A comparative runtime analysis of heuristic algorithms for satisfiability problems

Abstract

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, ( 1 + 1 ) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT ( k ⩾ 3 ) is O ( ( k − 1 ) n ) , and presents a k-SAT instance that has Θ ( ( k − 1 ) n ) expected runtime bound.