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Algorithm Configuration for Portfolio-based Parallel SAT-Solving Holger Hoos 1 , Kevin Leyton-Brown 1 , Torsten Schaub 2 , Marius Schneider 2 1 Department of Computer Science University of British Columbia Vancouver, BC, Canada 2 Institute of

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Algorithm Configuration for Portfolio-based Parallel SAT-Solving

Holger Hoos1, Kevin Leyton-Brown1, Torsten Schaub2, Marius Schneider2

1 Department of Computer Science

University of British Columbia Vancouver, BC, Canada

2Institute of Computer Science

University of Potsdam Potsdam, Germany

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The rise of main-stream multi-core computing

http://software.intel.com/en-us/articles/gaming-into-the-future Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 2

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Parallel SAT Solvers

2008 SAT RACE 2009 SAT Comp. 2010 SAT RACE 2011 SAT Comp. ManySat gNovelty+-T antom borg-sat MiraXT ManySAT ManySAT clasp pMiniSat satake plingeling csls ttsth PMiniSAT CryptoMiniSAT SArTagnan Plingeling ppfolio ◮ (Slowly) increasing number of parallel SAT solvers ◮ Designing effective parallel solvers is challenging!

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 3

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Key idea: Automatically generate parallel solver Key idea: from highly parametric sequential design / sources

application context planner planner solver

ptimised

solver parallel portfolio instance- based selector design space

f solvers

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 4

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Parallel SAT Solving

◮ Search space splitting

e.g., clasp with guiding path

◮ Competitive parallel portfolio with clause sharing

e.g., Plingeling and CryptoMiniSat

◮ Competitive parallel portfolio w/o clause sharing

e.g., Plingeling and CryptoMiniSat

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 5

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Ingredients for parallel SAT solver

based on competitive parallel portfolio ◮ Parametric solver A ◮ Configuration space C ◮ Instance set I ◮ Algorithm configurator AC

That’s all!

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 6

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Recipe for parallel SAT solver

based on competitive parallel portfolio

1. Use algorithm configurator to produce multiple configurations
f given solver that work well together
2. Run configurations in parallel until one solves given instance

Fully automatic method!

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 7

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Recipe: Global

for parallel SAT solver based on competitive parallel portfolio ◮ For k portfolio components (= processors/threads), consider

combined configuration space C k of k copies of given parametric solver

◮ Use configurator AC to find good joint configuration in C k

(standard protocol for current configurators: pick best result from multiple independent runs)

◮ Configurations are assessed using (training) instance set I

Challenge: Large configuration spaces (exponential in k)

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 8

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Recipe: Greedy

for parallel SAT solver based on competitive parallel portfolio ◮ Add portfolio components, one at a time,

starting from single solver

◮ Iteration 1: Configure given solver A using configurator AC

single-component portfolio A1

◮ Iteration j = 2 . . . k: Configure given solver A using AC

to achieve optimised performance of extended portfolio A j := A j−1 || A i.e., optimise improvement in A j over A j−1 Note: Similar idea to many greedy constructive algorithms (including Hydra, Xu et al. 2010)

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 9

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Product: parallel Lingeling (v.276)

n SAT Comp. Application instances

PAR10 Overall Speedup

Avg. Speedup

vs Configured-SP vs Configured-SP Default-SP 3747 0.93 1.44 Configured-SP 3499 1.00 1.00 Plingeling 3066 1.14 7.39 Global-MP4 2734 1.27 10.47 Greedy-MP4 1341 2.61 3.52

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 10

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Product: parallel Lingeling (v.276)

n SAT Comp. Application instances

1 10 100 1000 1 10 100 1000 runtime Greedy-MT4 [s] runtime Conf-SP [s]

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Product: parallel clasp (v.2.0.2)

n SAT Comp. Application instances

PAR10 Overall Speedup

Avg. Speedup

vs Configured-SP vs Configured-SP Default-SP 7560 0.82 4.46 Configured-SP 6170 1.00 1.00 Default-MP4 2324 2.65 7.58 Global-MP4 3604 1.71 6.36 Greedy-MP4 2277 2.71 9.47

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Product: parallel clasp (v.2.0.2)

n SAT Comp. Application instances

1 10 100 1000 1 10 100 1000 runtim Greedy-MT4 [s] runtime Conf-ST [s]

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 13

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Conclusions

◮ Parallel SAT solving is gaining importance ◮ Designing high-performance parallel SAT solvers can be

challenging

◮ Fully automatic method:

1. Use algorithm configurator to produce multiple configurations
f given solver that work well together
2. Run configurations in parallel until one solves given instance

◮ At least as good as hand-crafted parallel SAT solvers

Hoos, Leyton-Brown, Schaub, Schneider: Algorithm Configuration for Portfolio-based Parallel SAT-Solving 14

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Future Work

◮ Parallel portfolios with different solvers ◮ New configuration protocols / configurators ◮ Generic mechanisms for cooperation between

portfolio members

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