The Argmax Constraint

Graeme Gange, Peter J. Stuckey

Abstract: The argmax function returns the index of the (first copy of the) maximum value occuring in a list of values. argmax is important in models where we choose a characteristic value based on a seperate criteria, and for modelling neural networks which make use of argmax in their definition. The argmax constraint has been studied for the special case of its use to find the index of the first true in a list of Booleans, since this is useful for encoding if-then-else chains. Here we examine the general argmax constraint for the first time. We define an efficient domain consistent propagator and a decomposition for integers which implements domain consistency.