A new greedy randomised adaptive search procedure for solving the maximum satisfiability problem

The maximum satisfiability problem (Max‐Sat) is one of the most known variant of satisfiability problems. The objective is to find the best assignment for a set of Boolean variables that gives the maximum of verified clauses in a Boolean formula. Unfortunately, this problem was showed NP‐complete if the number of variable per clause is higher than 3. In this paper, a new incomplete algorithm based on a greedy randomised adaptive search procedure (GRASP) is presented to deal with Max 3‐Sat problem. The first GRASP's phase is a new greedy algorithm based on iterative application of a new version of pure literal elimination technique called weighted literal elimination. In the next stage of the GRASP algorithm, a modified version of the Walksat procedure is applied using, as initial solutions, the solutions found by the greedy procedure of the GRASP algorithm. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed approach.