发表机构
Eldorado Research Institute; Federal University of Santa Catarina; Informatics and Statistics Department, Federal University of Santa Catarina; Physics Department, Federal University of Santa Catarina; Quantuloop（埃尔多拉多研究所; 圣卡塔琳娜联邦大学; 圣卡塔琳娜联邦大学信息统计系; 圣卡塔琳娜联邦大学物理系; Quantuloop）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将QAOA参数迁移策略应用于TSP和VRP多目标路由问题，通过QUBO建模和归约至MAX-CUT，在经典模拟和IBM量子硬件上验证，发现其对TSP有效但对VRP稳定性较差，展示了超越概念验证的潜力。
AI 中文摘要
多目标优化（MOO）问题在物流领域十分常见，其中路由决策必须权衡相互冲突的目标，如行驶距离、交付时间和运营风险。最近提出的一种量子近似优化算法（QAOA）参数迁移策略，通过重用在小规模实例上训练得到的参数来解决多目标MAX-CUT问题，从而避免对每个标量化问题都进行代价高昂的重新优化。然而，其有效性仅在针对量子硬件连接性定制的概念验证实例上得到展示。在本工作中，我们评估了该策略在现实路由问题中的适用性。我们将旅行商问题（TSP）和车辆路径问题（VRP）建模为二次无约束二进制优化（QUBO）模型，将其归约为MAX-CUT问题，并在与原研究匹配的条件下评估参数迁移框架。验证通过经典模拟和在IBM量子硬件上的实验进行。所得Pareto前沿与使用改进的经典ε约束方法获得的结果进行比较，并以超体积作为主要质量指标。结果表明，参数迁移仍然有效，经常能获得更高的超体积，并且往往能更早找到有竞争力的解。然而，性能取决于问题结构。该方法对TSP实例始终有效，但对约束更强的VRP则稳定性较差，这表明随着优化景观变得更加复杂，QAOA参数的可迁移性会下降。这些结果首次对QAOA参数迁移在现实多目标路由问题上的表现进行了全面评估，并展示了其超越概念验证MAX-CUT基准的潜力。
英文摘要
Multi-objective optimization (MOO) problems are common in logistics, where routing decisions must balance conflicting objectives such as travel distance, delivery time, and operational risk. A recently proposed Quantum Approximate Optimization Algorithm (QAOA) parameter-transfer strategy solves multi-objective MAX-CUT problems by reusing parameters trained on smaller instances, avoiding costly reoptimization for each scalarized problem. However, its effectiveness has only been demonstrated on proof-of-concept instances tailored to quantum hardware connectivity. In this work, we evaluate the applicability of this strategy to realistic routing problems. We formulate the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) as Quadratic Unconstrained Binary Optimization (QUBO) models, reduce them to MAX-CUT, and assess the parameter-transfer framework under conditions matching the original study. Validation is performed through classical simulations and experiments on IBM quantum hardware. The resulting Pareto fronts are compared with those obtained using an adapted classical ε-constraint method, using hypervolume as the primary quality metric. Results indicate that parameter transfer remains effective, frequently achieving higher hypervolume and often finding competitive solutions earlier. However, performance depends on problem structure. The approach is consistently effective for TSP instances but less stable for the more constrained VRP, suggesting that QAOA parameter transferability decreases as the optimization landscape becomes more complex. These results provide the first comprehensive evaluation of QAOA parameter transfer on realistic multi-objective routing problems and demonstrate its potential beyond proof-of-concept MAX-CUT benchmarks.
