1. CS444-Autumn-20061 of 20 Planning as Satisfiability Henry Kautz University of Rochester in collaboration with Bart Selman and Jöerg Hoffmann

2. CS444-Autumn-20062 of 20 AI Planning Two traditions of research in planning: –Planning as general inference (McCarthy 1969) Important task is modeling –Planning as human behavior (Newell & Simon 1972) Important task is to develop search strategies

3. CS444-Autumn-20063 of 20 Satplan Model planning as Boolean satisfiability –(Kautz & Selman 1992): Hard structured benchmarks for SAT solvers –Pushing the envelope: planning, propositional logic, and stochastic search (1996) Can outperform best current planning systems Satplan (satz)Graphplan (IPP) log.a5 sec31 min log.b7 sec13 min log.c9 sec> 4 hours

4. CS444-Autumn-20064 of 20 Translating STRIPS Ground action = a STRIPS operator with constants assigned to all of its parameters Ground fluent = a precondition or effect of a ground action operator: Fly(a,b) precondition: At(a), Fueled effect: At(b), ~At(a), ~Fueled constants: NY, Boston, Seattle Ground actions: Fly(NY,Boston), Fly(NY,Seattle), Fly(Boston,NY), Fly(Boston,Seattle), Fly(Seattle,NY), Fly(Seattle,Boston) Ground fluents: Fueled, At(NY), At(Boston), At(Seattle)

5. CS444-Autumn-20065 of 20 Clause Schemas A large set of clauses can be represented by a schema

6. CS444-Autumn-20066 of 20 Satplan in 15 Seconds Time = bounded sequence of integers Translate planning operators to propositional schemas that assert:

7. CS444-Autumn-20067 of 20 Example If an action occurs at time i, then its preconditions must hold at time i If an action occurs at time i, then its effects must hold at time i+1

8. CS444-Autumn-20068 of 20 SAT Encoding If a fluent changes its truth value from time i to time i+1, one of the actions with the new value as an effect must have occurred at time i Like “for”, but connects propositions with OR

9. CS444-Autumn-20069 of 20 Plan Graph Based Instantiation initial state: p action a: precondition: p effect:  p action b: precondition:  p effect: p  q a0a1 p0p1p2 b1 m0m1 q2 ==

10. CS444-Autumn-200610 of 20 International Planning Competition IPC-1998: Satplan (blackbox) is competitive

11. CS444-Autumn-200611 of 20 International Planning Competition IPC-2000: Satplan did poorly Satplan

12. CS444-Autumn-200612 of 20 International Planning Competition IPC-2002: we stayed home. Jeb Bush

13. CS444-Autumn-200613 of 20 International Planning Competition IPC-2004: 1 st place, Optimal Planning –Best on 5 of 7 domains –2 nd best on remaining 2 domains PROLEMA / philosophers

14. CS444-Autumn-200614 of 20 The IPC-4 Domains Airport: control the ground traffic [Hoffmann & Trüg] Pipesworld: control oil product flow in a pipeline network [Liporace & Hoffmann] Promela: find deadlocks in communication protocols [Edelkamp] PSR: resupply lines in a faulty electricity network [Thiebaux & Hoffmann] Satellite & Settlers [Fox & Long], additional Satellite versions with time windows for sending data [Hoffmann] UMTS: set up applications for mobile terminals [Edelkamp & Englert]

15. CS444-Autumn-200615 of 20 International Planning Competition IPC-2006: Tied for 1 st place, Optimal Planning –Other winner, MAXPLAN, is a variant of Satplan! CPT2MIPS-BDDSATPLANMaxplanFDP Propositional Domains (1 st / 2 nd Places) 0 / 11 / 13 / 2 0 / 3 Temporal Domains (1 st / 2 nd Places) 2 / 0

16. CS444-Autumn-200616 of 20 What Changed? Small change in modeling –Modest improvement from 2004 to 2006 Significant change in SAT solvers!

17. CS444-Autumn-200617 of 20 What Changed? In 2004, competition introduced the optimal planning track –Optimal planning is a very different beast from non- optimal planning! –In many domains, it is almost trivial to find poor- quality solutions by backtrack-free search! E.g.: solutions to multi-airplane logistics planning problems found by heuristic state-space planners typically used only a single airplane! –See: Local Search Topology in Planning Benchmarks: A Theoretical Analysis (Hoffmann 2002)

18. CS444-Autumn-200618 of 20 Why Care About Optimal Planning? Real users want (near)-optimal plans! –Industrial applications: assembly planning, resource planning, logistics planning… –Difference between (near)-optimal and merely feasible solutions can be worth millions of dollars Alternative: fast domain-specific optimizing algorithms –Approximation algorithms for job shop scheduling –Blocks World Tamed: Ten Thousand Blocks in Under a Second (Slaney & Thiébaux 1995)

19. CS444-Autumn-200619 of 20 Domain-Independent Feasible Planning Considered Harmful Solution Quality? Speed? General optimizing planning algorithms BestModerate Domain-specific optimizing planning algorithms HighFast Domain-independent feasible planning ??

20. CS444-Autumn-200620 of 20 Objections Real-world planning cares about optimizing resources, not just make-span, and Satplan cannot handle numeric resources –We can extend Satplan to handle numeric constraints –One approach: use hybrid SAT/LP solver (Wolfman & Weld 1999) –Modeling as ordinary Boolean SAT is often surprisingly efficient! (Hoffmann, Kautz, Gomes, & Selman, under review)

21. CS444-Autumn-200621 of 20 Projecting Variable Domains initial state: r=5 action a: precondition: r>0 effect: r := r-1 Resource use represented as conditional effects a1 r=5 r=4 a0 r=4

22. CS444-Autumn-200622 of 20 2002 ICAPS Benchmarks

23. CS444-Autumn-200623 of 20 Large Numeric Domains Directly encode binary arithmetic action: a precondition: r  k effect: r := r-k a1 r1 1 + -k r2 1 r3 1 r4 1 r1 2 r2 2 r3 2 r4 2

24. CS444-Autumn-200624 of 20 Objections If speed is crucial, you still must use feasible planners –For highly constrained planning problems, optimal planners can be faster than feasible planners!

25. CS444-Autumn-200625 of 20 Constrainedness: Run Time

26. CS444-Autumn-200626 of 20 Constrainedness: Percent Solved

27. CS444-Autumn-200627 of 20 Further Extensions to Satplan Probabilistic planning –Translation to stochastic satisfiability (Majercik & Littman 1998) –Alternative untested idea: Encode action “failure” as conditional resource consumption Can find solutions with specified probability of failure-free execution (Much) less general than full probabilistic planning (no fortuitous accidents), but useful in practice

28. CS444-Autumn-200628 of 20 Encoding Bounded Failure Free Probabilistic Planning plan failure free probability  0.90 action: a failure probability: 0.01 preconditions: p effects: q action: a precondition: p  s  log(0.89) effect: q  s := s + log(0.99)

29. CS444-Autumn-200629 of 20 One More Objection! Satplan-like approaches cannot handle domains that are too large to fully instantiate –Solution: SAT solvers with lazy instantiation –Lazy Walksat (Singla & Domingos 2006) Nearly all instantiated propositions are false Nearly all instantiated clauses are true Modify Walksat to only keep false clauses and a list of true propositions in memory

30. CS444-Autumn-200630 of 20 Summary Satisfiability testing is a vital line of research in AI planning –Dramatic progress in SAT solvers –Recognition of distinct and important nature of optimizing planning versus feasible planning SATPLAN not restricted to STRIPS any more! –Numeric constraints –Probabilistic planning –Large domains