In traditional, constrained spatial interaction models, the number of
predicted movers leaving origins and entering destinations is constrai
ned to match exactly the observed number. In relaxed models, these con
straints are allowed to vary over a range of values in order to provid
e greater flexibility in calibration. This paper identifies a new, sev
en-member family of relaxed spatial interaction models, based upon the
generalization of the constraint sets used in model derivation. Three
categories are suggested, including single and doubly relaxed models,
cost-relaxed models, and totally relaxed models. This paper introduce
s these relaxed models as entropy-maximizing ones, proposes a terminol
ogy for them, and describes empirical situations in which they are use
ful.