The vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, we explore the use of a previously-introduced qubit encoding scheme to reduce the number of binary variables, to evaluate the effectiveness of NISQ devices when applied to industry relevant optimization problems. We apply a quantum variational approach to a testbed of multiple VRPTW instances ranging from 11 to 3964 routes. These intances were formulated as quadratic unconstrained binary optimization (QUBO) problems based on realistic shipping scenarios. We compare our results with standard binary-to-qubit mappings after executing on simulators as well as various quantum hardware platforms, including IBMQ, AWS (Rigetti), and IonQ. These results are benchmarked against the classical solver, Gurobi. Our approach can find approximate solutions to the VRPTW comparable to those obtained from quantum algorithms using the full encoding, despite the reduction in qubits required. These results suggest that using the encoding scheme to fit larger problem sizes into fewer qubits is a promising step in using NISQ devices to find approximate solutions for industry-based optimization problems, although additional resources are still required to eke out the performance from larger problem sizes.

翻译：带时间窗的车辆路径问题（VRPTW）是物流行业中常见的优化问题。本研究探索采用一种先前提出的量子比特编码方案，通过减少二进制变量数量，评估NISQ设备在应用于工业相关优化问题时的有效性。我们将量子变分方法应用于包含11至3964条路径的多个VRPTW实例测试集。这些实例基于现实货运场景，被构建为二次无约束二进制优化（QUBO）问题。我们在模拟器及多种量子硬件平台（包括IBMQ、AWS (Rigetti)和IonQ）上执行实验，并将结果与标准二进制到量子比特映射方法进行对比。这些结果以经典求解器Gurobi为基准进行评测。尽管所需量子比特数量减少，我们的方法仍能获得与使用完整编码的量子算法相当的VRPTW近似解。研究结果表明，采用该编码方案以更少量子比特适配更大规模问题，是利用NISQ设备解决工业优化问题近似解的重要进展，但若要进一步提升大规模问题的性能，仍需额外资源支持。