1 / 13

15-381 Artificial Intelligence

15-381 Artificial Intelligence. Means-Ends Analysis and Constraint Propagation Jaime Carbonell 24 January 2002 Topics Covered: Homework 1 (generalized state-space search) Means-Ends Analysis (backchaining) Search Control Rules in MEA Constraint-Based Search.

irma
Download Presentation

15-381 Artificial Intelligence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 15-381 Artificial Intelligence Means-Ends Analysis and Constraint Propagation Jaime Carbonell 24 January 2002 Topics Covered: • Homework 1 (generalized state-space search) • Means-Ends Analysis (backchaining) • Search Control Rules in MEA • Constraint-Based Search

  2. SearchPlanning: Parameterized Operations • Multi-State Transitions Instead of: Opi,j: Si Sj, We have Opk,l: {Sk}{ Sl} • Preconditions and Post-Conditions • Conjunctive set of first-order predicates • Arguments can be constants or (typed) variables • Intentional description of subset of all states • Pre-image {Sk} states where preconditions are true • Post-image {S1} states where post-conditions are true • Requires Consistent variable bindings within and across preconditions and post-conditions

  3. SearchPlanning: Parameterized Operations • First Example OPERATOR DRIVE-CAR(<car>, <driver>, <keys>, <loc-1>) [PRE: (AT <car> <loc-1>) (AT <driver> <loc-1>) (CONTAINS-GAS <car>) (HAVE <keys> <driver>) (CORRESPOND <keys> <car>)] [POST: (AT <car> <loc-2>) (AT <driver> <loc-2>) (NOT (AT <car> <loc-1>)) (NOT (AT <driver> <loc-1>))]]

  4. SearchPlanning: Parameterized Operations • Second Example (Previous example: LISP-style, Current one: PROLOG-style) OPERATOR: move-robot(r,x,y) TYPE: ROBOT(r) & LOC(x) & LOC(y) PRE: AT(r,x) & EMPTY(y) & CONNECTED(x,y) POST: AT(r,y), NOT(AT(r,x)) OPERATOR: pick-up(r,z) TYPE: ROBOT(r) & LOC(x) & LOC(y) PRE: AT(r,x) & AT(z,y) & NEXT-TO(x,y) & NOT(holding(r,w,)) POST: HOLDING(r,z) NOT(AT(z,y))

  5. SearchPlanning: Parameterized Operations • Interpretation • A plan is an o-path: S0 followed by a sequence of instantiated operators which result in the goal state. • Variables match objects in state of specified types only for which the preconditions hold at plan execution time. • Planning can proceed by forward or backward (or any other) search method. • More on Planning expected from Veloso (later lecture)

  6. Means-Ends Analysis • Backchaining/Subgoaling Search • Let Scurr:= S0 • If Scurr = SG, then go to next goal (or DONE) • Let OPSapp := match(SG {POST(Opi)}) • If OPSapp= empty, then FAIL • Else Select OP  OPSapp, (save alt's) • If match(PRE(OP), Scurr), a. let Scurr:= apply(OP, Scurr) b. Go to step 2 • Else (i.e. if NOT(match(PRE(OP), Scurr))) a. MEA(SG):= {unmatched(PRE(OP))}, SI := Scurr) b. If fail, go to step 4 c. If succeed, apply OP as above

  7. Control Rules for MEA • Choice Points in MEA • Choose Operator, if several applicable • Choose Goal, if > 1 subgoals pending • Choose Variable Bindings, if > 1 tuple • Types of Control Rules • Select – choose an alternative and eliminate other contenders • Reject – Reject an alternative and retain other contenders • Prefer – Try one alternative first and retain others for possible backtracking

  8. Control Rules for MEA • Example CONTROL-RULE: Carry-before-move TYPE: SELECT PRE: Goals(Move(r,x,y), Pick-up(r,z,v))) POST: Pick-up(r,z) CONTROL-RULE: Don’t polish before machining TYPE: REJECT PRE: Goals(Mill(p,f), Drill(p,l,d,s), Polish(p)) POST: Polish(p)

  9. Constraint-Based Search • Satisfiability problems • Find consistent bindings to a set of variables • Consistent = satisfy all constraints • Example: (X v Y) & (~X v ~Y) • Example: Match applicants to positions • Two families of search methods apply • State-space search on bindings • Satisfiability-search on constraints

  10. Constraint-Based Search • Example: How fast can you solve this? Find a way to fit components (1,2,3,4) into slots (A,B,C,D) such that: • Each slot only takes one component • Slots are in LEFT-RIGHT sequence A, B, C, D • Slots A and C are T-shaped • Slots B and D are I-shaped • Components 1,2, are 3-pronged • Components 3,4 are 2-pronged • 2-pronged fit into T-shaped or I-shaped • 3-pronged fit only into T-shaped • Component 3 must be LEFT of component 2

  11. Constraints • Least Commitment Method • For each Variable find all legal unary-constrained assignments. • If no assignments possible, return FAILURE • Assign most-constrained unassigned variable. • If all variables assigned, return SUCCESS • If the assigned variable is a member of a binary constraint, propagate instantiation • Delete all residual un-viable assignments • Go to 2

  12. Constraint-Based Search A = {1,2,3,4} B = {3,4} C = {1,2,3,4} D = {3,4} B4 B3 A = {1,2,4} C = {1,2,4} D = {4} A = {1,2,3} C = {1,2,3} D = {3} FAILURE D4 D3 A = {1,2} C = {1,2}C = {2} C2 A = {1} SUCCESS A1

  13. (Dis)Advantages of Constraints • Reduce the search space • Early failure (upon constraint violation) • Generate minimal-uncertainty step (least commitment strategy) • Only applicable to satisfiability problems • Finds an answer, not necessarily optimal • Not all problems can be cast as constraints to satisfy

More Related