Scaling and Probabilistic Smoothing: Dynamic Local Search for Unweighted MAX-SAT

In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAXSAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances. We present results showing that SAPS is also very effective at finding optimal solutions for unsatisfiable MAX-SAT instances, and in many cases performs better than state-of-the-art MAX-SAT algorithms, such as the Guided Local Search algorithm by Mills and Tsang [8]. With the exception of some configuration parameters, we found that SAPS did not require any changes to efficiently solve unweighted MAX-SAT instances. For solving weighted MAX-SAT instances, a modified SAPS algorithm will be necessary, and we provide some thoughts on this topic of future research.