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Inequality-sum: a global constraint capturing the objective function

Published online by Cambridge University Press:  15 October 2005

Jean-Charles Régin  and
Michel Rueher
Jean-Charles Régin
Affiliation:
ILOG Les Taissounieres HB2 1681, route des Dolines Sophia-Antipolis, 06560 Valbonne, France; regin@ilog.fr
Michel Rueher
Affiliation:
Université de Nice–Sophia-Antipolis, Projet COPRIN I3S/CNRS-INRIA-CERMICS, ESSI, 930, route des Colles, B.P. 145, 06903 Sophia-Antipolis, France; rueher@essi.fr
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Abstract

This paper introduces a new method to prune the domains of the variablesin constrained optimization problems where the objective function is defined by a sumy = ∑xi , and where the integer variables x i are subject to difference constraintsof 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 ofthe 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 pruningof the domains of the x i 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.

Keywords

Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 2 , April 2005 , pp. 123 - 139
Copyright
© EDP Sciences, 2005

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