Evolving Solutions to Community-Structured Satisfiability Formulas

We study the ability of a simple mutation -only evolutionary algorithm to solve propositional satisliability formulas with inherent community structure. We show that the community structure translates to good fitness -distance correlation properties, which implies that the objective function provides a strong signal in the search space for evolutionary algorithms to locate a satisfying assignment efficiently. We prove that when the formula clusters into communities of size s C (log n) fl ()(n (22i) for some constant 0 < < 1, and there is a nonuniform distribution over communities, a simple evolutionary algorithm called the (1+1) 1 i\ finds a satisfying assignment in polynomial time on a 1 ()(1) traction of formulas with at least constant constraint density. This is a significant improvement over recent results on uniform random formulas, on which the same algorithm has only been proven to he efficient on uniform formulas of at least logarithmic density.