Fuel-optimal truck path and speed profile in dynamic conditions: an exact algorithm

We consider optimizing a truck's choice of path and speed profile to minimise fuel consumption, exploiting real-time predictive information on dynamically varying traffic conditions. Time-varying traffic conditions provide particular challenges, both from network-level interactions (e.g. slowing to consume more fuel locally may be beneficial to avoid congested periods downstream) and link-level phenomena (e.g. interaction between acceleration and gradient profiles). A multi-level, discrete-time decomposition of the problem is presented in which: (i) [sub-problems] speed profiles are optimized within each link, given boundary conditions of entry/exit times and speeds; (ii) [master problem] a space-time extended network representation is used to encode the dynamic interactions, within which the joint choice of path and speed profile is made. By instantiating the space-time network in (ii) with the optimal link profiles from (i), we are able to devise a tractable algorithm while optimizing speed profiles over a fine timescale. The solution approach is to pre-solve offline the computationally-intensive step (i), meaning that the representation in (ii) can be efficiently produced online in response to the real-time predictive information, whereby optimization of the path and speed profile is solved by a single shortest path search in the space-time network, for which many exact algorithms exist. The method is extended to additionally consider choice of discretionary stops and (pre-trip) departure time. Two representations are presented and investigated, depending on whether constraints are additionally imposed to ensure consistency of speed profiles across link boundaries. Numerical experiments are reported on a small illustrative example and a case-study network.