The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is a fundamental NP-hard optimization problem in logistics. Solving large-scale instances remains computationally challenging for exact solvers. This paper introduces a multilevel graph coarsening and refinement strategy that aggregates customers into meta-nodes based on a spatio-temporal distance metric. The reduced problem is solved using both classical heuristics and quantum annealing hardware, then expanded back into the original space with arrival times recomputed and constraint violations recorded. Comprehensive experiments on Solomon benchmarks demonstrate that our method significantly reduces computation time while preserving solution quality for classical heuristics. For quantum solvers, experiments across all 56 Solomon instances at $N=5$ and $N=10$ customers show that coarsening consistently reduces computation time and, on clustered (C-type) instances, simultaneously reduces vehicle count and route duration with no feasibility loss. Coarsening effectiveness is strongly instance-structure dependent: C-type instances achieve %100 post-coarsening feasibility with measurable quality improvements, while narrow-window random (R-type) instances present structural constraints that limit achievable coarsening depth.

翻译：容量约束车辆路径问题（CVRPTW）是物流领域一类基础的NP-hard优化问题。对于精确求解器而言，大规模实例的计算仍具有挑战性。本文提出了一种多级图粗化与精化策略，该策略基于时空距离度量将客户聚合成元节点。简化后的问题分别采用经典启发式算法和量子退火硬件求解，随后在通过计算到达时间和记录违反约束条件的方式扩展回原始空间。在Solomon基准上的综合实验表明，我们的方法在保持经典启发式算法解质量的同时显著减少了计算时间。对于量子求解器，在全部56个Solomon实例（$N=5$和$N=10$客户）上的实验显示，粗化能够持续降低计算时间，并且在聚类（C型）实例中同时减少了车辆数和路线持续时间且未损失可行性。粗化效果强烈依赖于实例结构：C型实例在粗化后实现了100%的可行性并伴有可量化的质量提升，而窄窗随机（R型）实例的结构性约束限制了可实现的粗化深度。