KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering
Abstract
Time-dependent routing recognizes that the same journey can take a different time depending on when it begins. Under duration minimization, even the departure time of each vehicle becomes a decision. Exact methods for this setting exist in the literature, but researchers and practitioners have lacked a ready-to-use open solver that combines rich piecewise-linear travel times, early feasible solutions and optimality claims. KAYROS fills this gap with two modes on one checker-consistent engine: an Iterated Local Search that streams improving solutions and a Branch-Price-and-Cut method that can issue computational optimality certificates under explicit arithmetic and search assumptions. It installs with one command and has no proprietary dependency. The public MAMUT-routing store currently contains 704 KAYROS certificates under a four-solve publication protocol, which has also led to the retraction and repair of invalid earlier claims. The report presents two complementary benchmark contributions to MAMUT-routing. The first integrates Blauth2024, a benchmark from the literature whose travel times derive from measured Uber speeds, for which KAYROS provides new best-known solutions on all 40 instances. The second proposes Poryos2026, a new benchmark of 1,080 paired static and time-dependent instances built from OpenStreetMap road networks and controlled synthetic traffic. Finally, the report describes the intensive human-AI collaboration behind this work and the verification practices that kept its outputs independently verifiable.
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BibTeX
@misc{rascoussier2026kayros,
title = {{KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering}},
author = {Florian Rascoussier and Romain Billot and Lina Fahed and Christine Solnon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.23116},
eprint = {2607.23116},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23116},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering
AU - Florian Rascoussier
AU - Romain Billot
AU - Lina Fahed
AU - Christine Solnon
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2607.23116
UR - https://arxiv.org/abs/2607.23116
AB - Time-dependent routing recognizes that the same journey can take a different time depending on when it begins. Under duration minimization, even the departure time of each vehicle becomes a decision. Exact methods for this setting exist in the literature, but researchers and practitioners have lacked a ready-to-use open solver that combines rich piecewise-linear travel times, early feasible solutions and optimality claims. KAYROS fills this gap with two modes on one checker-consistent engine: an Iterated Local Search that streams improving solutions and a Branch-Price-and-Cut method that can issue computational optimality certificates under explicit arithmetic and search assumptions. It installs with one command and has no proprietary dependency. The public MAMUT-routing store currently contains 704 KAYROS certificates under a four-solve publication protocol, which has also led to the retraction and repair of invalid earlier claims. The report presents two complementary benchmark contributions to MAMUT-routing. The first integrates Blauth2024, a benchmark from the literature whose travel times derive from measured Uber speeds, for which KAYROS provides new best-known solutions on all 40 instances. The second proposes Poryos2026, a new benchmark of 1,080 paired static and time-dependent instances built from OpenStreetMap road networks and controlled synthetic traffic. Finally, the report describes the intensive human-AI collaboration behind this work and the verification practices that kept its outputs independently verifiable.
ER -