# Inequality-sum : a global constraint capturing the objective function

Jean-Charles Régin; Michel Rueher

RAIRO - Operations Research - Recherche Opérationnelle (2005)

- Volume: 39, Issue: 2, page 123-139
- ISSN: 0399-0559

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topRégin, Jean-Charles, and Rueher, Michel. "Inequality-sum : a global constraint capturing the objective function." RAIRO - Operations Research - Recherche Opérationnelle 39.2 (2005): 123-139. <http://eudml.org/doc/245189>.

@article{Régin2005,

abstract = {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 $y=\Sigma x_i$, and where the integer variables $x_i$ are subject to difference constraints of the form $x_j-x_i \le c$. 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 $x_i$ 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.},

author = {Régin, Jean-Charles, Rueher, Michel},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

language = {eng},

number = {2},

pages = {123-139},

publisher = {EDP-Sciences},

title = {Inequality-sum : a global constraint capturing the objective function},

url = {http://eudml.org/doc/245189},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Régin, Jean-Charles

AU - Rueher, Michel

TI - Inequality-sum : a global constraint capturing the objective function

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 2

SP - 123

EP - 139

AB - 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 $y=\Sigma x_i$, and where the integer variables $x_i$ are subject to difference constraints of the form $x_j-x_i \le c$. 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 $x_i$ 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.

LA - eng

UR - http://eudml.org/doc/245189

ER -

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