Plateaus and Plateau Search in Boolean Satis ability Problems: When to Give Up Searching and Start Again

We empirically investigate the properties of the search space and the behavior of hill-climbing search for solving hard, random Boolean satis ability problems. In these experiments it was frequently observed that rather than attempting to escape from plateaus by extensive search, it was better to completely restart from a new random initial state. The optimumpoint to terminate search and restart was determined empirically over a range of problem sizes and complexities. The growth rate of the optimum cuto is faster than linear with the number of features, although the exact growth rate was not determined. Based on these empirical results, a simple run-time heuristic is proposed to determine when to give up searching a plateau and restart. This heuristic closely approximates the empirically determined optimum values over a range of problem sizes and complexities, and consequently allows the search algorithm to automatically adjust its strategy for each particular problem without prior knowledge of the problem's complexity.