A gentle introduction to NUMERICA
Artificial Intelligence - Special issue: artificial intelligence 40 years later
Universally Quantified Interval Constraints
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Approximation Techniques for Non-linear Problems with Continuum of Solutions
Proceedings of the 5th International Symposium on Abstraction, Reformulation and Approximation
Consistency Maintenance for ABT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Interval propagation and search on directed acyclic graphs for numerical constraint solving
Journal of Global Optimization
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In recent years, interval constraint-based solvers have shown their ability to efficiently 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 specific 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 efficiency.