International audienceThis paper provides a short system description of our new portfolio-based solver called PeneLoPe, based on ManySat. Particularly, this solver focuses on collaboration between threads, providing different policies for exporting and importing learnt clauses between CDCL searches. Moreover, different restart strategies are also available, together with a deterministic mode

Audemard, Gilles

Hoessen, Benoît

Jabbour, Said

Lagniez, Jean-Marie

Piette, Cédric

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PeneLoPe, a Parallel Clause-Freezer Solver

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PeneLoPe, a Parallel Clause-Freezer SolverGilles Audemard, Benoˆıt Hoessen, Said Jabbour, Jean-Marie Lagniez, Ce´dricPietteTo cite this version:Gilles Audemard, Benoˆıt Hoessen, Said Jabbour, Jean-Marie Lagniez, Ce´dric Piette. PeneLoPe,a Parallel Clause-Freezer Solver. SAT Challenge 2012: Solver and Benchmarks Descriptions,2012, France. pp.43-44, 2012. <hal-00865592>HAL Id: hal-00865592https://hal.archives-ouvertes.fr/hal-00865592Submitted on 24 Sep 2013HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.PeneLoPe, a parallel clause-freezer solverGilles Audemard, Benoıˆt Hoessen, Saı¨d Jabbour, Jean-Marie Lagniez, Ce´dric PietteUniversite´ Lille-Nord de FranceCRIL - CNRS UMR 8188Artois, F-62307 Lens{audemard,hoessen,jabbour,lagniez,piette}@cril.frAbstract—This paper provides a short system descriptionof our new portfolio-based solver called PeneLoPe, basedon ManySat. Particularly, this solver focuses on collaborationbetween threads, providing different policies for exporting andimporting learnt clauses between CDCL searches. Moreover,different restart strategies are also available, together with adeterministic mode.I. OVERVIEWPeneLoPe is a portfolio parallel SAT solver that uses themost effective techniques proposed in the sequential frame-work: unit propagation, lazy data structures, activity-basedheuristics, progress saving for polarities, clause learning, etc.As for most of existing solvers, a first preprocessing step isachieved. For this step -which is typically sequential- we havechosen to make use of SatElite [3].In addition, PeneLoPe includes a recent technique forits learnt clause database management. Roughly, this newapproach follows this schema: each learnt clause c is peri-odically evaluated with a so-called psm measure [1], whichis equal to the size of the set-theoretical intersection of thecurrent interpretation and c. Clauses that exhibit a low psmare considered relevant. Indeed, the lower is a psm value, themore likely the related clause is about to unit-propagate someliteral, or to be falsified. On the opposite, a clause with a largepsm value has a lot of chance to be satisfied by many literals,making it irrelevant for the search in progress.Thus, only clauses that exhibit a low psm are selectedand currently used by the solver, the other clauses beingfrozen. When a clause is frozen, it is removed from the listof the watched literals of the solver, in order to avoid thecomputational over-cost of maintaining the data structure ofthe solver for this useless clause. Nevertheless, a frozen clauseis not erased but it is kept in memory, since this clause maybe useful in the next future of the search. As the currentinterpretation evolves, the set of learnt clauses actually usedby the solver evolves, too. In this respect, the psm valueis computed periodically, and sets of clauses are frozen orunfrozen with respect to their freshly computed new value.Let Pk be a sequence where P0 = 500 and Pi+1 =Pi+500+100× i. A function ”updateDB” is called each timethe number of conflict reaches Pi conflicts (where i ∈ [0..∞]).This function computes new psm values for every learntclauses (frozen or activated). A clause that has a psm valueless than a given limit l is activated in the next part of thesearch. If its psm does not hold this condition, then it is frozen.Moreover, a clause that is not activated after k (equal to 7 bydefault) time steps is deleted. Similarly, a clause remainingactive more than k steps without participating to the search isalso permanently deleted (see [1] for more details).Besides the psm technique, PeneLoPe also makes use ofthe lbd value defined in [2]. lbd is used to estimate the qualityof a learnt clause. This new measure is based on the numberof different decision levels appearing in a learnt clause and iscomputed when the clause is generated. Extensive experimentsdemonstrates that clauses with small lbd values are used moreoften than those with higher lbd ones. Note also that lbdof clauses can be recomputed when they are used for unitpropagations, and updated if it becomes smaller. This updateprocess is important to get many good clauses.Given these recently defined heuristic values, we present inthe next Section several strategies implemented in PeneLoPe.II. DETAILLED FEATURESPeneLoPe proposes a certain number of strategies regard-ing importation and exportation of learnt clauses, restarts, andthe possibility of activating a deterministic mode.Importing clause policy: When a clause is imported, we canconsider different cases, depending on the moment the clauseis attached for participating to the search.• no-freeze: each imported clause is actually stored with thecurrent learnt database of the thread, and will be evaluated(and possibly frozen) during the next call to updateDB.• freeze-all: each imported clause is frozen by default, andis only used later by the solver if it is evaluated relevantw.r.t. unfreezing conditions.• freeze: each imported clause is evaluated as it wouldhave been if locally generated. If the clause is consideredrelevant, it is added to the learnt clauses, otherwise it isfrozen.Exporting clause policy: Since PeneLoPe can freezeclauses, each thread can import more clauses than it wouldwith a classical management of clauses, where all of them areattached. Then, we propose different strategies, more or lessrestrictive, to select which clauses have to be shared:• unlimited: any generated clause is exported towards thedifferent threads.• size limit: only clauses whose size is less than a givenvalue are exported [5].• lbd limit: a given clause c is exported to other threads ifits lbd value lbd(c) is less than a given limit value d (8by default). Let us also note that the lbd value can varyover time, since it is computed with respect to the currentinterpretation. Therefore, as soon as lbd(c) is less than d,the clause is exported.Restarts policy: Beside exchange policies, we define tworestart strategies.• Luby: Let li be the ith term of the Luby serie. The ithrestart is achieved after li × α conflicts (α is set to 100by default).• LBD [2]: Let LBDg be the average value of the LBD ofeach learnt clause since the beginning. Let LBD100 bethe same value computed only for the last 100 generatedlearnt clause. With this policy, a restart is achieved assoon as LBD100×α > LBDg (α is set to 0.7 by default).In addition, the VSIDS score of variables that are unit-propagated thank for a learnt clause whose lbd is equalto 2 are increased, as detailled in [2].Furthermore, we have implemented in PeneLoPe a deter-ministic mode which ensures full reproducibility of the resultsfor both runtime and reported solutions (model or refutationproof). Large experiments show that such mecanism does notaffect significantly the solving process of portfolio solvers[4]. Quite obviously, this mode can also be unactivated inPeneLoPe.III. FINE TUNING PARAMETERS OF PENELOPEPeneLoPe is designed to be fine-tuned in an easy way,namely without having to modify its source code. To thisend, a configuration file (called configuration.ini, anexample is provided in Figure 1) is proposed to describe thedefault behavior of each thread. This file actually containsnumerous parameters that can be modified by the user beforerunning the solver. For instance, besides export, import andrestart strategies, one can choose the number of threads thatthe solver uses, the α factor if the Luby techniques is activatedfor the restart strategy, etc. Each policy and/or value canobviouly differ from one thread to the other, in order to ensurediversification.ACKNOWLEDGMENTPeneLoPe has been partially developped thank to thefinancial support of CNRS and OSEO, under the ISI project“Pajero”.REFERENCES[1] Gilles Audemard, Jean-Marie Lagniez, Bertrand Mazure, and LakhdarSaı¨s. On freezeing and reactivating learnt clauses. In proceedings ofSAT, pages 147–160, 2011.[2] Gilles Audemard and Laurent Simon. Predicting learnt clauses quality inmodern SAT solvers. In proceedings of IJCAI, pages 399–404, 2009.[3] N. Ee´n and A. Biere. Effective preprocessing in SAT through variableand clause elimination. In proceedings of SAT, pages 61–75, 2005.[4] Youssef Hamadi, Said Jabbour, Ce´dric Piette, and Lakhdar Saı¨s. Deter-ministic parallel DPLL. Journal on Satisfiability, Boolean Modeling andComputation, 7(4):127–132, 2011.[5] Youssef Hamadi, Saı¨d Jabbour, and Lakhdar Sais. Control-based clausesharing in parallel SAT solving. In proceedings of IJCAI, pages 499–504,2009.1 ncores = 82 d e t e rm i n i s t i c = f a l s e3 ; t h i s i s t h e d e f a u l t b e h a v i o r o f each4 ; t h r e a d , can be m o d i f i e d o r s p e c i f i e d5 ; a f t e r each [ s o l v e r X ] i t em6 [ d e f a u l t ]7 ; i f s e t t o t r u e , t h e n psm i s used8 usePsm = t r u e9 ; a l l o w e d v a l u e s : avgLBD , luby10 r e s t a r t P o l i c y = avgLBD11 ; a l l o w e d v a l u e s : lbd , u n l i m i t e d , s i z e12 expor tPo l i c y = l b d13 ; a l l o w e d v a l u e s :14 ; f r e e z e , no−f r e e z e , f r e e z e−a l l15 impor tPo l i cy = f r e e z e16 ; number o f f r e e z e b e f o r e t h e c l a u s e17 ; i s d e l e t e d18 maxFreeze = 719 ; i n i t i a l # c o n f l i c t b e f o r e t h e f i r s t20 ; updateDB21 i n i t i a lNbCon f l i c tBe f o r eReduce = 50022 ; i n c r e m e n t a l f a c t o r f o r updateDB23 nbConf l ic tBeforeReduceIncrement = 10024 ; maximum l b d v a l u e f o r exchanged c l a u s e s25 maxLBDExchange = 826 [ s o l v e r 0 ]27 impor tPo l i cy = no−f r e e z e28 [ s o l v e r 1 ]29 i n i t i a lNbCon f l i c tBe f o r eReduce = 500030 nbConf l ic tBeforeReduceIncrement = 100031 [ s o l v e r 2 ]32 maxFreeze = 833 ; s o l v e r 3 i s t h e d e f a u l t s o l v e r34 [ s o l v e r 3 ]35 [ s o l v e r 4 ]36 r e s t a r t P o l i c y = l uby37 lubyFactor = 10038 [ s o l v e r 5 ]39 expor tPo l i c y = s i z e40 [ s o l v e r 6 ]41 maxFreeze = 442 [ s o l v e r 7 ]43 impor tPo l i cy = f r e e z e−a l lFig. 1. Configuration.ini file

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PeneLoPe, a Parallel Clause-Freezer Solver

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