Search Techniques for Non-linear Constraint Satisfaction Problems with Inequalities

In recent years, interval constraint-based solvers have shown their ability to ef£ciently solve challenging non-linear real constraint problems. However, most of the working systems limit themselves to delivering point-wise solutions with an arbitrary accuracy. This works well for equalities, or for inequalities stated for specifying tolerances, but less well when the inequalities express a set of equally relevant choices, as for example the possible moving areas for a mobile robot. In that case it is desirable to cover the large number of point-wise alternatives expressed by the constraints using a reduced number of sets, as interval boxes. Several authors [2, 1, 7] have proposed set covering algorithms speci£c to inequality systems. In this paper we propose a lookahead backtracking algorithm for inequality and mixed equality/inequality constraints. The proposed technique combines a set covering strategy for inequalities with classical interval search techniques for equalities. This allows for a more compact representation of the solution set and improves ef£ciency.