An empirical investigation of the forward checking algorithm and its derivatives

Forward checking (FC) is one of the most popular algorithms used to solve constraint satisfaction problems. A lazy variant of FC has been proposed called minimal forward checking (MFC). Previous empirical results suggest that MFC substantially outperforms FC when the fail first (FF) heuristic is not used. These results also suggest that the laziness of MFC can have substantial negative effects when the FF heuristic is used. To overcome this problem two extensions to the MFC algorithm are proposed, a new heuristic, called extra pruning (EXP), and the addition of conflict-directed backjumping (CBJ). An empirical investigation on a large test suite of hard randomly generated problems suggests that adding both EXP and CBJ to MFC-FF (MFC-CBJ-EXP-FF) is the best forward checking algorithm. Some theoretical relationships among the various algorithms are discussed.