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Revisiting the soft global cardinality constraint

TitleRevisiting the soft global cardinality constraint
Publication TypeConference Paper
Year of Publication2010
AuthorsSchaus, Pierre, Van Hentenryck Pascal, and Zanarini Alessandro
Conference NameThe seventh International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) techniques in Constraint Programming (CPAIOR)

he Soft Global Cardinality Constraint (softggc) relaxes the Global Cardinality Constraint (gcc) by introducing a violation variable representing unmet requirements on the number of value occur- rences. A first domain consistent filtering algorithm was introduced by Van Hoeve et al. in 2004 using a minimum cost flow algorithm. A simpler and more efficient filtering algorithm was introduced in 2006 by Zanarini et al. using matchings in bipartite graphs. While the consistency check introduced in the second algorithm is correct, we show that the algorithm may not achieve domain consistency when cardinality requirements con- tain zeroes. We give new domain consistent conditions and show how to achieve domain consistency within the same time bounds. The softggc constraint was implemented in Comet (now also available in OscaR and OR-Tools).