The Proportional Constraint and Its Pruning -- Continued

Abstract

Motivated by the necessity to model the adaptation of water levels in locks, a new variant of the Proportional Constraint is introduced in finite integer domain Constraint Programming using rounding-up (ceiling) instead of rounding. For its practical use in applications of finite domain Constraint Programming pruning rules are presented and their correctness is proven. Further, it is shown by examples that the number of iterations necessary to reach a fixed-point while pruning depends on the considered constraint instances. Importantly, fixed-point iteration always results in the strongest notion of bounds consistency which is proved, too. Furthermore, an alternative modelling of this constraint is presented. The run-times of the implementations of both alternatives are compared showing that the pruning rules introduced herein perform always better than the alternative approach on the chosen problem samples.