发表机构
Alamein International University; Jagiellonian University; Fundacja Quantum AI（阿拉曼国际大学; 雅盖隆大学; 量子人工智能基金会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对量子退火器上的带时间窗带容量车辆路径问题，提出GNN引导图粗化与自适应QUBO惩罚方法，提升了解的可行性，且在实例规模较大时效果显著。
AI 中文摘要
图粗化可减少用量子退火器求解车辆路径问题时产生的大规模二次无约束二元优化（QUBO）公式，将时间窗兼容的邻近客户合并为超级节点，求解简化后的问题后再将解扩展至原始图。对于带时间窗的带容量车辆路径问题（CVRPTW），现有粗化启发式方法需针对特定问题族进行调参，且在随机实例上仍不可靠。我们在所罗门基准测试上，采用模拟退火和D-Wave Advantage2处理器解决这些局限。首先引入自适应惩罚校准：均匀惩罚缩放效果甚微，而控制内部系数范围可显著提升原始样本质量；移除非绑定约束、归一化绑定约束并缩放剩余惩罚，在相同求解器预算下，平均原始约束违反从33.0降至0.06（p=3.7e-11，n=56）；保持变量数的对照实验表明，该提升源于条件优化而非问题规模。其次，我们用图神经网络（GNN）替代手动调参的合并评分，该网络在所有问题族中采用同一配置；在N=10时，其在所罗门所有族上的可行性达100%，其中R型为100%（调参启发式为80%）；在N=10至100时，可行性为83%（调参启发式为69%），且在85/90个实例规模对上，GNN表现更优或持平；在N=80、100时，差异显著（p=0.002，25/25对），同时QUBO规模仍缩小约5-6倍。最后，硬件实验在固定逻辑变量数下复现了条件优化效应：13个实例的可行样本从0.02%升至39%；局部搜索的经典修复仍是端到端解成本的参考基准。
英文摘要
Graph coarsening reduces the large Quadratic Unconstrained Binary Optimization (QUBO) formulations arising when vehicle-routing problems are solved by quantum annealing. Nearby customers with compatible time windows are merged into super-nodes, the reduced problem is solved, and the solution is expanded to the original graph. For the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), existing coarsening heuristics require family-specific tuning and remain unreliable on random instances. We address these limitations on the Solomon benchmark using simulated annealing and a D-Wave Advantage2 processor. We first introduce adaptive penalty calibration. Uniform penalty scaling has little effect, whereas controlling the internal coefficient range substantially improves raw samples. Removing non-binding constraints, normalising binding ones, and scaling the remaining penalties reduces mean raw constraint violations from 33.0 to 0.06 at the same solver budget (p=3.7e-11, n=56). A variable-count-preserving control attributes this gain to conditioning rather than problem size. Second, we replace the hand-tuned merge score with a graph neural network (GNN) using one configuration across all families. At N=10, it achieves 100% feasibility across all Solomon families, including R-type (100% vs. 80% for the tuned heuristic). Across N=10,...,100, feasibility is 83% vs. 69%, with the GNN better or tied on 85/90 instance-size pairs. At N=80,100, the difference is significant (p=0.002; 25/25 pairs), while the QUBO remains approximately 5-6 times smaller. Finally, hardware experiments reproduce the conditioning effect at fixed logical variable count: feasible samples increase from 0.02% to 39% across 13 instances. Classical repair with local search remains a reference bound for end-to-end solution cost.
