KAYROS：一种用于带时间窗的时变车辆路径问题的任意时间精确求解器 - 扩展版
KAYROS: An Anytime and Exact Solver for the Time-Dependent Vehicle Routing Problem with Time Windows - Extended Version
- IMT Atlantique, Lab-STICC, CNRS, UMR 6285（大西洋高等理工学院，实验室科学与技术，法国国家科学研究中心）
- INSA Lyon, Inria, CITI, UR3720（里昂国立应用科学学院，法国国家信息与自动化研究所，信息与技术创新中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
KAYROS是面向带时间窗时变车辆路径问题的开源任意时间精确求解器，通过分支定价切平面与混合局部搜索，在212个实例上显著优于现有求解器并发布704个最优性证书。
AI中文摘要：
带时间窗的时变车辆路径问题（TDVRPTW）捕捉了城市物流的一个核心难点：出行时间随一天中的时段而变化，因此路线的成本取决于何时行驶。本文介绍了KAYROS，一个用于最小化时长的TDVRPTW的开源求解器，它既是任意时间的又是精确的。它在时间预算内不断返回改进的有效解，并可通过集成的分支定价切平面组件以最优性证书关闭实例。我们将文献中连续到达时间函数的复合（此前仅在证明或命题层面描述）扩展到逐步基准所需的左连续函数。我们证明了检查器中内置的复合例程精确计算了该操作。我们分析了其评估和断点归一化在IEEE-754双精度算术中何时是精确的，并论证了一个规范的、无epsilon的检查器必须定义目标函数。任意时间层结合了贪心构造、基于平衡路线树的粒度时变局部搜索和迭代局部搜索，并带有针对车队成本目标的车辆感知下降。我们进一步提出了一种基于预先承诺的统计设计下归一化符号原始积分的任意时间评估方法。在五个族群的212个实例上，在单线程一小时预算下，KAYROS实现了比三个可用竞争者（Timefold、Hexaly、jsprit）中最强者低63.3%的汇总任意时间得分。所有三个对比在Holm校正下均显著。KAYROS改进了Blauth等人的所有30个高努力参考和10个文献最佳已知解，并发布了704个计算最优性证书。求解器、基准和活动数据已公开释放。
英文摘要：
The Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW) captures a central difficulty of urban logistics: travel times vary with the time of day, so the cost of a route depends on when it is driven. This paper introduces KAYROS, an open-source solver for the duration-minimization TDVRPTW that is both anytime and exact. It returns improving valid solutions throughout its time budget and can close instances with conditional computational optimality certificates through an integrated branch-price-and-cut component. We extend the composition of continuous arrival-time functions from the literature, previously described only at proof or proposition level, to the left-continuous functions that stepwise benchmarks require. We prove that the composition routine shipped in the checker computes that operation exactly. We analyze when its evaluation and breakpoint normalization are exact in IEEE-754 double-precision arithmetic, and argue that a canonical, epsilon-free checker must define the objective. The anytime layer combines greedy construction, granular time-dependent local search over balanced route trees, and iterated local search, with a fleet-aware descent for a fleet-cost objective. We further propose an anytime evaluation methodology based on a normalized signed primal integral under a pre-committed statistical design. On 212 instances from five families at a one-hour single-threaded budget, KAYROS achieves a pooled anytime score 63.3% lower than the strongest of three available contenders (Timefold, Hexaly, jsprit). All three contrasts are significant under Holm correction. KAYROS improves all 30 high-effort references of Blauth et al. and 10 literature best-known solutions, and publishes 704 such certificates. The solver, benchmarks and campaign data are openly released.
