This paper introduces a new method to prune the domains of the variables
in constrained optimization problems where the objective function is
defined by a sum
y = ∑xi, and where the integer variables xi are subject to difference constraints
of the form xj - xi ≤ c. An important application area where such
problems occur is deterministic scheduling with the mean flow time as
optimality criteria.
This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical approaches perform a local consistency filtering after
each reduction of
the bound of y. The drawback of these approaches comes from the fact that the constraints are handled independently.
We introduce here a global constraint that enables to tackle simultaneously the whole constraint system, and thus, yields a more effective pruning
of the domains of the xi when the bounds of y are reduced.
An
efficient algorithm,
derived from Dijkstra's shortest path algorithm, is introduced to achieve
interval consistency on this global constraint.