g5baim artificial intelligence methods graham kendall searching

G5BAIMArtificial Intelligence Methods

Graham KendallSearching

G5BAIM SearchingG5BAIM Searching

Problem Definition - 1

• Initial State– The initial state of the problem,

defined in some suitable manner

• Operator– A set of actions that moves the

problem from one state to another



• Neighbourhood (Successor Function)– The set of all possible states

reachable from a given state

• State Space– The set of all states reachable from

the initial state



• Goal Test– A test applied to a state which

returns if we have reached a state that solves the problem

• Path Cost– How much it costs to take a

particular path


Problem Definition - Example

5 4

6 1 8

7 3 2

1 2 3

8 4

7 6 5

1 2 3

4 5 6

7 8

1 4 7

2 5 8

3 6

Initial State Goal State



• States– A description of each of the eight

tiles in each location that it can occupy. It is also useful to include the blank

• Operators– The blank moves left, right, up or

down



• Goal Test– The current state matches a

certain state (e.g. one of the ones shown on previous slide)

• Path Cost– Each move of the blank costs 1


Problem Definition - Datatype

• Datatype PROBLEM– Components

• INITIAL-STATE,

• OPERATORS,

• GOAL-TEST,

• PATH-COST-FUNCTION


How Good is a Solution?

• Does our search method actually find a solution?

• Is it a good solution?– Path Cost

– Search Cost (Time and Memory)

• Does it find the optimal solution?– But what is optimal?


Evaluating a Search

• Completeness– Is the strategy guaranteed to find a

solution?

• Time Complexity– How long does it take to find a

solution?


Evaluating a Search

• Space Complexity– How much memory does it take to

perform the search?

• Optimality– Does the strategy find the optimal

solution where there are several solutions?


Search Trees

xx x x

x xx x x

o

x

o

xx

o

x………..


Search Trees

• ISSUES– Search trees grow very quickly

– The size of the search tree is governed by the branching factor

– Even this simple game has a complete search tree of 984,410 potential nodes

– The search tree for chess has a branching factor of about 35

G5BAIM SearchingG5BAIM SearchingImplementing a Search - What we need to store

• State– This represents the state in the state

space to which this node corresponds

• Parent-Node– This points to the node that generated

this node. In a data structure representing a tree it is usual to call this the parent node

G5BAIM SearchingG5BAIM SearchingImplementing a Search - What we need to store

• Operator– The operator that was applied to generate

this node

• Depth– The number of nodes from the root (i.e.

the depth)

• Path-Cost– The path cost from the initial state to this

node


Implementing a Search - Datatype

• Datatype node– Components:

• STATE,

• PARENT-NODE,

• OPERATOR,

• DEPTH,

• PATH-COST


Using a Tree – The Obvious Solution?

• Advantages– It’s intuitive

– Parent’s are automatically catered for


Using a Tree – The Obvious Solution?

• But– It can be wasteful on space

– It can be difficult the implement, particularly if there are varying number of children (as in tic-tac-toe)

– It is not always obvious which node to expand next. We may have to search the tree looking for the best leaf node (sometimes called the fringe or frontier nodes). This can obviously be computationally expensive


Using a Tree – Maybe not so obvious

• Therefore– It would be nice to have a

“simpler” data structure to represent our tree

– And it would be nice if the next node to be expanded was an O(1) operation


Basic Queue Operations

• Make-Queue(Elements)– Create a queue with the given elements

• Empty?(Queue)– Returns true if the queue is empty

• Remove-Front(Queue)– Removes the element at the head of the

queue and returns it


Queue Operations - Adding Elements

• Queuing-FN(Elements,Queue)– Inserts a set of elements into the

queue. Different queuing functions produce different search algorithms.


General Search

• Function GENERAL-SEARCH(problem, QUEUING-FN) returns a solution or failure

– nodes = MAKE-QUEUE(MAKE-NODE(INITIAL-STATE[problem]))

– Loop do

• If nodes is empty then return failure

• node = REMOVE-FRONT(nodes)

• If GOAL-TEST[problem] applied to STATE(node) succeeds then return node

• nodes = QUEUING-FN(nodes,EXPAND(node,OPERATORS[problem]))

– End

• End Function


General Search• Function GENERAL-SEARCH(problem, QUEUING-FN) returns a solution or failure


– Loop do





– End

• End Function




– Loop do• If nodes is empty then return failure




– End

• End Function




– Loop do

• If nodes is empty then return failure• node = REMOVE-FRONT(nodes)



– End

• End Function




– Loop do


• node = REMOVE-FRONT(nodes)• If GOAL-TEST[problem] applied to STATE(node) succeeds then return node


– End

• End Function




– Loop do





– End

• End Function

G5BAIMArtificial Intelligence Methods

Graham KendallEnd of Searching

g5baim artificial intelligence methods graham kendall searching

Documents

initial state slide

pathcost slide

initial stategoal state

function slide

parent node slide

particular path slide

previous slide path

given state state space