Scatter search for SAT and W-MAX-SAT problems

SAT, the decision version of the satisfiability problem, which consists in verifying that a conjunction of clauses is satisfied by at least one variables interpretation, has been shown to be the first NP-complete satisfiability problem. In this paper, scatter search is used for the first time to solve the problems SAT and weighted maximum SAT (W-MAX-SAT). We present hereafter this approach and the general algorithm. We describe the issues of the method in the general context and then we propose an implementation for SAT and W-MAX-SAT. A procedure to generate good initial scattered solutions as well as an operator to combine solutions and a classical technique to improve the solutions quality are presented. We compare our empirical results with those obtained by GRASP