A multicriteria districting heuristic for the aggregation of zones and its use in computing origin-destination matrices

Territorial aggregation is an important issue in many traditional applications, such as political districting, plant location, health care zoning, and travel demand study. In particular, in travel demand analysis one is interested in estimating travel flows between origins and destinations. The number of trips performed between origin i and destination j is represented by the (i, j)-th entry of an Origin-Destination (OD) matrix. In order to define the OD matrix, a discrete set of origins and destinations is needed, and territorial aggregation methods are used precisely to choose these origins and destinations. Typically, a survey is performed to collect data on travel between the selected origins and destinations. However, when the survey OD matrix is large and sparse, problems in the estimation of travel demand may arise. This drawback can be avoided by further aggregating the origins and destinations on which travel demand is evaluated and by obtaining a new and smaller OD matrix where each cell entry carries a greater value. The corresponding map is then exploited to calibrate the statistical model used to estimate the original disaggregated travel flows. In this work, we first suggest a set of optimality criteria which can be used to find "good" territorial aggregations and we adopt the Old Bachelor Acceptance heuristic to identify them. In order to understand the trade-off between these criteria, we introduce appropriate optimality indexes and we minimize their weighted combinations with several different sets of weights. Our application refers to the city of Rome and the actual study, which involved statisticians, engineers and operations researchers, was supported by the local government (Comune di Roma). Our experimental results on the city of Rome show that the Old Bachelor Acceptance heuristic finds aggregations with low values for all the indexes simultaneously. In particular, our results lead to the conclusion that certain sets of weights must be adopted if one wants to be sure to find "good" aggregations.