Improving Parallel Local Search for SAT

Abstract

Abstract. In this work, our objective is to study the impact of knowledge sharing on the performance of portfolio-based parallel local search algorithms. Our work is motivated by the demonstrated importance of clause-sharing in the performance of complete parallel SAT solvers. Unlike complete solvers, state-of-the-art local search algorithms for SAT are not able to generate redundant clauses during their execution. In our settings, each member of the portfolio shares its best configuration (i.e., one which minimizes conflicting clauses) in a common structure. At each restart point, instead of classically generating a random configuration to start with, each algorithm aggregates the shared knowledge to carefully craft a new starting point. We present several aggregation strategies and evaluate them on a large set of problems.

Large-scale parallelism for constraint-based local search: the costas array case study

“…It is also interesting to link these results to the experiments described in [7] for parallel SAT with the Sparrow solver [10], the best local search SAT solver in the 2011 SAT competition. These experiments compare parallel algorithms with and without cooperation, although communication is performed in a different manner than the one proposed here: parallel processes communicate their configurations at each restart (restart is an important feature for SAT local search) and the Prob NormalizedW heuristics [9] is used for aggregating those configurations and defining a good restart configuration, supposedly better than a random restart. This paper shows, in a different problem domain and with a different solver, that it is difficult to perform better than the independent multi-walk version, both in capacity solving (number of instance solved) and with respect to the PAR-10 metrics [46].…”

“…More recently, algorithms such as the ASAT heuristics or Focused Metropolis Search, which incorporate even more stochastic aspects, seem to be among the most effective methods for solving random 3-SAT problems [4]. A few parallel implementations of Local Search solvers have been done, see for instance [9] and [52], but limited to multi-core machines (i.e., up to 8 cores). Recently, parallel extensions of several Local Search SAT solvers have been done on massively parallel machines up to several hundreds of cores [7,8].…”

An overview of parallel SAT solving

“…Otherwise, the master creates work by ordering an active slave process to divide its search space into two (line 9). The dynamic work Algorithm 2 Master CDCL SAT solver (ϕ) 1: answer ← UNKNOWN 2: ProduceInitialGP() 3: LaunchSlaves() 4: while (answer == UNKNOWN) do 5: if (RequiredGP()) then 6: if (NoActiveProcesses()) then 7: answer ← UNSATISFIABLE 8: else 9: GenerateGP() 10: return answer stealing procedure guarantees that all slave processes have work, minimizing the idle time of those processes. If the current status of the formula (answer) is no longer unknown then the master stops its procedure and returns satisfiable (if a slave has found a solution) or unsatisfiable (if the formula does not have a solution) (line 10).…”

“…Nevertheless, there has also been some work done in incomplete methods for parallel SAT [1,73,83]. In addition, parallel approaches have been the target of research in extensions of SAT, namely, in Quantified Boolean Formulas (QBF) [28,58,60] and in Satisfiability Modulo Theories (SMT) [51,106].…”

A survey of SAT solver

“…In competitive parallelism, Pha [32] uses competitive parallelism of gNovelty+.There is no interaction between the solvers. Arbelaez [33] gives seven strategies for collaboration. Each solver shares the best value found in the variable assignment as the starting point for the next run.…”