UC Irvine Institute of Transportation Studies

The solution algorithms for the family of flow distribution problems, which include (1) the trip distribution problem of travel forecasting, (2) the OD estimation from link counts problem, and (3) the trip matrix disaggregation problem, are usually based on the Maximum Entropy (ME) principle. ME-based optimization problems are hard to solve directly by optimization techniques due to the complexity of the objective function. Thus, in practice, iterative procedures are used to find approximate solutions. These procedures, however, cannot be easily applied if additional constraints are needed to be included in the problem. In this paper a new approach for balancing trip matrices with application in trip matrix disaggregation is introduced. The concept of generating the most similar distribution (MSD) instead of the Most Probable Distribution of Maximum Entropy principle is the basis of this approach. The goal of MSD is to minimize the deviation from the initial trip distribution, while satisfying additional constraints. This concept can be formulated in different ways. Two MSD-based objective functions have been introduced in this paper to replace the ME-based objective function. One is the Sum of Squared Deviations MSD (SSD-MSD), and the other is Minimax-MSD. While SSD-MSD puts more emphasis on maintaining the base year trip shares as a whole, Minimax-MSD puts more emphasis on maintaining the share of each individual element in the trip table. The main advantage of replacing the entropy-based objective functions with any of these functions is that the resulting problems can include additional constraints and still be readily solved by standard optimization engines. In addition, these objective functions could produce more meaningful results than entropy-based functions in regional transportation planning studies, as shown in the case study and some of the examples in the paper. Several examples and a case study of the California Statewide Freight Forecasting Model (CSFFM) are presented to demonstrate the merits of using MSD-based formulations.