Anytime algorithms for constraint satisfaction and SAT problems

Abstract

The constraint satisfaction problem (CSP) is a potential area of application for anytime methods. In this work we derive anytime curves using a partial constraint satisfaction framework that encompasses problems with complete solutions and those that allow only partial solutions of varying quality. In either case, the curves should converge on optimal solutions with respect to some measure of cost (here, the number of violated constraints). Binary CSPs and k-satisfiability problems were tested, using heuristic repair and branch and bound methods. Curves for heuristic methods either start at a lower level than curves for branch and bound (min-conflicts with binary CSPs) or have a steeper initial descent (GSAT with k-SAT problems). Techniques for randomization such as random walks or restarting with a new random solution appear to be necessary with heuristic procedures for complete convergence to an optimal solution. Branch and bound algorithms are usefully employed in tandem with heuristic methods, especially to verify optimality and, therefore, the quality of solution returned by the latter.