A Family of Relaxed Spatial Interaction Models

In traditional, constrained spatial interaction models, the number of predicted movers leaving origins and entering destinations is constrained to match exactly the observed number. In relaxed models, these constraints are allowed to vary over a range of values in order to provide greater flexibility in calibration. This paper identifies a new, seven-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 introduces these relaxed models as entropy-maximizing ones, proposes a terminology for them, and describes empirical situations in which they are useful.

Key Words:

• spatial interaction models
• constrained optimization
• entropy maximization
• relaxed interaction models
• family of relaxed models