Minimising GEH in static OD estimation

One of the essential quantities in macro traffic simulation is the ‘who goes where’ OD matrix. This is usually estimated through an optimization problem of minimizing the squared differences between observed and simulated traffic counts. The choice of the mean square error loss is due to its good statistical properties and the fact that the related quadratic optimization problem is easy to deal with. However, in many applications following the recommendations of validation criteria suggested in many guidelines published by different road administrations, such as FHWA in USA, ARRB in Australia or Highways Agency in UK, the quality of a static OD adjustment is assessed with other quantities such as the relative error or the GEH index. A direct minimization of the GEH index involves technical difficulties. However, recent developments in optimization theory give the opportunity of solving such problem using gradient descent techniques. We apply this method to some static OD estimation problems in real traffic networks. Empirical evidence show that GEH minimization converges slower than least squares. On the other hand the former is more robust against measurement errors on data. This paper show numerical results of real networks, comparing the OD estimation using least squares and GEH index, concluding with the benefit of including this optimization method for static OD estimation.