Using Mean Field Methods for Boosting Backtrack Search in Constraint Satisfaction Problems

Exact and inexact methods can be used for solving Constraint Satisfaction Problems (CSP), i.e. for finding a variable assignment which violates none of the constraints or minimizes the number of violated constraints. Based on a Backtrack tree search, exact methods are able to produce an optimal assignment, when no time limit is imposed. Based on local improvement mechanisms, inexact methods cannot guarantee that, but may produce better quality assignments in a limited time. In this paper, we show how an inexact method, coming from statistical physics, and more precisely from the Mean Field Theory, can boost an exact method by providing it with a good quality assignment, whose valuation can be used as an initial upper bound, and with two heuristics for ordering variables and values. Experiments on randomly generated classical and partial CSPs show significative gains in terms of time, even when adding the times used by both the Mean Field and the Backtrack methods.