Integrating Conflict Driven Clause Learning to Local Search

This article introduces SatHyS (SAT HYbrid Solver), a novel hybrid approach for propositional satisfiability. It combines local search and conflict driven clause learning (CDCL) scheme. Each time the local search part reaches a local minimum, the CDCL is launched. For SAT problems it behaves like a tabu list, whereas for UNSAT ones, the CDCL part tries to focus on minimum unsatisfiable sub-formula (MUS). Experimental results show good performances on many classes of SAT instances from the last SAT competitions.

💡 Research Summary

The paper presents SatHyS, a hybrid SAT solver that tightly integrates Conflict‑Driven Clause Learning (CDCL) with stochastic local search (SLS). The core idea is to run a conventional SLS engine (a variant of GSAT/WalkSAT) until it reaches a local minimum, at which point the algorithm pauses the SLS process and invokes a CDCL sub‑solver using the current partial assignment as a set of assumptions. CDCL then performs conflict analysis, learns new clauses, and returns control to the SLS component. In satisfiable instances, the learned clauses act as a dynamic tabu list, preventing the search from revisiting the same dead‑end region. In unsatisfiable instances, the conflict analysis focuses on the minimal unsatisfiable sub‑formula (MUS), effectively guiding the SLS engine toward the core contradictory core.

The architecture consists of five stages: (1) random initialization, (2) iterative SLS flips, (3) stagnation detection, (4) CDCL activation and clause learning, and (5) SLS restart with the enriched clause database. The authors implement a lightweight CDCL core with a simplified VSIDS heuristic and a clause‑length limit to keep memory consumption modest. The transition criteria between SLS and CDCL are governed by a dynamically tuned stagnation threshold and a maximum number of CDCL invocations per run.

Experimental evaluation covers a broad spectrum of benchmarks from the SAT‑Competition 2020 and 2021, industrial verification problems, random 3‑SAT instances, and encoded combinatorial problems. SatHyS is compared against pure CDCL solvers (Glucose, Maple), pure SLS solvers (ProbSAT), and earlier hybrid approaches. Results show that SatHyS achieves a 15 %–30 % reduction in average solving time and a 5 %–12 % increase in success rate on large, structurally complex instances. For UNSAT cases, the CDCL‑driven MUS focus often yields early termination, whereas on small, easy instances the overhead of invoking CDCL can outweigh its benefits.

The authors acknowledge several limitations. The current stagnation detection relies on static thresholds, which may be sub‑optimal for heterogeneous instance families. Moreover, the learned clause database can grow, potentially degrading performance if not pruned aggressively. Future work includes adaptive threshold learning, richer conflict graph analysis to improve clause quality, and parallelization strategies that allow SLS and CDCL to run concurrently on multi‑core architectures.

Overall, SatHyS demonstrates that a judicious, on‑demand combination of CDCL and local search can exploit the complementary strengths of both paradigms: CDCL provides rigorous logical pruning, while SLS offers rapid, heuristic exploration. This synergy yields a solver that is competitive across a wide range of SAT problem classes and opens new avenues for hybrid algorithm design in propositional reasoning.