Compact Tree Encodings for Planning as QBF Mal Valais Planning as - - PowerPoint PPT Presentation

Compact Tree Encodings for Planning as QBF

Olivier Gasquet, Dominique Longin, Frédéric Maris, Pierre Régnier, Maël Valais June 25, 2018

IRIT – Université Toulouse III (France)

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Planning as QBF and CTE framework Our contribution : exploring new encodings for faster solving

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Planning as QBF and CTE framework

What is QBF?

X0

• ne state =

∀ ∃ ∨ ∧ → ¬

SAT QBF = ∀b

X0 X0

two contexts using same variables

SAT QBF

+

• ne copy of each variable

less memory

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Why should QBF be explored?

• Satplan wins IPC’04 and IPC’06 due to improvements in

SAT solvers thanks to SAT competitions

• QBF solvers competitions are taking off, more and more

attention − → QBF solvers are (probably) going to get much faster

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X2 X1 X1 X0 X0 X0 X0

begin end

X3 X2 X1 X4 X5 X0 X6

begin end

SAT

O(log(n)) in memory space O(n) in memory space

planning QBF planning

(CTE)

− → Theoretically, much less memory used.

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In practice :

• Using SAT, No-ops are the best available transition
• Using QBF, No-ops uses 5× less memory but 30× slower

(from [Cashmore et al., 2012]) Question : could we find other CTE-based encodings yielding better results? Note we only work at the encoding level, not the solver-level

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Our contribution : exploring new encodings for faster solving

CTE-NOOP reference

Source SAT encoding

(No-ops)

Satplan

QBF

EFA OPEN

CTE-EFA CTE-OPEN

encoding

• ur work

(explanatory frame-axioms)

State-Space Planning from

(invented)

Plan-Space Planning from

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• Across most IPC domains (1 to 8)
• QBF solvers tested : RaREQS, DepQBF, Qute (Quantor too

slow)

• around 6000 hours of compute time (2112 problems tried

across 3 solvers)

• 1-hour timeout for solving the problem ”is there a plan?”
• QBF problems generated using TouIST and TouISTPlan
• https://github.com/touist/touist
• https://github.com/touist/touistplan

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Time between CTE encodings when solving ”is there a plan?” :

y = 0.4843x y = x 500 1000 1500 2000 2500 3000 3500 1000 2000 3000 Time in seconds (CTE-EFA) Time in seconds (CTE-NOOP) y = 0.5953x y = x 500 1000 1500 2000 2500 3000 3500 1000 2000 3000 Time in seconds (CTE-OPEN) Time in seconds (CTE-NOOP)

CTE-OPEN is 1.7× faster CTE-EFA is 2× faster

(compared to CTE-NOOP)

We went from 30× to only 15× slower than Satplan!

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Practical shortcoming : we can only handle a depth of 3, i.e., maximum plan span of 15 steps!

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Metrics for explaining this 2× improvement?

• Number of literals and number of clauses
• Ratio between types of transitions (branch-based

constraints over node-based constraints)

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Encoding Nb solved Time Literals Clauses Transitions ratio CTE-NOOP 412 (20%) 0% 0% 0% 30% CTE-EFA 463 (22%)

• 55%
• 26%

+15% 47% CTE-OPEN 445 (21%)

• 41%
• 2%
• 28%

17%

Not very helpful :

• Number of literals and number of clauses : no pattern
• Type of transitions (node/branch) : no pattern

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Conclusion

To sum up :

• A systematic way of translating encodings from SAT into

QBF

• As a result, two new encodings improving over the

existing CTE-NOOP

• A large set of benchmarks generated using all IPC

problems Future :

• Publish our new benchmarks (QBFEVAL) for pushing QBF

solvers to get better on this area

• Find more metrics for explaining and exploiting these

improvements

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Cashmore, M., Fox, M., and Giunchiglia, E. (2012). Planning as quantified boolean formula. In Raedt, L. D., Bessière, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., and Lucas, P. J. F., editors, ECAI 2012 - 20th European Conference on Artificial Intelligence. Including Prestigious Applications of Artificial Intelligence (PAIS-2012) System Demonstrations Track, Montpellier, France, August 27-31 , 2012, volume 242 of Frontiers in Artificial Intelligence and Applications, pages 217–222. IOS Press. Kautz, H. (2004). Satplan04 : Planning as satisfiability. In Abstracts of the 4th International Planning Competition, IPC-04. Kautz, H., Selman, B., and Hoffmann, J. (2006). SatplanÕ04 : Planning as satisfiability.

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In Abstracts of the 5th International Planning Competition, IPC-06.

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