Graphplan CSE 574 April 4, 2003 Dan Weld

Schedule BASICS Intro Graphplan SATplan State-space Refinement SPEEDUP EBL & DDB Heuristic Gen TEMPORAL Partial-O Graphplan Forward- chaining Stochastic Linear prog

Graphplan Review Expand plan graph Derive mutex relationships If goals are present & consistent search for a solution

The Plan Graph … … … level 0level 2level 4level 6 level 1level 3level 5

Graph Expansion Proposition level 0 initial conditions Action level i no-op for each proposition at level i-1 action for each operator instance whose preconditions exist at level i-1 Proposition level i effects of each no-op and action at level i … … … … i-1ii+10

Mutual Exclusion Two actions are mutex if one clobbers the other’s effects or preconditions they have mutex preconditions Two proposition are mutex if all ways of achieving them are mutex

Searching for a solution If goals are present & non-mutex: Choose action to achieve each goal Add preconditions to next goal set

Wrinkles Forward checking Memoization Consider only minimal {a} achieving G

Important Ideas Polytime graph construction Use for deriving properties, termination, admissible heuristic, unsolvable problems Mutex for pruning search Insensitivity to goal ordering Knows when no plan exists

Experiments Fairness Different machines, languages Testing what? Using what? “Natural domains” Artifical Domains Conclusions (no ablation) Effect of mutex, parallelism, memoizing, preproc

Flaws? When / why does GP perform poorly? (figs 6-8) Independent goals?

Optimality Does GP generate optimal plans in any sense? Could it be made to do so?

Future Work Space Usage Connection to CSP Search methods Symmetry detection Complexity of determining true mutex Expressive Languages Conditional effects,  Stochastic actions Temporal planning Continuous parameters Propagate More Info thru Graph Backward or bidirectional search

Observation 1 Propositions monotonically increase (always carried forward by no-ops) p ¬q ¬r p q ¬q ¬r p q ¬q r ¬r p q ¬q r ¬r A A B A B

Observation 2 Actions monotonically increase p ¬q ¬r p q ¬q ¬r p q ¬q r ¬r p q ¬q r ¬r A A B A B

Observation 3 Proposition mutex relationships monotonically decrease pqr…pqr… A pqr…pqr… pqr…pqr…

Observation 4 Action mutex relationships monotonically decrease pq…pq… B pqrs…pqrs… pqrs…pqrs… A C B C A pqrs…pqrs… B C A

New Representation Propositions Actions pqrs…pqrs… ABCD…ABCD…

Mutex Relationships pqrs…pqrs… ABCD…ABCD…  7 8 Propositions Actions

Plan Graph pqrs…pqrs… ABCD…ABCD…  7 6 Props & actions: start level  start time Mutex relations: end level  end time

Perverting Graphplan ADL Gazen & Knoblock Koehler Anderson, Smith & Weld Boutilier Uncertainty Rao Graphplan Time Smith & Weld Koehler ? PGP Blum & Langford Conformant Smith & Weld Sensory/Contingent Weld, Anderson & Smith ?

Expressive Languages 1 Negated preconditions Disjunctive preconditions Universally quantified preconditions, effects Conditional effects

Negated Preconditions Graph expansion P,  P mutex Action deleting P must add  P at next level Solution extraction

Disjunctive Preconditions Convert precondition to DNF Disjunction of conjunctions Graph expansion Add action if any disjunct is present, nonmutex Solution extraction Consider all disjuncts

Universal Quantification Graph Expansion Solution Extraction

Universal Quantification Graph Expansion Expand action with Herbrand universe  block x P(x)  P(o 17 )  P(o 74 )  …  P(o 126 ) Solution Extraction No changes necessary What if an action creates or delete objs?

Conditional Effects

Full Expansion in-keys in-pay

Comments?

Factored Expansion Treat conditional effects as primitive “component” = pair DNF pure conj. STRIPS action has one component Consider action A Precond: p Effect: e (when q (f   g) (when (r  s)  q) A has three components: antecedant consequent p e p  q f   g p  r  s  q

Changes to Expansion Components C1 and C2 are mutex at level I The antecedants of C1 and C2 are mutex at I-1 C1, C2 come from different action instances, & The consequent of C1 deletes the antecedant of C2 Or vice versa  C, C1 induces C and C is mutex with C2 Intuitively, C1 induces C if it is impossible to execute C1 without executing C. C1 and C are parts of same action instance C1 and C aren’t mutex (antecedants not inconsistent) The negation of C’s antecedant can’t be satisfied at level I-1

Induced Mutex

Revised Backchaining Confrontation Subgoaling on negation of something