Experiments with a Reassignment Heuristic for Large Constraint Satisfaction Problems

A reassignment heuristic, originally designed to produce good solutions to an optimisation problem in rostering, is generalised so that it can, at least in theory, nd a feasible solution to any constraint satisfaction problem (CSP), if one exists. The heuristic requires an initial solution which is consistent but incomplete, in that some variables may be unassigned. Each unassigned variable is considered in turn and the heuristic attempts to nd reassignments of other variables which will allow the unassigned variable to be given a value consistent with the rest of the current solution. If this cannot be done, a value is chosen for the unassigned variable, the assignments which are inconsistent with the new assignment are deleted from the solution, and their variables are made unassigned in turn. The heuristic proceeds in this fashion until there are no remaining unassigned variables, or it reaches its iteration limit. In order to investigate the strengths and weaknesses of the reassignment heuris-tic, a series of experiments on randomly-generated CSPs have been carried out. These show the importance of randomn choice in the heuristic; for instance, if the initial solution is based on a random assignment, the performance is much better than if a good initial solution is constructed. The experiments also compare the performance of the heuristic with the forward checking algorithm. The reassignment heuristic nds a feasible solution more quickly than forward checking to problems which have a large number of possible solutions, but does less well when solutions are sparse; in particular, it cannot detect when a problem is insoluble. It is suggested that other repair-based heuristics for constraint satisfaction problems will behave similarly.