Enhancements of Branch and Bound Methods for the Maximal Constraint Satisfaction Problem

Two methods are described for enhancing performance of branch and bound methods for overconstrained CSPS. These methods improve either the upper or lower bound, respectively, during search, so the two can be combined. Upper bounds are improved by using heuristic repair methods before search to find a good solution quickly, whose cost is used as the initial upper bound. The method for improving lower bounds is an extension of directed arc consistency preprocessing, used in conjunction with forward checking. After computing directed arc consistency counts, inferred counts are computed for all values based on minimum counts for values of adjacent variables that are later in the search order. This inference process can be iterated, so that counts are cascaded from the end to the beginning of the search order, to augment the initial counts. Improvements in time and effort are demonstrated for both techniques using random problems.