Inequality-sum : a global constraint capturing the objective function
RAIRO - Operations Research - Recherche Opérationnelle, Tome 39 (2005) no. 2, pp. 123-139.

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=Σx i , and where the integer variables x i are subject to difference constraints of the form x j -x i 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.

@article{RO_2005__39_2_123_0,
     author = {R\'egin, Jean-Charles and Rueher, Michel},
     title = {Inequality-sum : a global constraint capturing the objective function},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {123--139},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {2},
     year = {2005},
     doi = {10.1051/ro:2005007},
     zbl = {1104.90051},
     mrnumber = {2181795},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro:2005007/}
}
Régin, Jean-Charles; Rueher, Michel. Inequality-sum : a global constraint capturing the objective function. RAIRO - Operations Research - Recherche Opérationnelle, Tome 39 (2005) no. 2, pp. 123-139. doi : 10.1051/ro:2005007. http://www.numdam.org/articles/10.1051/ro:2005007/

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