Maximum satisfiability: How good are tabu search and plateau moves in the worst-case?

Tabu search algorithms are amongst the most successful local search based methods for the maximum satisfiability problem. The practical superiority of tabu search over local search alone has been already shown experimentally several times. A natural question addressed here is to understand if this superiority holds also from the worst-case point of view. Moreover, it is well known that a critical parameter of tabu techniques is the tabu list length. Focusing on MAX-2-SAT problem, the main contribution of this paper is a worst-case analysis of tabu search as a function of the tabu list length. We give the first theoretical evidence of the advantage of a tabu search strategy over the basic local search alone that critically depends on the tabu list length. Our second contribution is about a widespread belief that when a local optimal solution is reached then simply continuing to search by making non–deteriorating, “plateau” moves, dramatically increases the success rate of local search based algorithms. We start by observing that no plateau search strategy can help to improve the approximation ratio of the basic local search. However, for a restricted version of the problem, we prove that plateau moves can enhance the approximation ratio of the basic local search from 1/2 to 2/3.