Cost Evaluation of Soft Global Constraints

This paper shows that existing definitions of costs associated with soft global constraints are not sufficient to deal with all the usual global constraints. We propose more expressive definitions: refined variablebased cost, object-based cost and graph properties based cost. For the first two ones we provide ad-hoc algorithms to compute the cost from a complete assignment of values to variables. A representative set of global constraints is investigated. Such algorithms are generally not straightforward and some of them are even NP-Hard. Then we present the major feature of the graph properties based cost: a systematic way for evaluating the cost with a polynomial complexity.