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 developed as part of my PhD and installable with pip install kayros (MIT, Python 3.11+). The Kayros paper evaluates its anytime and exact components, while the technical report documents the solver, benchmarks, and verification process. See the original announcement and the research overview for more.
Links
- Source (GitHub)https://github.com/0nyr/kayros
- PyPIhttps://pypi.org/project/kayros/
- Reddit r/optimization posthttps://www.reddit.com/r/optimization/comments/1v8t68v/kayros_an_opensource_exact_and_anytime_solver_for/
- LinkedIn announcement posthttps://www.linkedin.com/posts/florian-rascoussier-onyr_kayros-an-anytime-and-exact-open-source-activity-7487836560994824192-ahZs?utm_source=share&utm_medium=member_desktop&rcm=ACoAACcIsOkB0IhxGhcova4MtLZJQQzTt0Z5e0Q
- Kayros paper (arXiv v2)https://arxiv.org/abs/2609.29597v2
- Technical report (arXiv v2)https://arxiv.org/abs/2607.23116v2