Sampling of Alternatives for Route Choice Modeling

This paper presents a new paradigm for choice set generation in the context of route choice. We assume that the choice sets contain all paths connecting each origin-destination pair. These sets are in general impossible to generate explicitly. Therefore, we propose an importance sampling approach to generate subsets of paths suitable for model estimation. Using only a subset of alternatives requires the path utilities to be corrected according to the sampling protocol in order to obtain unbiased parameter estimates. We derive such a sampling correction for the proposed algorithm. Estimating models based on samples of alternatives is straightforward for some types of models, in particular the Multinomial Logit (MNL) model. In order to apply MNL for route choice, the utilities must also be corrected to account for the correlation using, for instance, a Path Size (PS) formulation. We show that the PS should be computed based on the full choice set. Again, this is not feasible in general, and we propose an operational solution, called the Extended PS. We present numerical results based on synthetic data. The results show that models including a sampling correction are remarkably better than the ones that do not. Moreover, the Extended PS appears to be a good approximation of the true one.