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15-381 Artificial Intelligence

Means-Ends Analysis andConstraint Propagation

Jaime Carbonell4 September 2001

Topics Covered:

Means-Ends Analysis

Search Control Rules in MEA

Constraint-Based Search

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Searc 

Planning:

Para!eteri"ed #perations

M$lti-State Transitions

nstead o!" #pi$%" Si S %$ &e ha'e #p($l" )S( *) Sl*

Preconditions and Post-Conditions Con%uncti'e set o! !irst-order predicates

Ar+uments can be constants or ,typed 'ariables

ntentional description o! subset o! all states

 Pre-image )S( * states .here preconditions are true Post-image )S1* states .here post-conditions are true

Re/uires Consistent 'ariable bindin+s .ithin andacross preconditions and post-conditions

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Searc 

Planning:

Para!eteri"ed #perations

%irst E&a!ple

#ERA#R R3E-CAR,car5$ dri'er5$ (eys5$ loc-15

6RE" ,A car5 loc-15

,A dri'er5 loc-15,C#7A7S-8AS car5

,9A3E (eys5 dri'er5

,C#RRES#7 (eys5 car5:

6#S" ,A car5 loc-25,A dri'er5 loc-25

,7# ,A car5 loc-15

,7# ,A dri'er5 loc-15::

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Searc 

Planning:

Para!eteri"ed #perations

Second E&a!ple

,re'ious e;ample"

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Searc 

Planning:

Para!eteri"ed #perations

Interpretation

A plan is an o-path" S0 !ollo.ed by a se/uence o!

instantiated operators .hich result in the +oal state

3ariables match ob%ects in state o! specified types

only !or .hich te preconditions old at plan

e;ecution time

lannin+ can proceed by !or.ard or bac(.ard ,orany other search method

More on lannin+ !rom 3eloso ,later lecture

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Means-Ends Analysis

'ac(caining)S$*goaling Searc1

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Control +$les for MEA

Coice Points in MEA Choose #perator$ i! se'eral applicable

Choose 8oal$ i! 5 1 sub+oals pendin+

Choose 3ariable Bindin+s$ i! 5 1 tuple

Types of Control +$les  Select  I choose an alternati'e

and eliminate other contenders

 Reject  I Re%ect an alternati'e

and retain other contenders

 Prefer I ry one alternati'e !irst

and retain others !or possible bac(trac(in+

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Control +$les for MEA

E&a!ple

C#7R#

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Constraints

E&a!ple

Lind a .ay to !it components ,1$2$$4 into slots,A$B$C$ such that" Each slot only ta(es one component

Slots are in

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Constraints

,east Co!!it!ent Metod

1 Lor each 3ariable !ind all le+al unary-constrainedassi+nments

2 ! no assi+nments possible$ return LA

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Constraint-'ased Searc

A )1$2$$4*

B )$4*

C )1$2$$4*

)$4*

A )1$2$4*C )1$2$4*

)4*

A )1$2*

C )1$2*C )2*

A )1*

SCCESS

A )1$2$*

C )1$2$*

)*

LA

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.is/Advantages of Constraints

Reduce the search space Early !ailure ,upon constraint 'iolation

8enerate minimal-uncertainty step ,least

commitment strate+y

#nly applicable to satis!iability problems Linds an ans.er$ not necessarily optimal

 7ot all problems can be cast as constraints to

satis!y