Many researchers have focused on the satisfiability problem and on many of its variants due to its applicability in many areas of artificial intelligence. This NP-complete problem refers to the task of finding a satisfying assignment that makes a Boolean expression evaluate to True. In this work, we introduce a memetic algorithm that makes use of the multilevel paradigm. The multilevel paradigm refers to the process of dividing large and difficult problems into smaller ones, which are hopefully much easier to solve, and then work backward toward the solution of the original problem, using a solution from a previous level as a starting solution at the next level. Results comparing the memetic with and without the multilevel paradigm are presented using problem instances drawn from real industrial hardware designs.