Machine Learning-Based Restart Policy for CDCL SAT Solvers

Jia, Liang; Oh, Chanseok; Mathew, Minu; Thomas, Ciza; Li, Chunxiao; Ganesh, Vijay

doi:10.1007/978-3-319-94144-8_6

Cited by 38 publications

(28 citation statements)

References 21 publications

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“…We have implemented in Python the ILP model and in PySat [12] the SAT Encoding discussed in Section 3. We use Gurobi 9.1.1 as ILP solver and Maplesat [15] as SAT solver. The experiments are run on a Dell Workstation with a Intel Xeon W-2155 CPU with 10 physical cores at 3.3GHz and 32 GB of RAM.…”

Section: Computational Resultsmentioning

confidence: 99%

A SAT Encoding to Compute Aperiodic Tiling Rhythmic Canons

Auricchio¹,

Ferrarini²,

Gualandi³

et al. 2021

Preprint

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In Mathematical Music theory, the Aperiodic Tiling Complements Problem consists in finding all the possible aperiodic complements of a given rhythm A. The complexity of this problem depends on the size of the period n of the canon and on the cardinality of the given rhythm A. The current state-of-the-art algorithms can solve instances with n smaller than 180. In this paper we propose an ILP formulation and a SAT Encoding to solve this mathemusical problem, and we use the Maplesat solver to enumerate all the aperiodic complements. We validate our SAT Encoding using several different periods and rhythms and we compute for the first time the complete list of aperiodic tiling complements of standard Vuza rhythms for canons of period n " t180, 420, 900u.

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Section: Computational Resultsmentioning

confidence: 99%

A SAT Encoding to Compute Aperiodic Tiling Rhythmic Canons

Auricchio¹,

Ferrarini²,

Gualandi³

et al. 2021

Preprint

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“…The SAT-based solvers expected to perform better as the state of the art in SAT solving advances. In fact, in the course of writing the paper, a new SAT solver appeared, namely MapleCOMSPS (Liang, 2018;Liang, Oh, Mathew, Thomas, Li, & Ganesh, 2018), that according to the results in recent SAT competitions outperforms the Glucose SAT solver (Balyo et al, 2017), originally used in MDD-SAT. Indeed, the integration of this new solver resulted in an improvement of MDD-SAT in some cases.…”

Section: Reflecting Advances Of Recent Sat Solversmentioning

confidence: 99%

Migrating Techniques from Search-based Multi-Agent Path Finding Solvers to SAT-based Approach

Surynek¹,

Stern²,

Boyarski³

et al. 2022

jair

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In the multi-agent path finding problem (MAPF) we are given a set of agents each with respective start and goal positions. The task is to find paths for all agents while avoiding collisions, aiming to minimize a given objective function. Many MAPF solvers were introduced in the past decade for optimizing two specific objective functions: sum-of-costs and makespan. Two prominent categories of solvers can be distinguished: search-based solvers and compilation-based solvers. Search-based solvers were developed and tested for the sum-of-costs objective, while the most prominent compilation-based solvers that are built around Boolean satisfiability (SAT) were designed for the makespan objective. Very little is known on the performance and relevance of solvers from the compilation-based approach on the sum-of-costs objective. In this paper, we start to close the gap between these cost functions in the compilation-based approach. Our main contribution is a new SAT-based MAPF solver called MDD-SAT, that is directly aimed to optimally solve the MAPF problem under the sum-of-costs objective function. Using both a lower bound on the sum-of-costs and an upper bound on the makespan, MDD-SAT is able to generate a reasonable number of Boolean variables in our SAT encoding. We then further improve the encoding by borrowing ideas from ICTS, a search-based solver. In addition, we show that concepts applicable in search-based solvers like ICTS and ICBS are applicable in the SAT-based approach as well. Specifically, we integrate independence detection, a generic technique for decomposing an MAPF instance into independent subproblems, into our SAT-based approach, and we design a relaxation of our optimal SAT-based solver that results in a bounded suboptimal SAT-based solver. Experimental evaluation on several domains shows that there are many scenarios where our SAT-based methods outperform state-of-the-art sum-of-costs search-based solvers, such as variants of the ICTS and ICBS algorithms.

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“…The main techniques used in CDCL solvers include clause-based learning of conflicts, random restarts, heuristic variable selection, and effective constraintpropagation data structures (Gong and Zhou 2017). Examples of highly efficient complete SAT solvers include Min-iSat (Eén and Sörensson 2003), BerkMin (Goldberg and Novikov 2007), PicoSAT (Biere 2008), Lingeling (Biere 2010), Glusose (Audemard and Simon 2014) and MapleSAT (Liang 2018). Overall, CDCL-based SAT solvers constitute a huge success for SAT problems, and have been dominating in the research of SAT solving.…”

Section: Introductionmentioning

confidence: 99%

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

Kyrillidis

Shrivastava

Vardi

et al. 2020

AAAI

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The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well-studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

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Machine Learning-Based Restart Policy for CDCL SAT Solvers

Cited by 38 publications

References 21 publications

A SAT Encoding to Compute Aperiodic Tiling Rhythmic Canons

A SAT Encoding to Compute Aperiodic Tiling Rhythmic Canons

Migrating Techniques from Search-based Multi-Agent Path Finding Solvers to SAT-based Approach

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

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