Scatter Search with Random Walk Strategy for SAT and MAX-W-SAT Problems

The recent evolutionary approach called scatter search is studied for solving the satisfiability problem designated by SAT and its weighted version MAX-W-SAT. It is a population-based meta-heuristic founded on a formulation proposed two decades ago by Fred Glover. It uses linear combination on a population subset to create new solutions while other evolutionary approaches like genetic algorithms resort to randomization.First we propose a scatter search algorithm for SAT and MAX-W-SAT, namely SS-SAT. We present a procedure to generate good scattered initial solutions, a combination operator and a technique for improving the solutions quality. The method is tested and various experimental results show that SS-SAT performs better than or as well as GRASP for most benchmark problems.Secondly, we augment scatter search with the random walk strategy and compare its performance to the standard version. It appears that the added strategy does not lead to increased performance.

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