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

Abstract

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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.

How to cite

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Régin, 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 -

References

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