Captain Jack: New Variable Selection Heuristics in Local Search for SAT

Transcription

1 Captain Jack: New Variable Selection Heuristics in Local Search for SAT Dave Tompkins, Adrian Balint, Holger Hoos SAT 2011 :: Ann Arbor, Michigan

2 Key Contribution: Captain Jack is a highly parametric algorithm Incorporates elements from Sparrow [Balint, Fröhlich, SAT 2010] & VE-Sampler [Tompkins, Hoos, SAT 2010] good performance "jack of all trades" "interesting" configuration space 2

3 Algorithm Design Philosophy Parameterless Algorithm 3

4 Algorithm Design Philosophy Algorithm Parameters Parameterless Algorithm 4

5 Algorithm Design Philosophy Parameterless Algorithm Highly Parametric Algorithm 5

6 Automated Configuration We can use automated configuratorsto determine the optimal algorithm parameters for a target instance set We used ParamILS [Hutteret al., 2007, 2009] Offload tedious human tasks to machines 6

7 Automated Configuration Training Instance Set Automated Configurator (here: ParamILS) Highly Parametric Algorithm Tuned (configured) Algorithm 7

8 Instance "Space" pt 8

9 Instance "Space" Software Verification a graph colouring... SWV b SWV c pt Hardware Verification x HWV y 4.2 c/v pt planning... 9

10 Algorithm "Space" 10

11 Captain Jack good performance "interesting" configuration space 11

12 Overview Motivation Captain Jack Background Design New Contributions Results Future Work Conclusions 12

13 Stochastic Local Search (SLS) for SAT ( x 1 x 2 x 5 ) randomly initialize all variables while (formula not satisfied) select a variable and flip it Evaluate each variable (Variable Expression) Variable Selection Mechanism (VSM) 13

14 Captain Jack Controller Promising Variable? no select UNSAT clause Captain Jack can use promising variables (if they exist) [G 2 WSAT: Li, Huang, 2005] Select UNSAT clause uniformly at random [Papadimitriou, 1991] [WalkSAT: Selman, Kautz, Cohen, 1994] 14

15 Captain Jack Controller promising variable? no select UNSAT clause select type: greedy / div. / mixed Captain Jack can use promising variables (if they exist) [G 2 WSAT: Li, Huang, 2005] Select UNSAT clause uniformly at random [Papadimitriou, 1991] [WalkSAT: Selman, Kautz, Cohen, 1994] select property(ies) select VSM: max or distribution 15

16 Variable Properties Greedy Properties make= # of clauses that become satisfiedif we flip x break =... unsatisfied score = (make break) [GSAT: Selman, Levesque, Mitchell, 1992] 16

17 Variable Properties Greedy Properties make = # of clauses that become satisfied if we flip x break =... unsatisfied score = (make break) [GSAT: Selman, Levesque, Mitchell, 1992] Diversification Properties age= # of steps since x was flipped[tabu: Glover, 1986] flips= # of times x has been flipped [HSAT: Gent, Walsh, 1993] 17

18 Variable Properties Greedy Properties make = # of clauses that become satisfied if we flip x break =... unsatisfied score = (make break) [GSAT: Selman, Levesque, Mitchell, 1992] Diversification Properties age = # of steps since x was flipped[tabu: Glover, 1986] flips = # of times x has been flipped [HSAT: Gent, Walsh, 1993] Variable Expressions sparrowage 18

19 Captain Jack Variable Properties Greedy make break score sparrowscore 2 score scoreratio rel* Diversification rand flat fair last age age 1 age 5 agerange sparrowage tabu flips flops normflops resetflops rel* 19

20 New Variable Properties scoreratio: (make)/(make + break) flops: flops++ flops++ ( x 1 x 2 x 5 ) flips++ 20

21 age k property age 5 age x 1 T F time age 1 21

22 Captain Jack Controller promising variable? no select UNSAT clause select type: greedy / div. / mixed select property(ies) select VSM: max or distribution 22

23 Mixed Variable Expressions VE-Sampler f(greedy) + f(diversification) Sparrow f(greedy) f(diversification) both use a mixedve First introduced with VW2 [Prestwich, 2005] Captain Jack 3 Options: greedy, diversification, mixed greedy diversification 23

24 Variable Selection Mechanism ( x 1 x 2 x 5 ) Variable Expression Maximum ("best") select x 1 x 1 5 x 2 4 x 5 1 Probability Distribution select x 1 50% select x 2 40% select x 5 10% 24

25 Captain Jack Controller promising variable? no select UNSAT clause select type: greedy / div. / mixed Each type of step assigned a weight (%) select property(ies) Each property is assigned a weight (%) (both a greedy & div. property selected for mixed) select VSM: max or distribution Prob. of selecting the VSM is based on the type 25

26 Captain Jack good performance "interesting" configuration space 26

27 Instance "Space" Industrial-Like Random (Ansótegui et. al., 2009) Software Verification CBMC (binary search) SWV (static checking) Random k-sat: 3-SAT pt, large 4.2) 5-SAT pt, large) 7-SAT pt, large) 27

28 Performance Results 3-SAT 5-SAT 7-SAT 1k 10k IL50k CBMC SWV Captian Jack Sparrow* VE-Sampler* SATenstein* TNM , gnovelty ,291 AG , time relative to fastest solver [PAR10]

29 Greedy Properties (%) 3-SAT 5-SAT 7-SAT 1k 10k IL50k CBMC SWV make* break* score* sparrowscore scoreratio* property weights as percentages, values 1 not shown 29

30 Diversification Properties 3-SAT 5-SAT 7-SAT 1k 10k IL50k CBMC SWV random/flat/fair last age* flips* flops* property weights as percentages, values 1 not shown 30

31 Age-based Properties 3-SAT 5-SAT 7-SAT 1k 10k IL50k CBMC SWV age age age agerange 7 3 sparrowage tabu property weights as percentages, values 1 not shown 31

32 Cross-Testing time relative to target configuration [PAR10] 32

33 Additional Observations No promising steps for CMBC & SWV Mixed Steps were preferred Variable Selection: No clear winner between: Max/Probability Distribution No clear results on clause-length settings 33

34 Key Contributions CJ is a new highly parametricsls algorithm Introduced several new variable properties Performs well on both random, industrial* and industrial-like Insights into configurations and properties used on different instances 34

35 Future Work age k properties framework to introduce new properties "knock-out" algorithm properties adaptive strategies lead to specialized light-weight algorithms thanks... 35

36 arrrr... there any questions? 36