发表机构
IMT Atlantique; CNRS; INSA Lyon; Inria（大西洋国立高等矿业电信学院; 法国国家科学研究中心; 里昂国立应用科学学院; 法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究时长最小化的时间相关车辆路径规划问题，核心方法是基于现有技术扩展开源求解器KAYROS，具有随时、精确等特性，主要贡献是在基准测试集上取得成果并介绍新基准测试集，展示求解器及相关内容，体现人类与人工智能协作。
AI 中文摘要
KAYROS是一个用于时长最小化的时间相关车辆路径规划问题（有无时间窗）的开源求解器。在这些变体中，出行时间随出发时间变化，每条路径的调度时间是一个决策。据作者所知，它是首个随时可用且精确的公开求解器，能从最初几秒就流式改进解决方案，并通过公开可验证证书证明最优性，适用于丰富的分段线性出行时间函数而非时间离散化情况。它无专有依赖，一键安装。基于时间相关函数合成和精确求解的现有技术构建，扩展了开源分支定界切割求解器，具有随时和热启动行为、检查器精确定价等。在MAMUT路由基准测试集上，KAYROS有468个已发布的最优性证书，5个证书严格改进了已发布的参考值。报告还介绍了Poryos2026基准测试集，由作者从真实的OpenStreetMap城市道路网络设计生成。其1080个配对的CVRP、VRPTW、TDVRP和TDVRPTW实例结合了真实道路几何形状与可控的合成需求、时间窗和拥堵情况。每个实例都有经检查器验证的最佳已知解决方案。本报告展示了求解器、其认证协议、基准测试集的生成和可行性保证，以及它们的实验联系，这也是人类与人工智能密集协作的案例研究，使这项工作可行且其声明可独立验证。
英文摘要
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.
Commentsv2: 30 pages, 7 figures, 4 tables. Substantially revised. Updated certificate counts and literature comparison, new subsection on a falsified certificate and the re-derivation of the certified set, integration of the Blauth2024 benchmark family, and regenerated figures. Technical report accompanying the KAYROS solver and Poryos2026 benchmark family
