Using Island Model in Asynchronous Evolutionary Strategy to Search for Backdoors for SAT

In this paper we propose new evolutionary algorithms for finding the so-called backdoors - special structures that make it possible to simplify the solving of combinatorial problems expressed as systems of constraints. In particular, we consider the Boolean satisfiability problem (SAT) and search for ρ-backdoors for Boolean formulas. We analyze the problem of finding ρ-backdoors of small fixed size and adapt (1+1)-EA for its solving: in the proposed algorithm the mutation is performed in such a way that it transitions between Boolean vectors of fixed weight. The proposed algorithm was implemented in the context of a parallel asynchronous strategy based on the island paradigm. In the experimental part we demonstrate the applicability of this algorithm by using the found backdoors to solve extremely hard instances from the area of Logical Equivalence Checking for Boolean circuits: our approach on this class of benchmarks outperforms the best state-of-the-art SAT solvers.