Distribution-free tight lower bounds on the average performance ratio for random search, for a greedy heuristic and for a probabilistic greedy heuristic are derived for an optimization version of satisfiability. On average, the random solution is never worse than of the optimal, regardless of the data-generating distribution. The lower bound on the average greedy solution is at least of the optimal, and this bound increases with the probability of the greedy heuristic selecting the optimal at each step. In the probabilistic greedy heuristic, probabilities are introduced into the search strategy so that a decrease in the probability of finding the optimal solution occurs only if the nonoptimal solution becomes closer to the optimal. Across problem instances, and regardless of the distribution giving rise to data, the minimum average value of the solutions identified by the probabilistic greedy heuristic is no less than of the optimal.
SIAM Journal on Discrete Mathematicsvol.
2, (November 01, 1989):