representation and search techniques - artificial intelligence

8/20/2019 Representation and Search Techniques - Artificial Intelligence

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copyright 2005

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L. Manevitz Lecture 2 1

Artificial IntelligenceRepresentation and Search

Techniques

L. Manevitz


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L. Manevitz Lecture 2

2

!oals of Lecture

" Representing #ro$le%s & ' (arious Issues and )onsiderations.

' #roduction Syste%s." #roduction syste%s &

' State Space.

' !oals.

' Transfor%ation Rules.

' )ontrol *Search Techniques+.


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,

-le%ents of #roduction Syste%s

" Representation & ' State Space.

' !oal States. ' Initial States.

' Transfor%ation Rules.

" Search Algorith%s & ' ninfor%ed.

' /euristic1.


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-3a%ples of #ro$le%s

" /Toy1 #ro$le%s &

' 4ater 5ug.

' )anni$als. ' 6 ' 7ueens.

' 6 #uzzle.


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-3a%ples of #ro$le%s cont.

" /Real1 #ro$le%s &

" Schedules.

" Traveling Sales%an." Ro$ot navigation.

" Language Analysis *#arsers8 !ra%%ars+.

" (LSI design.


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9

#oints to )onsider :hen

Representing #ro$le%s" ;eco%posa$le <

" )an partial steps $e ignored or undone <

" #redicta$le <

A

A

=

)=

)

Theore% proving vs. chess

=ridge


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>

#oints to )onsider :hen

Representing #ro$le%s cont." Is /good1 solution easily recogniza$le <

" Is ?no:ledge =ase consistent <

" o: %uch ?no:ledge is needed <

" Stand'alone vs. Inter'active.

Traveling Sales%an

=ig ;ata =ase and li%itations of logic

)hess8 @e:spapernderstanding


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6

)ontrol

;ATA

Rules


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B

Issues In Representing #ro$le%

C+ )hoice of representation of ;ata =ase.

C+ Specify initial states

2+ Specify goal states

2+ Appropriate Rules.

C+ Issues&

C+ Assu%ptions in pro$le%

2+ o: general,+ o: %uch :orD preco%puted and put into rules

,+ )ontrol *later+


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C0

4ater Eug #ro$le%

, liters liters

F38 yG 38 y real nu%$ers

F38 yG 3 integers $et:een 0 and

38 y $et:een 0 and


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CC

4ater Eugs cont.

" Rules &

' F38yG 3F F8yG * Hill liters +

' F38yG yF, F38,G * Hill , liters +

' F38yG Fo8yG * ;u%p liters +

' F38yG F380G * ;u%p , liters +

' F38yG 3Jy GK F8y*3+G

' F38yG 3Jy GK ,

F3*,y+8yG ' F38yG 3Jy FK F3Jy80G

' F38yG 3Jy FK , F083JyG


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C2

-3a%ple no.C

" CHESS :

' RC ' If pa:n not $locDed then %ove it

one space for:ard. ' R2 ' If pa:n in original position and not

$locDed for t:o spaces %ove it t:o

spaces. ' -tc.


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C,

-3a%ple no.2

" SPEECH&

' RC ' If input not analyzed try and

identify phone%es. ' R2 ' TaDe so%e possi$le sylla$les and

try and for% :ords.

' -tc.


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C

#roduction

C. ;ATA initial data$ase.

2. ntil ;ATA satisfies ter%ination

condition do&,. $egin& Select so%e rule8 R8 in the set of rules that

can $e applied to ;ATA.

;ATA result of applying R to ;ATA.

. end.


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C

#ro$le% ;escription

C+ ;efine State Space containing all

possi$le configurations of relevant

o$5ects.2+ Specify so%e states as initial states.

,+ Specify so%e states as goal states.

+ Specify Rules


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C9

Search Through StateSpace

Initial state

!oal state


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C>

)ontrol Strategies

" 4hat do :e :ant<

' )ause %otion

' =e syste%atic

-3a%ples

=readth first

;epth first

=acD TracDingill )li%$ing

=est Hirst


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C6

)ontrol via Search Techniques

" /ninfor%ed1 &

' =readth ' Hirst.

' ;epth ' Hirst. ' =acDtracDing.

" /Infor%ed1 ' euristic &

' ill )li%$ing. ' =est Hirst8 A.


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CB

)osts of #roduction Syste%

Level of /Infor%edness1

)ost

Rules Control

Total )ost


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20

=readth Hirst cont.


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2C

=readth Hirst

$ K $ranching factor dKdepth

C J $ J $ J J $

Ti%e )o%ple3ity ' N*$ +

Space )o%ple3ity ' N*$ +

2 d

d

d


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=readth Hirst fi3 e3ponents

;epth @odes Ti%e Me%ory

2 CCC .C sec C D$

CC8CCC CC sec C %ega

9 C09 C6 %in CCC %ega

6 C06 ,C hours CC giga

C0 C0C0 C26 days C tera

C2 C0C2 , years CCC tera

C C0C ,00 years CC8CCC tera


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2,

;epth Hirst cont.


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2

;epth Hirst *so%e ad5ust%ents

needed for depth $ound+;-#T HIRST *I@ITIAL ;ATA+

C. ;ATA I@ITIAL ;ATA

2. IH ;ATA K !NAL T-@ -OIT 4IT @LL

,. RL-S A##RL-S *;ATA+

. IH RL-S K @LL -OIT 4IT HAILR-

. R HIRST *RL-S+

9. ;ATA R *;ATA+

>. IH ;ATA AT !NAL -OIT 4IT R

6. #AT ;-#T HIRST *;ATA+

B. IH #AT K HAILR- -OIT 4IT HAILR-

C0. -OIT 4IT RP#AT


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2

=acDtracDing cont.


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=acDtracDing Algorith%

=A)?TRA)? *;ATA+

C. IH T-RMI@AL *;ATA+ R-TR@ @LL

2. IH ;-A;-@; *;ATA+ R-TR@ HAIL

,. RL-S A##RL-S *;ATA+

. LNN# & IH RL-S K @LL R-TR@ HAIL

. R =-ST *RL-S8;ATA+

9. RL-S RL-S ' QR

>. @-4;ATA R *;ATA+

6. #AT =A)?TRA)? *@-4;ATA+B. IH #AT K HAIL T-@ !N TN LNN#

C0. R-TR@ RP#AT


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2>

=acDtracDing

" 4orDs liDe ;epth Hirst.

" Stores only last path.

";isadvantages & ' May never ter%inate '

" @e: nonter%inal data$ase al:ays generates.

" )ycle.

' o:ever can apply heuristics to choose ' " =est rule.

" =etter heuristics ' less $acDtracDing.


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=acDtracDing cont.

Try a rule ' if not successful go $acD and try

a different one.

-3a%ple ' try rules in this order& L8 8 R8 ;.

=acD up if '

C. Repeat position on path '

$acD to initial state.

2. 4henever have already applied of rules ' depth $ound.

,. 4hen no %ore rules can $e found.


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=acDtracDingC Algorith%

*checDing for loops+=A)?TRA)?C *;ATALIST+C. ;ATA HIRST *;ATALIST+

2. IH M-M=-R *;ATA8TAIL*;ATALIST++ R-TR@ HAIL

,. IH T-RMI@AL *;ATA+ R-TR@ @LL

. IH ;-A;-@; *;ATA+ R-TR@ HAIL

. IH L-@!T *;ATALIST+ G =N@; R-TR@ HAIL

9. RL-S A##RL-S *;ATA+

>. LNN# & IH RL-S K @LL R-TR@ HAIL

6. R HIRST *RL-S+

B. RL-SRL-S R

C0. R;ATA R *;ATA+

CC. R;ATALIST )N@S *R;ATA8;ATALIST+

C2. #AT =A)?TRA)?C *R;ATALIST+

C,. IH #AT K HAIL T-@ !N TN LNN#

C. R-TR@ )N@S *R8#AT+


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Search Tree

R C

R C

R 2

R ,

R

R 2

R C

R , R 2

R C

R 2 R

R ,

R ,

R C R

goal


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6 #uzzle

" #ro$le% &

" ;ata =ase & ,3, Matri3 or a (ector :ithlength B.

" Rules & #recondition &

C+ Move =lanD Left @ot at e3tre%e left

2+ Move =lanD Right @ot at e3tre%e right

,+ Move =lanD p @ot at top ro:

+ Move =lanD ;o:n @ot at $otto% ro:

C ,2

>

9

6 C ,2

> 96


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6 #uzzle cont.

" Initial State &

Move =lanD p

Move =lanD pMove =lanD Left

Move =lanD ;o:n

Move =lanD Right" !oal State &

9

,C

6

>

2

C ,2

> 96


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ill )li%$ing

C+ se heuristic function as %easure of ho:

far off the nu%$er of tiles out of place.

2+ )hoose rule giving $est increase infunction.


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-3a%ple

9

,C

6

>

2

9

,C

6

>

2

9

,C 6>

2

, ,

L

9

,

C 6>

2

9

,C

6>

2

9

,C

6>

2

2 C 0

; R


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ill )li%$ing cont.

#ro$le%s &

C+ Local Ma3i%a '

Initial !oal

2+ #lateaus.

,+ Ridge.

9,

C>

6

2

9

,C>

6

2


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)ontrol

;ata =ase*state+

;ata =ase

;ata =ase;ata =ase

R2?R3?

R5?


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!raphs ;igraphs

" !raph ' @odes and -dges.

" ;igraph ' @odes and directed arcs.

" Tree ' each @ode has one parent & ' Root ' no parent.

' Leaf ' no successors.

" #ath ' nCnD .


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!raphs ' ;igraphs cont.

I%plicit vs. -3plicit !raph

generally8 %aDe e3plicit su$graph of

i%plicit graph.I%plicit !raph

-3plicit !raph


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!raph Search ' ;ata Structures

" 2 List of /discovered nodes1

' Npen *not yet /e3panded1+

' )losed *already /e3panded1+

" !raph

" #ointers on !raph *liDe /ansel and !retel1+

" The graph gro:s as nodes are e3panded ' -3plicit versus I%plicit !raph


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!raph Search

C. ! s U Npen s U )losed @LL

2. LNN#& -OIT 4IT HAILR- IH

NpenK@LL.

C. TaDe first node n fro% Npen 8 Add to )losed.

2. If n is goal e3it :ith S))-SS.

*solution o$tained $y pointer path fro% n to s+.

,. -3pand n & generate M set of Successors J add to !

as successors to n.


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!raph Search

. Hor each % fro% M &

C. If % is ne: add to Npen and pointer $acD to n.

2. If % is already on Npen8 see if to redirect pointer

to n.

,. If % already on )losed8 see if to redirect pointer

to n. Then checD all descendants as :ell.

. Reorder Npen.

9. !o to LNN#.


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-3a%ple

A node :ith not yet checDed successors

A node :ith checDed successors


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-3a%ple cont.

The changes in the graph are &


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;isadvantage of !raphs

C+ ave to verify that a ne: node hasnVt

appeared $efore *e3pensive+.

2+ If donVt verify ' then redundant successor

co%putations.


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Nrdering of @odes *in !raph

Search+" ;escending Nrder *e3pand deepest first+ '

;epth Hirst Search *:ith cutoff+.

" Ascending Nrder '=readth Hirst Search.

"euristic =est Hirst h*n+ K g*n+ J d*n+A Algorith%


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Tree Search

" Hor% a 7ueue consisting of root node

" ntil 7ueue K @ull or !oal achieved '

See if Cst

ele%ent is goal. ;o nothing if yes ' If not8 re%ove ele%ent fro% queue and add itschildren

" in $acD of queue *$readthfirst+

" in front of queue *depthfirst+" resort queue *$estfirst+

" front of queue *sorted $y esti%ate+ hillcli%$ing


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A Algorith%

" T:o Lists '

' Npen.

' )losed." #arent List.

" euristic Hunction

f*n+ K g*n+ J h*n+*cost of solution constrained through n+


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A Algorith% cont.

" Npen K QsU g*s+ K 0U f*s+ K h*s+

)losed K @LL

" Npen K @LL Return Hailure" =estnode =est *Npen+

" Npen Npen ' Q=estnode

" !oal *=estnode+ Return Solution

" Successors Successor *=estnode+


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A Algorith% cont.

" Hor each S Successors ;o&∈

' #arent *S+ =estnode

' g*S+ K g*=estnode+ J c*=estnode8S+

' ;oes S Npen < *i.e. identify :ith NL;+∈

" Add NL; to )hildren *=estnode+

" If g*S+ F g*NL;+

' g*NL;+ g*S+ ' #arent *NL;+ =estnode

' f*NL;+ g*NL;+ J h*NL;+


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A Algorith% cont.

' ;oes S )losed


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A Algorith% cont.

' #ropagate change do:n:ards

' ;o ;epth Hirst traversal fro% NL;

' Ter%inate if g*node+ FK path fro% NL;

or :o successors

or on Npen

' Nther:ise change g*node+

f*node+

change #arent *node+


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Npti%ality of A

" euristics& f*3+ K g*3+ Jh*3+

" ere g*3+ is esti%ate of g*3+ the actual

cost to get to 3 fro% s." h*3+ is esti%ate of h*3+ the %ini%l cost to

get to any goal fro% 3.

' )hoose g*3+ to $e cost in -O#LI)IT !RA# ' )hoose h*3+ such that h*3+ FK h*3+


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L. Manevitz L

ecture 2

,

" In such a circu%stance A returns opti%al path.

" -3a%ples&

" h*3+ K 0

" Hor 6 puzzle h*3+ K nu%$er of tiles in:rong position

" Hor 6 puzzle h*3+ K su% of distances

each tile is fro% ho%e" sequence scores #*3+ J , S*3+


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L. Manevitz L

ecture 2

#roof of Npti%ality

N@ =lacD$oard.

Main points& If doesnVt ter%inate8

eventually all points in open have very large f valuesince they :ill have large g value.

=ut al:ays a point in N#-@ on opti%al pathU

thus f value $ounded.

Moreover 5ust prior to ter%ination8 %ust choose a node

:ith s%all f valueU so cant ter%inate erroneously.


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ecture 2

#roof *in %ore detail+

" Assu%ing there is a solution and an opti%al one&

" Let *s K n08 nC8 n28 8 nD K goal+ $e an

opti%al path.

" Hact C& There is al:ays one ele%ent on the

opti%al path on N#-@ $efore success8 for :hich

all predecessors in this path are in )LNS-;.

' #roof& Initially s is on N#-@8 then its childrenU if nogoal then let n $e first one on path :ith this condition.


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ecture 2

9

" Hact 2& Hor an ele%ent on opti%al path in

N#-@ :hose predecessors on path are in

)LNS-;8

f*n+ K g*n+ J h*n+ K g *n+ Jh*n+ F g*n+

Jh*n+ K f *n+ K f *s+.

So al:ays an ele%ent in N#-@ :ith value

s%aller than true opti%al cost fro% start *s+.


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L. Manevitz L

ecture 2

>

" Hact ,& -ach step in path taDes at least an e G0.

" So if node has shortest path to it of length d8g*n+ G de.

" So8 if it does not ter%inate8 eventually all nodeson N#-@ have ar$itrarily large g*n+U hencef*n+

" ence eventually e3pands all nodes of eachlength *liDe $readth first+.


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ecture 2

6

" Hact 2 J Hact , %eans A finds a solution.

" It is opti%al solution since A ter%inates either

$ecause N#-@ is e%pty *HAILR-+ or finds a!oal. =y Hact C8 found a goal

" @o nonopti%al path& ' Nther:ise8 last choice of node fro% N#-@ :ith f*n+

Kg*n+ G f*s+. =ut $y Hact C8 there :as a $etter choicethan n on opti%al path and :ould not have chosen n.

' 7-;


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L. Manevitz L

ecture 2

B

A@;NR !RA#S

" ypergraphs.

" yperarcs connects node :ith S-T of

nodes." )onnectors are Cary8 2ary and so on.

S l i $ h !V f ! f


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ecture 2

90

Solution su$graph !V of ! fro%

node n to @ ter%inals" If n in @8 !V is 5ust n

" If n has outgoing connector to set of nodes

a8 $8 c such that there is solution graph fro%

each of a8 $ 8c separately to @U

then !V consists of n8 connector8 a8 $8 c8

and each of the solution graphs fro% a8 $8c

Nther:ise no solution graph e3ists


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ecture 2

9C

)osts

" Include cost of connector.

" Then cost fro% node n to @8 D*n8@+ is

defined recursively $y ' if n in @ D*n8@+ K 0

' n has connector to a8 $8 c in solution graph

:ith cost c

" D*n8@+ K c J D*a8 @+ J D*$8 @+ J D *c8 @+ J

" )reate a search graph !8 consisting solely of start node8 s. #uts on list N#-@


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copyright 200 L Manevitz L 92

s on list N#-@

" )reate a list called )LNS-; K @ull

" LNN#& if N#-@ K @ull8 e3it HAILR-

' Move Cst

node of N#-@8 n8 to )LNS-; ' If n !NAL e3it :ith solution via pointers fro% n to s. *pointers placed

later+

' Let M $e set of successors of n8 place in !

' MaDe a pointer to n fro% %e%$ers of M not already in !. Add these%e%$ers to N#-@.

' Hor %e%$ers of M already on N#-@ decide if to change pointer to n.

' Hor %e%$ers of M already on )LNS-;" ;ecide if to change pointer to n

" ;ecide for each of its descendents in ! :hether to change pointer

Reorder N#-@

representation and search techniques - artificial intelligence

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