Deconstructing Planning as Satisfiability

1. Deconstructing Planning as Satisfiability Henry Kautz University of Rochester in collaboration with Bart Selman and Jöerg Hoffmann

2. 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. 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

4. Satplan in 15 Seconds • Time = bounded sequence of integers • Translate planning operators to propositional schemas that assert:

5. International Planning Competition • IPC-1998: Satplan (blackbox) is competitive

6. International Planning Competition • IPC-2000: Satplan did poorly Satplan

7. International Planning Competition • IPC-2002: we stayed home. Jeb Bush

8. International Planning Competition • IPC-2004: 1st place, Optimal Planning • Best on 5 of 7 domains • 2nd best on remaining 2 domains PROLEMA / philosophers

9. International Planning Competition • IPC-2006: Tied for 1st place, Optimal Planning • Other winner, MAXPLAN, is a variant of Satplan!

10. What Changed? • Small change in modeling • Modest improvement from 2004 to 2006 • Significant change in SAT solvers!

11. 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)

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

13. Domain-Independent Heuristic Planning Considered Harmful

14. 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)

15. Objections • If speed is crucial, you still must use heuristic planners • For highly constrained planning problems, optimal planning is often faster than heuristic planning!

16. Constrainedness: Run Time

17. Constrainedness: Percent Solved

18. Further Extensions to Satplan • Probabilistic planning • Translation to stochastic satisfiability (Majercik & Littman 1998) • Translation to weighted model-counting (Hoffmann 2006) • Solved by modified DPLL solver, Cachet (Sang, Beame, & Kautz 2005) • Competitive with best probabilistic planners

19. 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

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 optimal planning • Not restricted to STRIPS any more! • Numeric constraints • Probabilistic planning • Large domains