  We define a multi-variable version of the Affine Index Polynomial for virtual
links. This invariant reduces to the original Affine Index Polynomial in the
case of virtual knots, and also generalizes the version for compatible virtual
links recently developed by L. Kauffman. We prove that this invariant is a
Vassiliev invariant of order one, and study what happens as we shift the
coloring of one or more components.
