Solving Hierarchies of Finite-domain Constraints 1 2

In the past we presented an algorithm to solve ordered constraint hierarchies based on a non-trivial error function using standard constraint satisfaction techniques. We extended this previous work and herewith present a new method to transform hierarchies of inequalities over the integers based on global comparators into equivalent ordered constraint hierarchies. The correctness of this method is proven. Using the results of our previous work, we present another method transforming the resulting ordered constraint hierarchies into ordinary constraint systems. These systems of algebraic equalities and inequalities over the integer domain are soluble with available nite-domain constraint solvers. At last we propose some modi cations and simpli cations of the considered constraint hierarchies improving the search for solutions and being useful in practical applications like job-shop scheduling. The modi cations are the combinations of consecutive hierarchy levels in one level where the constraints are considered with di erent priorities/weights. The simpli cations are incomplete search strategies resulting in run-time improvements and in sub-optimal solutions, too. Solving Hierarchies of Finite-Domain Constraints 1