Heuristic methods for over-constrained constraint satisfaction problems

Heuristic repair methods have successfully solved constraint satisfaction problems (CSPs) and satisfiability problems (SAT) that are too large to be solved by complete algorithms. In this paper we develop methods for testing the efficiency and quality of solution returned by these methods when applied to overconstrained CSPs and SAT. The key strategy is to test heuristic methods on problems of moderate size with known optimal distances (number of constraint violations), as determined with complete algorithms. This allows us to determine whether heuristic methods find optimal distances and allows us to carry out more incisive analyses of efficiency when different strategies are incorporated into these methods and parameter values are varied. The present work tested the min-conflicts algorithm with CSPs, either alone or in combination with walk, reset or tabu strategies. SAT was tested with GSAT and walk-SAT. The best results for min-conflicts were found with the walk strategy, when the probability of random assignment was set at 0.10 or 0.15. Both GSAT and walk-SAT readily found optimal solutions for 3-SAT, the latter being somewhat faster overall.