The proportional constraint and its pruning

Motivated by the necessity to model the energy loss of energy storage devices, a Proportional Constraint is introduced in finite integer domain Constraint Programming. Therefore rounding is used within its definition. For practical applications in 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. However, fixed-point iteration always results in the strongest notion of bounds consistency. Furthermore, an alternative modeling of the Proportional Constraint is presented. The run-times of the implementations of both alternatives are compared showing that the implementation of the Proportional Constraint on the basis of the presented pruning rules performs always better on sample problem classes.