An empirical validation and data-driven extension of continuum approximation approaches for urban route distances

We introduce a data-driven extension to continuum approximation (CA)-based methods used to predict urban route distances. This extension efficiently incorporates the circuity of the underlying road network into the approximation method to improve distance predictions in more realistic settings. The proposed extension significantly outperforms traditional methods, which build on the assumption of travel according to the rectilinear distance metric. While only marginally increasing the data collection effort, the proposed extension yields reductions of 26 percent points in mean absolute percentage error compared to traditional approximation methods. The obtained distance estimates are within 5%-15% of near-optimal solutions obtained with a large neighborhood search heuristic, depending on the circuity of the region and the density of stops. Further, by providing a real-world validation of CA methods, we explore how novel sources of geo-spatial and traffic-related data can be efficiently leveraged to improve the predictive performance of CA methods. The proposed extension is particularly relevant to increase the real-world validity of CA methods applied to large-scale optimization problems in logistics system design and planning within urban areas.