Search Space Features Underlying the Performance of Stochastic Local Search Algorithms for MAX-SAT

MAX-SAT is a well-known optimisation problem that can be seen as a generalisation of the propositional satisfiability problem. In this study, we investigate how the performance of stochastic local search (SLS) algorithms — a large and prominent class of algorithms that includes, for example, Tabu Search, Evolutionary Algorithms and Simulated Annealing — depends on features of the underlying search space. We show that two well-known measures of search space structure, the autocorrelation length of random walks and the so-called fitness distance correlation, reflect complementary factors underlying instance hardness for high-performance SLS algorithms. While the autocorrelation measure is computationally cheap, the fitness distance correlation serves mainly as an a posteriori measure for explaining performance. We also study the dependence of SLS performance on features of the distribution of clause weights for individual instances and show that, depending on the variance of the clause weight distribution, different search strategies seem to be suited best for dealing with the structure of the respective search spaces.