Estimation of origin-destination matrices from traffic counts using multiobjective programming formulations

Origin-destination (O-D) trip matrices can be estimated by methods that use traffic volume counts. Assuming that we know the proportionate usage of each link by the interzonal traffic, a system of linear equations combining the O-D flow and the observed volumes can be formulated. This system is, in general, underspecified. To obtain a unique solution, additional information, often a target trip matrix, has to be used. The estimation problem can be interpreted as a problem that has two types of objectives, one of which is to satisfy the traffic counts constraints and the other to search for a solution as "close" as possible to the target matrix. Errors are normally present in the input data, and it is therefore reasonable to allow for solutions where the observed traffic volumes are not reproduced exactly. Depending on his/her degree of uncertainty or belief in the available information, the planner can choose to give more or less weight to the different objectives. To satisfy all the constraints to equality is only one extreme case in a continuum of possibilities. In this paper, we present multiobjective programming formulations for estimating O-D matrices. The main emphasis is to point out that multiobjective theory can be used in the interpretation of the problem. In a two-objective model, an aggregated entropy measure is defined for each type of information (targets and observations), and is used as the objective. In addition, a totally disaggregated multiobjective model is presented in which one objective for each target matrix element and each traffic count observation is defined. These models are then combined to make a general model. Different approaches for estimation of the magnitude of uncertainty and for specification of the weights of the objectives are discussed.