A Multilevel Memetic Algorithm for Large SAT-Encoded Problems
Noureddine Bouhmala [email protected] Department of Maritime Technology and Innovation, Vestfold University College, Norway
Abstract Many researchers have focused on the satisfiability problem and on many of its vari- ants 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 ex- pression 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 divid- ing 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.
Keywords Satisfiability problem, memetic algorithms, multilevel techniques, boundary model checking, Wilcoxon rank test.
1 Introduction A major challenge in solving large and complex problems is that there is no mathe- matical basis for efficiently reaching the global solution. Over the past few years, there has been increasing interest in solving these problems using memetic algorithms (MAs). MAs are a special kind of genetic algorithm (GA) with local hill climbing. Unfortunately, the performance of MAs as well as other available optimization techniques deteriorates very rapidly mostly due to two reasons. First, the complexity of the problem usu- ally increases with its size, and second, the solution space of the problem increases exponentially with the problem size. Because of these two issues, optimization search techniques tend to spend most of the time exploring a restricted area of the search space, preventing the search from visiting more promising areas, and thus leading to solutions of poor quality. Designing efficient optimization search techniques requires a tactical balance between diversification and intensification (Blum and Roli, 2003). Diversifica- tion refers to the ability to explore many different regions of the search space, whereas intensification refers to the ability to obtain high quality solutions within those regions. While the combination of a population of solutions and genetic operators constitutes the main component of MAs that act as a diversification factor on the search space, the use of local search methods helps to quickly identify better solutions in a localized region of the search space. Lozano and Martinez (2010), discuss the latest design of hybrid approaches in order to find an adequate balance between diversification and intensification.