillclimbing. The difference is that with best-first search the queue is

sorted after the new paths have been added to it, rather than adding

a set of sorted paths.

Best-first search follows the best path available from the current

(partially developed) tree, rather than always follow a depth-firstapproach.


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Identifying Optimal Paths

Optimal path path that involves the lowest cost or travels theshortest distance from the start to goal node.

Sophisticated techniques to identify optimal paths:

A*

Uniform cost search (Branch & Bound)

Greedy search


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The Missionaries and Cannibals problem

3 missionaries and 3 cannibals are on the one side of a river,

with a canoe. They all want to get to the other side of the river.

The canoe can only hold 1 or2 people at a time. At no time

should there be more cannibals than missionaries on either

side of the river, as this would probably result in the

missionaries being eaten.

What is the start state? What is the goal state?

What is the state space? What is the state that we have

to avoid or the illegal state?

Start state: 0, 0, 0 Goal state: 3, 3, 1

State space: All possible states in between.

Illegal state orconstraint: 2, 1, 1 or 2, 1, 0

Problem Solving Example


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ExerciseExercise


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The Missionaries and Cannibals problem

3, 3, 1 0, 0, 0

3, 3, 10, 0, 0

River

bank A

C, M, Canoe C, M, Canoe

Initial

state

Goal

state

River

bank B

Apply any of the operators given to

move from the Initial state to the

Goal state:

1) Move 1 C totheothersideoftheriver

2) Move2 C totheothersideoftheriver

3) Move 1 M totheothersideoftheriver

4) Move2 M totheothersideoftheriver

5) Move 1 C & 1M totheothersideofthe

river.

lect topic3 search sem1 0910[1]

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