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

Jean-Charles Régin; Michel Rueher

RAIRO - Operations Research (2010)

- 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 39.2 (2010): 123-139. <http://eudml.org/doc/105325>.

@article{Régin2010,

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 = ∑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.
},

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

journal = {RAIRO - Operations Research},

language = {eng},

month = {3},

number = {2},

pages = {123-139},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/105325},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Régin, Jean-Charles

AU - Rueher, Michel

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

JO - RAIRO - Operations Research

DA - 2010/3//

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 = ∑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.

LA - eng

UR - http://eudml.org/doc/105325

ER -

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