AAAI of 20 Deconstructing Planning as Satisfiability Henry Kautz University of Rochester in collaboration with Bart Selman and Jöerg Hoffmann

AAAI 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

AAAI 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

AAAI of 20 Satplan in 15 Seconds Time = bounded sequence of integers Translate planning operators to propositional schemas that assert:

AAAI of 20 International Planning Competition IPC-1998: Satplan (blackbox) is competitive

AAAI of 20 International Planning Competition IPC-2000: Satplan did poorly Satplan

AAAI of 20 International Planning Competition IPC-2002: we stayed home. Jeb Bush

AAAI 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

AAAI 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

AAAI of 20 What Changed? Small change in modeling –Modest improvement from 2004 to 2006 Significant change in SAT solvers!

AAAI 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)

AAAI of 20 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)

AAAI of 20 Domain-Independent Heuristic Planning Considered Harmful Solution Quality? Speed? Optimal planning algorithms BestModerate Domain-specific algorithms HighFast Domain-independent heuristic planning PoorHard to predict

AAAI 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)

AAAI of 20 Objections If speed is crucial, you still must use heuristic planners –For highly constrained planning problems, optimal planning is often faster than heuristic planning!

AAAI of 20 Constrainedness: Run Time

AAAI of 20 Constrainedness: Percent Solved

AAAI of 20 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

AAAI 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

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