Planning by Rewriting José-Luis Ambite University of Southern California Information Sciences Institute and Computer Science Department José-Luis Ambite
Outline Planning by Rewriting (PbR): A new paradigm for efficient high-quality domain-independent planning � Motivation and Thesis Statement � Planning by Rewriting as Local Search � Query Planning in Mediators � Experimental Results � Related Work � Future Work � Contributions José-Luis Ambite
Domain-Independent Planning initial state Planner goal state plan domain specification � Many practical problems can be cast as planning � Domain independence => Flexibility, Reusability � But it is computationally hard [Bylander 94, Erol et al. 95] � Moreover, plan quality is also critical PbR addresses planning efficiency and plan quality in a domain-independent framework José-Luis Ambite
Planning = Satisfiability + Optimization � Two sources of complexity in planning: � satisfiability: find any valid plan � optimization: find the best plan (wrt given cost metric) � Optimization domains: � dominated by optimization complexity � finding a valid plan is easy (polynomial) � many practical domains: – query planning – manufacturing operations – transportation ... José-Luis Ambite
Transforming a suboptimal plan U(x y): Unstack x from y A S(x y z): Stack x on y from z Initial Plan: B B C U(B D) U(D E) S(D E T) D C D S(C D T) E E A S(B C T) S(A B T) U(C A) José-Luis Ambite
Transforming a suboptimal plan U(x y): Unstack x from y A S(x y z): Stack x on y from z Initial Plan: B avoid-undo B C U(B D) U(D E) S(D E T) D C D S(C D T) E E A S(B C T) S(A B T) U(C A) Transformations: • avoid-undo: U(x y) --- S(y x T) => 0 José-Luis Ambite
Transforming a suboptimal plan U(x y): Unstack x from y A S(x y z): Stack x on y from z Initial Plan: B avoid-undo B C U(B D) U(D E) S(D E T) D C D S(C D T) E E A avoid-move-twice S(B C T) S(A B T) U(C A) Transformations: • avoid-undo: U(x y) --- S(y x T) => 0 • avoid-move-twice: U(x y) --- S(x z T) => S(x z y) José-Luis Ambite
Transforming a suboptimal plan U(x y): Unstack x from y A S(x y z): Stack x on y from z Initial Plan: B avoid-undo B C U(B D) U(D E) S(D E T) D C D S(C D T) E E A avoid-move-twice S(B C T) S(A B T) U(C A) Transformations: • avoid-undo: U(x y) --- S(y x T) => 0 • avoid-move-twice: U(x y) --- S(x z T) => S(x z y) Rewritten Plan: U(B D) S(C DA) S(B C T) S(A B T) José-Luis Ambite
New approach: Planning by Rewriting � Efficiently generate an initial solution plan (possibly of low quality) � Iteratively rewrite the current plan � using a set of plan rewriting rules � improving plan quality � until an acceptable solution or resource limit reached Efficient High-Quality Planning José-Luis Ambite
Manufacturing Operations Planning Lathe A IPaint A Red Punch A 2 Punch C 1 IPaint C Blue Roll B IPaint B Red Cost: 6 Rule 1: Reorder Parts on a Machine Lathe A IPaint A Red Punch A 2 Cost: 4 Punch C 1 IPaint C Blue Roll B IPaint B Red Rule 2: Immersion-Paint => Spray-Paint Lathe A IPaint A Red Punch A 2 Cost: 3 Punch C 1 IPaint C Blue Domain: [Minton88] Roll B Spray-Paint B Red Cost = Schedule Length José-Luis Ambite
Thesis Statement Declarative plan rewriting combined with local search provide Efficient High-Quality Domain-Independent Planning José-Luis Ambite
Planning by Rewriting as Local Search � PbR: efficient high-quality planning using local search � Main issues: � Selection of initial feasible point : Initial plan generation. � Generation of a local neighborhood : Set of plans obtained from application of the plan rewriting rules. � Cost function to minimize : Measure of plan quality. � Selection of next point : Next plan to consider. Determines how the global space is explored. Start Neighborhood José-Luis Ambite
Generation of an Initial Plan � Biased generative planners � Domain-independent: HSP (heuristic search) � Domain-specific search control rules: – Directly specified: UCPOP, TLPlan (temporal logic) – Learning, abstraction: Prodigy, IPP-GAM � Example: process planning, depth-first search and search control automatically generated by an abstraction hierarchy � Programmatically � Approximation algorithms. Examples: – query planning: any parse of the query (or a greedy one) – blocksworld: “put all blocks in the table, then build towers” (linear) � Provided high-level plan construction language José-Luis Ambite
Generation of a Local Neighborhood � Declarative plan rewriting rules: express concisely complex transformations � More natural than search control: complete plan and cost � Intention: Move towards higher quality solutions � Result of a rewriting rule is always a solution plan � Two types of rewriting rules: � Fully-specified: typical of graph rewriting � Partially-specified: exploit semantics of planning José-Luis Ambite
Partially-Specified Rewriting Rules � Embedding of rule consequent is not explicit in rule antecendent � Uses semantics of partial order planning to compute the embedding ( d e f i n e - r u l e : n a me avo i d -move- tw i c e : i f ( : o pe r a t o r s ( ( ? n1 ( un s t a c k ?b1 ? b2 ) ) ( ? n 2 ( s t a ck ? b1 ? b 3 Tab l e ) ) ) : l i n k s ( ? n1 ( on ? b1 T ab l e ) ?n2 ) : c o n s t r a i n t s ( ( po s s i b l y - ad j a c en t ? n1 ?n2 ) ( : neq ?b2 ? b3 ) ) ) : r e p l a c e ( : op e r a t o r s ( ?n1 ?n2) ) :w i t h ( : o p e r a t o r s ( ? n 3 ( s t a ck ? b1 ? b 3 ?b2 ) ) ) ) subplans José-Luis Ambite
Fully-Specified Rewriting Rules Fully-Specified Rewriting Rules � Embedding of rule consequent fully specified � All anchors present in antecedent ( d e f i n e - r u l e : n ame a vo i d - move - twi c e - f u l l - s pec : i f ( : o p e r a t o r s ( ( ? n3 ( un s t a ck ?b1 ? b2 ) ) ( ? n8 ( s t a ck ? b 1 ?b3 Tab l e ) ) ) : l i n k s ( ( ? n1 ( c l e a r ? b1) ? n3 ) ( ? n2 ( on ? b1 ?b2 ) ? n3 ) ( ? n3 ( c l e a r ? b2 ) ?n4 ) ( ? n 3 ( on ?b 1 Tab l e ) ?n5 ) ( ? n6 ( on ? b1 ? b3 ) ? n9 ) ( ? n 7 ( c l e a r ? b1 ) ? n9 ) ( ? n8 ( c l e a r ? b3 ) ?n9 ) ( ? n 9 ( on ?b 1 ?b3 ) ? n 10 ) ) : c ons t r a i n t s ( ( po s s i b l y - a d j a c en t ? n3 ? n8 ) ( : n eq ? b 2 ?b3 ) ) ) : r e p l a c e ( : o p e r a t o r s ( ? n1 ?n2 ) ) :w i t h ( : ope r a t o r s ( ( ? n11 ( s t a ck ? b 1 ?b3 ? b 2 ) ) ) : l i n k s ( ( ? n1 ( c l e a r ? b 1 ) ? n11 ) ( ? n8 ( c l e a r ? b3 ) ? n11 ) ( ? n2 ( o n ?b1 ?b2 ) ? n11 ) ( ? n11 ( on ?b1 ? b3 ) ? n10 subplans José-Luis Ambite
Plan Rewriting clear B on A T ⎤ on A T ⎤ on C A clear A ⎤ clear B Stack A B T Unstack C A ⎤ on B T on C A on A B ⎤ clear C on C T clear C Stack B C T on B C on D T clear C on C D Stack C D T Goal INIT ⎤ clear D clear B clear D on B D ⎤ on C T on B T Unstack B D ⎤ on B D clear B clear C A B C C B Causal link Unstack x (from y) Ordering Constraint D D Stack x on y (from z) A José-Luis Ambite
Plan Rewriting clear B on A T ⎤ on A T ⎤ on C A clear A ⎤ clear B Stack A B T Unstack C A ⎤ on B T on C A on A B ⎤ clear C on C T clear C Stack B C T on B C on D T clear C on C D Stack C D T Goal INIT ⎤ clear D clear B clear D on B D ⎤ on C T on B T Unstack B D ⎤ on B D clear B clear C A B C C B Causal link Unstack x (from y) Ordering Constraint D D Stack x on y (from z) A José-Luis Ambite
Plan Rewriting clear B on A T ⎤ on A T ⎤ on C A clear A ⎤ clear B Stack A B T Unstack C A ⎤ on B T on C A on A B ⎤ clear C on C T clear C Stack B C T on B C on D T clear C on C D Stack C D T Goal INIT ⎤ clear D clear B clear D on B D ⎤ on C T on B T Unstack B D ⎤ on B D clear B clear C A B C C B Causal link Unstack x (from y) Ordering Constraint D D Stack x on y (from z) A José-Luis Ambite
Plan Rewriting clear B on A T ⎤ on A T ⎤ clear B Stack A B T clear A ⎤ on B T clear C on A B ⎤ clear C Stack B C T on D T on B C on C A Goal INIT on C D clear B on B D clear D on B T Unstack B D ⎤ on B D clear B clear C A B C C B Causal link Unstack x (from y) Ordering Constraint D D Stack x on y (from z) A José-Luis Ambite
Plan Rewriting clear B on A T ⎤ on A T ⎤ clear B Stack A B T clear A ⎤ on B T clear C on A B ⎤ clear C clear C Stack B C T on D T on B C on C A clear A on C A Stack C D A Goal INIT on C D on C D clear B ⎤ clear D clear D on B D ⎤ on C A clear D on B T Unstack B D ⎤ on B D clear B clear C A B C C B Causal link Unstack x (from y) Ordering Constraint D D Stack x on y (from z) A José-Luis Ambite
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