Kayros
An anytime and exact open-source solver for time-dependent vehicle routing.
Kayros is an open-source solver for duration-minimization time-dependent vehicle routing, covering both the time-window variant (TDVRPTW) and the plain TDVRP. Time-dependent means travel times change with the time of day, which Kayros represents with continuous piecewise-linear arrival-time functions rather than a coarse time discretization.
It runs in two modes on a single engine: an anytime heuristic that returns steadily improving solutions under any time budget, and an exact branch-price-and-cut mode that can certify optimality. The exact side runs on the open-source HiGHS solver, so no commercial license is required.
It is beta (currently version 1.1.3), developed as part of my PhD, and installable with pip install kayros (MIT, Python 3.11+). A technical report is forthcoming. See the announcement post for more.