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On global warming: Flow-based soft global constraints

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Abstract

In case a CSP is over-constrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then computing a minimum-weight flow in the extended graph to measure the violation. We present efficient propagation algorithms, based on different violation measures, achieving domain consistency for the alldifferent constraint, the global cardinality constraint, the regular constraint and the same constraint.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, 4130 Upson Hall, Ithaca, NY, 14853, USA

    Willem-Jan Van Hoeve

  2. École Polytechnique de Montréal, Montreal, Canada

    Gilles Pesant & Louis-Martin Rousseau

  3. Centre for Research on Transportation (CRT), Université de Montréal, C.P. 6128, succ. Centre-ville, Montreal, H3C 3J7, Canada

    Gilles Pesant & Louis-Martin Rousseau

Authors
  1. Willem-Jan Van Hoeve
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  2. Gilles Pesant
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  3. Louis-Martin Rousseau
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Corresponding author

Correspondence to Gilles Pesant.

Additional information

This work was for a large part carried out while the author was at the Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands

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Van Hoeve, WJ., Pesant, G. & Rousseau, LM. On global warming: Flow-based soft global constraints. J Heuristics 12, 347–373 (2006). https://doi.org/10.1007/s10732-006-6550-4

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  • DOI: https://doi.org/10.1007/s10732-006-6550-4

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